Articles | Volume 24, issue 3
https://doi.org/10.5194/npg-24-379-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/npg-24-379-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
25 Jul 2017
Research article |
| 25 Jul 2017
Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex
Jezabel Curbelo
Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM. C/ Nicolás Cabrera 15, Campus de Cantoblanco UAM, 28049 Madrid, Spain
Departamento de Matemáticas, Facultad de Ciencias, Universidad Autonóma de Madrid, 28049 Madrid, Spain
Víctor José García-Garrido
Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM. C/ Nicolás Cabrera 15, Campus de Cantoblanco UAM, 28049 Madrid, Spain
Carlos Roberto Mechoso
Department of Atmospheric and Oceanic Sciences, University of California at Los Angeles, Los Angeles, California, USA
Ana Maria Mancho
CORRESPONDING AUTHOR
Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM. C/ Nicolás Cabrera 15, Campus de Cantoblanco UAM, 28049 Madrid, Spain
Stephen Wiggins
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
Coumba Niang
Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM. C/ Nicolás Cabrera 15, Campus de Cantoblanco UAM, 28049 Madrid, Spain
Laboratoire de Physique de l'Atmosphere et de l'Ocean Simeon Fongang, Ecole Superieure Polytechnique, Universite Cheikh Anta Diop, 5085, Dakar-Fann, Senegal
Related authors
Víctor José García-Garrido, Jezabel Curbelo, Carlos Roberto Mechoso, Ana María Mancho, and Stephen Wiggins
Nonlin. Processes Geophys., 24, 265–278, https://doi.org/10.5194/npg-24-265-2017, https://doi.org/10.5194/npg-24-265-2017, 2017
Short summary
Short summary
Our work shows that a simple kinematic model is able to retain the fundamental mechanisms responsible for complex fluid parcel evolution in the stratosphere. Our analysis justifies in a controlled manner the formation of filaments eroding the polar vortex and shows that the breaking and splitting of the polar vortex is explained by the sudden growth of a planetary wave and the decay of the axisymmetric flow.
Ana M. Mancho, Emilio Hernández-García, Cristóbal López, Antonio Turiel, Stephen Wiggins, and Vicente Pérez-Muñuzuri
Nonlin. Processes Geophys., 25, 125–127, https://doi.org/10.5194/npg-25-125-2018, https://doi.org/10.5194/npg-25-125-2018, 2018
Víctor José García-Garrido, Jezabel Curbelo, Carlos Roberto Mechoso, Ana María Mancho, and Stephen Wiggins
Nonlin. Processes Geophys., 24, 265–278, https://doi.org/10.5194/npg-24-265-2017, https://doi.org/10.5194/npg-24-265-2017, 2017
Short summary
Short summary
Our work shows that a simple kinematic model is able to retain the fundamental mechanisms responsible for complex fluid parcel evolution in the stratosphere. Our analysis justifies in a controlled manner the formation of filaments eroding the polar vortex and shows that the breaking and splitting of the polar vortex is explained by the sudden growth of a planetary wave and the decay of the axisymmetric flow.
V. J. García-Garrido, A. M. Mancho, S. Wiggins, and C. Mendoza
Nonlin. Processes Geophys., 22, 701–712, https://doi.org/10.5194/npg-22-701-2015, https://doi.org/10.5194/npg-22-701-2015, 2015
Short summary
Short summary
The disappearance of Malaysia Airlines flight MH370 on 8 March 2014 is one of the great mysteries of our time. The most relevant aspect is that not a piece of debris was found during the intensive surface search carried out for roughly 2 months following the crash. By combining different ocean data with dynamical systems tools, we propose a revised search strategy by showing why debris could not have been expected in some targeted search areas and determining regions where debris could be.
C. Mendoza, A. M. Mancho, and S. Wiggins
Nonlin. Processes Geophys., 21, 677–689, https://doi.org/10.5194/npg-21-677-2014, https://doi.org/10.5194/npg-21-677-2014, 2014
S. Wiggins and A. M. Mancho
Nonlin. Processes Geophys., 21, 165–185, https://doi.org/10.5194/npg-21-165-2014, https://doi.org/10.5194/npg-21-165-2014, 2014
Related subject area
Subject: Bifurcation, dynamical systems, chaos, phase transition, nonlinear waves, pattern formation | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
Transformation of internal solitary waves at the edge of ice cover
Review article: Interdisciplinary perspectives on climate sciences – highlighting past and current scientific achievements
Variational techniques for a one-dimensional energy balance model
A new approach to understanding fluid mixing in process-study models of stratified fluids
Sensitivity of the polar boundary layer to transient phenomena
Aggregation of slightly buoyant microplastics in 3D vortex flows
Existence and influence of mixed states in a model of vegetation patterns
Rate-induced tipping in ecosystems and climate: the role of unstable states, basin boundaries and transient dynamics
Review article: Dynamical systems, algebraic topology and the climate sciences
An approach for projecting the timing of abrupt winter Arctic sea ice loss
An adjoint-free algorithm for conditional nonlinear optimal perturbations (CNOPs) via sampling
Review article: Large fluctuations in non-equilibrium physics
On the interaction of stochastic forcing and regime dynamics
Applying dynamical systems techniques to real ocean drifters
Observations of shoaling internal wave transformation over a gentle slope in the South China Sea
Climate bifurcations in a Schwarzschild equation model of the Arctic atmosphere
Effects of rotation and topography on internal solitary waves governed by the rotating Gardner equation
Estimate of energy loss from internal solitary waves breaking on slopes
Regional study of mode-2 internal solitary waves at the Pacific coast of Central America using marine seismic survey data
The effect of strong shear on internal solitary-like waves
Enhanced diapycnal mixing with polarity-reversing internal solitary waves revealed by seismic reflection data
Enhanced internal tidal mixing in the Philippine Sea mesoscale environment
Detecting flow features in scarce trajectory data using networks derived from symbolic itineraries: an application to surface drifters in the North Atlantic
Review article: Hilbert problems for the climate sciences in the 21st century – 20 years later
Anthropocene climate bifurcation
Effects of upwelling duration and phytoplankton growth regime on dissolved-oxygen levels in an idealized Iberian Peninsula upwelling system
Baroclinic and barotropic instabilities in planetary atmospheres: energetics, equilibration and adjustment
Numerical bifurcation methods applied to climate models: analysis beyond simulation
Lyapunov analysis of multiscale dynamics: the slow bundle of the two-scale Lorenz 96 model
Competition between chaotic advection and diffusion: stirring and mixing in a 3-D eddy model
Climatic responses to systematic time variations of parameters: a dynamical approach
Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance
Wave propagation in the Lorenz-96 model
Dynamical properties and extremes of Northern Hemisphere climate fields over the past 60 years
On the CCN (de)activation nonlinearities
Detecting changes in forced climate attractors with Wasserstein distance
Subvisible cirrus clouds – a dynamical system approach
Influence of finite-time Lyapunov exponents on winter precipitation over the Iberian Peninsula
Dynamics of the Hadley circulation in an axisymmetric model undergoing stratification periodic forcing
Detecting and tracking eddies in oceanic flow fields: a Lagrangian descriptor based on the modulus of vorticity
Oscillations in a simple climate–vegetation model
A novel method for analyzing the process of abrupt climate change
Equilibrium temperature distribution and Hadley circulation in an axisymmetric model
Kateryna Terletska, Vladimir Maderich, and Elena Tobisch
Nonlin. Processes Geophys., 31, 207–217, https://doi.org/10.5194/npg-31-207-2024, https://doi.org/10.5194/npg-31-207-2024, 2024
Short summary
Short summary
The transformation of internal waves at the edge of ice cover can enhance the turbulent mixing and melting of ice in the Arctic Ocean and Antarctica. We studied numerically the transformation of internal solitary waves of depression under smooth ice surfaces compared with the processes beneath the ridged underside of the ice. For large keels, more than 40% of wave energy is lost on the first keel, while for relatively small keels energy losses on the first keel are less than 6%.
Vera Melinda Galfi, Tommaso Alberti, Lesley De Cruz, Christian L. E. Franzke, and Valerio Lembo
Nonlin. Processes Geophys., 31, 185–193, https://doi.org/10.5194/npg-31-185-2024, https://doi.org/10.5194/npg-31-185-2024, 2024
Short summary
Short summary
In the online seminar series "Perspectives on climate sciences: from historical developments to future frontiers" (2020–2021), well-known and established scientists from several fields – including mathematics, physics, climate science and ecology – presented their perspectives on the evolution of climate science and on relevant scientific concepts. In this paper, we first give an overview of the content of the seminar series, and then we introduce the written contributions to this special issue.
Gianmarco Del Sarto, Jochen Bröcker, Franco Flandoli, and Tobias Kuna
Nonlin. Processes Geophys., 31, 137–150, https://doi.org/10.5194/npg-31-137-2024, https://doi.org/10.5194/npg-31-137-2024, 2024
Short summary
Short summary
We consider a one-dimensional model for the Earth's temperature. We give sufficient conditions to admit three asymptotic solutions. We connect the value function (minimum value of an objective function depending on the greenhouse gas (GHG) concentration) to the global mean temperature. Then, we show that the global mean temperature is the derivative of the value function and that it is non-decreasing with respect to GHG concentration.
Samuel George Hartharn-Evans, Marek Stastna, and Magda Carr
Nonlin. Processes Geophys., 31, 61–74, https://doi.org/10.5194/npg-31-61-2024, https://doi.org/10.5194/npg-31-61-2024, 2024
Short summary
Short summary
Across much of the ocean, and the world's lakes, less dense water (either because it is warm or fresh) overlays denser water, forming stratification. The mixing of these layers affects the distribution of heat, nutrients, plankton, sediment, and buoyancy, so it is crucial to understand. We use small-scale numerical experiments to better understand these processes, and here we propose a new analysis tool for understanding mixing within those models, looking at where two variables intersect.
Amandine Kaiser, Nikki Vercauteren, and Sebastian Krumscheid
Nonlin. Processes Geophys., 31, 45–60, https://doi.org/10.5194/npg-31-45-2024, https://doi.org/10.5194/npg-31-45-2024, 2024
Short summary
Short summary
Current numerical weather prediction models encounter challenges in accurately representing regimes in the stably stratified atmospheric boundary layer (SBL) and the transitions between them. Stochastic modeling approaches are a promising framework to analyze when transient small-scale phenomena can trigger regime transitions. Therefore, we conducted a sensitivity analysis of the SBL to transient phenomena by augmenting a surface energy balance model with meaningful randomizations.
Irina I. Rypina, Lawrence J. Pratt, and Michael Dotzel
Nonlin. Processes Geophys., 31, 25–44, https://doi.org/10.5194/npg-31-25-2024, https://doi.org/10.5194/npg-31-25-2024, 2024
Short summary
Short summary
This paper investigates the aggregation of small, spherical, slightly buoyant, rigid particles in a simple 3D vortex flow. Our goal was to gain insights into the behaviour of slightly buoyant marine microplastics in a flow that qualitatively resembles ocean eddies. Attractors are mapped out for the steady, axisymmetric; steady, asymmetric; and nonsteady, asymmetric vortices over a range of flow and particle parameters. Simple theoretical arguments are used to interpret the results.
Lilian Vanderveken, Marina Martínez Montero, and Michel Crucifix
Nonlin. Processes Geophys., 30, 585–599, https://doi.org/10.5194/npg-30-585-2023, https://doi.org/10.5194/npg-30-585-2023, 2023
Short summary
Short summary
In semi-arid regions, hydric stress affects plant growth. In these conditions, vegetation patterns develop and effectively allow for vegetation to persist under low water input. The formation of patterns and the transition between patterns can be studied with small models taking the form of dynamical systems. Our study produces a full map of stable and unstable solutions in a canonical vegetation model and shows how they determine the transitions between different patterns.
Ulrike Feudel
Nonlin. Processes Geophys., 30, 481–502, https://doi.org/10.5194/npg-30-481-2023, https://doi.org/10.5194/npg-30-481-2023, 2023
Short summary
Short summary
Many systems in nature are characterized by the coexistence of different stable states for given environmental parameters and external forcing. Examples can be found in different fields of science, ranging from ecosystems to climate dynamics. Perturbations can lead to critical transitions (tipping) from one stable state to another. The study of these transitions requires the development of new methodological approaches that allow for modeling, analyzing and predicting them.
Michael Ghil and Denisse Sciamarella
Nonlin. Processes Geophys., 30, 399–434, https://doi.org/10.5194/npg-30-399-2023, https://doi.org/10.5194/npg-30-399-2023, 2023
Short summary
Short summary
The problem of climate change is that of a chaotic system subject to time-dependent forcing, such as anthropogenic greenhouse gases and natural volcanism. To solve this problem, we describe the mathematics of dynamical systems with explicit time dependence and those of studying their behavior through topological methods. Here, we show how they are being applied to climate change and its predictability.
Camille Hankel and Eli Tziperman
Nonlin. Processes Geophys., 30, 299–309, https://doi.org/10.5194/npg-30-299-2023, https://doi.org/10.5194/npg-30-299-2023, 2023
Short summary
Short summary
We present a novel, efficient method for identifying climate
tipping pointthreshold values of CO2 beyond which rapid and irreversible changes occur. We use a simple model of Arctic sea ice to demonstrate the method’s efficacy and its potential for use in state-of-the-art global climate models that are too expensive to run for this purpose using current methods. The ability to detect tipping points will improve our preparedness for rapid changes that may occur under future climate change.
Bin Shi and Guodong Sun
Nonlin. Processes Geophys., 30, 263–276, https://doi.org/10.5194/npg-30-263-2023, https://doi.org/10.5194/npg-30-263-2023, 2023
Short summary
Short summary
We introduce a sample-based algorithm to obtain the conditional nonlinear optimal perturbations. Compared with the classical adjoint-based method, it is easier to implement and reduces the required storage for the basic state. When we reduce the number of samples to some extent, it reduces the computation markedly more when using the sample-based method, which can guarantee that the CNOP obtained is nearly consistent with some minor fluctuating errors oscillating in spatial distribution.
Giovanni Jona-Lasinio
Nonlin. Processes Geophys., 30, 253–262, https://doi.org/10.5194/npg-30-253-2023, https://doi.org/10.5194/npg-30-253-2023, 2023
Short summary
Short summary
Non-equilibrium is dominant in geophysical and climate phenomena. Most of the processes that characterize energy flow occur far from equilibrium. These range from very large systems, such as weather patterns or ocean currents that remain far from equilibrium, owing to an influx of energy, to biological structures. In the last decades, progress in non-equilibrium physics has come from the study of very rare fluctuations, and this paper provides an introduction to these theoretical developments.
Joshua Dorrington and Tim Palmer
Nonlin. Processes Geophys., 30, 49–62, https://doi.org/10.5194/npg-30-49-2023, https://doi.org/10.5194/npg-30-49-2023, 2023
Short summary
Short summary
Atmospheric models often include random forcings, which aim to replicate the impact of processes too small to be resolved. Recent results in simple atmospheric models suggest that this random forcing can actually stabilise certain slow-varying aspects of the system, which could provide a path for resolving known errors in our models. We use randomly forced simulations of a
toychaotic system and theoretical arguments to explain why this strange effect occurs – at least in simple models.
Irina I. Rypina, Timothy Getscher, Lawrence J. Pratt, and Tamay Ozgokmen
Nonlin. Processes Geophys., 29, 345–361, https://doi.org/10.5194/npg-29-345-2022, https://doi.org/10.5194/npg-29-345-2022, 2022
Short summary
Short summary
Techniques from dynamical systems theory have been widely used to study transport in ocean flows. However, they have been typically applied to numerically simulated trajectories of water parcels. This paper applies different dynamical systems techniques to real ocean drifter trajectories from the massive release in the Gulf of Mexico. To our knowledge, this is the first comprehensive comparison of the performance of different dynamical systems techniques with application to real drifters.
Steven R. Ramp, Yiing Jang Yang, Ching-Sang Chiu, D. Benjamin Reeder, and Frederick L. Bahr
Nonlin. Processes Geophys., 29, 279–299, https://doi.org/10.5194/npg-29-279-2022, https://doi.org/10.5194/npg-29-279-2022, 2022
Short summary
Short summary
Earlier work in the vicinity of the shelf and slope in the northeastern South China Sea serendipitously revealed the presence of large, stunning bed forms (sand dunes) whose height (>15 m) and length (>350 m) are quite unique and unusual. We hypothesize that the dunes formed due to shoaling very large-amplitude nonlinear internal waves that scour the bottom and resuspend and redistribute the sediments. As a first step, the wave characteristics are observed and described in detail.
Kolja L. Kypke, William F. Langford, Gregory M. Lewis, and Allan R. Willms
Nonlin. Processes Geophys., 29, 219–239, https://doi.org/10.5194/npg-29-219-2022, https://doi.org/10.5194/npg-29-219-2022, 2022
Short summary
Short summary
Climate change is causing rapid temperature increases in the polar regions. A fundamental question is whether these temperature increases are reversible. If we control carbon dioxide emissions, will the temperatures revert or will we have passed a tipping point beyond which return to the present state is impossible? Our mathematical model of the Arctic climate indicates that under present emissions the Arctic climate will change irreversibly to a warm climate before the end of the century.
Karl R. Helfrich and Lev Ostrovsky
Nonlin. Processes Geophys., 29, 207–218, https://doi.org/10.5194/npg-29-207-2022, https://doi.org/10.5194/npg-29-207-2022, 2022
Short summary
Short summary
Internal solitons are an important class of nonlinear waves commonly observed in coastal oceans. Their propagation is affected by the Earth's rotation and the variation in the water depth. We consider an interplay of these factors using the corresponding extension of the Gardner equation. This model allows a limiting soliton amplitude and the corresponding increase in wavelength, making the effects of rotation and topography on a shoaling wave especially significant.
Kateryna Terletska and Vladimir Maderich
Nonlin. Processes Geophys., 29, 161–170, https://doi.org/10.5194/npg-29-161-2022, https://doi.org/10.5194/npg-29-161-2022, 2022
Short summary
Short summary
Internal solitary waves (ISWs) emerge in the ocean and seas in various forms and break on the shelf zones in a variety of ways. This results in intensive mixing that affects processes such as biological productivity and sediment transport. Mechanisms of wave interaction with slopes are related to breaking and changing polarity. Our study focuses on wave transformation over idealized shelf-slope topography using a two-layer stratification. Four types of ISW transformation over slopes are shown.
Wenhao Fan, Haibin Song, Yi Gong, Shun Yang, and Kun Zhang
Nonlin. Processes Geophys., 29, 141–160, https://doi.org/10.5194/npg-29-141-2022, https://doi.org/10.5194/npg-29-141-2022, 2022
Short summary
Short summary
Compared with mode-1 internal solitary waves (ISWs), mode-2 ISWs in the ocean require further study. A mass of mode-2 ISWs developing at the Pacific coast of Central America have been imaged using seismic reflection data. We find that the relationship between the mode-2 ISW propagation speed and amplitude is diverse. It is affected by seawater depth, pycnocline depth, and pycnocline thickness. The ISW vertical amplitude structure is affected by the ISW nonlinearity and the pycnocline deviation.
Marek Stastna, Aaron Coutino, and Ryan K. Walter
Nonlin. Processes Geophys., 28, 585–598, https://doi.org/10.5194/npg-28-585-2021, https://doi.org/10.5194/npg-28-585-2021, 2021
Short summary
Short summary
Large-amplitude waves in the interior of the ocean-internal waves in the ocean propagate in a dynamic, highly variable environment with changes in background current, local depth, and stratification. These waves have a well-known mathematical theory that, despite considerable progress, has some gaps. In particular, waves have been observed in situations that preclude an application of the mathematical theory. We present numerical simulations of the spontaneous generation of such waves.
Yi Gong, Haibin Song, Zhongxiang Zhao, Yongxian Guan, Kun Zhang, Yunyan Kuang, and Wenhao Fan
Nonlin. Processes Geophys., 28, 445–465, https://doi.org/10.5194/npg-28-445-2021, https://doi.org/10.5194/npg-28-445-2021, 2021
Short summary
Short summary
When the internal solitary wave propagates to the continental shelf and slope, the polarity reverses due to the shallower water depth. In this process, the internal solitary wave dissipates energy and enhances diapycnal mixing, thus affecting the local oceanic environment. In this study, we used reflection seismic data to evaluate the spatial distribution of the diapycnal mixing around the polarity-reversing internal solitary waves.
Jia You, Zhenhua Xu, Qun Li, Robin Robertson, Peiwen Zhang, and Baoshu Yin
Nonlin. Processes Geophys., 28, 271–284, https://doi.org/10.5194/npg-28-271-2021, https://doi.org/10.5194/npg-28-271-2021, 2021
Short summary
Short summary
Turbulent mixing in the ocean is mainly attributed to internal wave breaking, but the modulation of the mesoscale environment is unclear. The spatially inhomogeneous and seasonally variable diapycnal diffusivities in the upper Philippine Sea were estimated from Argo float data using a strain-based, fine-scale parameterization. Internal tides contributed significant diapycnal mixing here, with the mesoscale environment greatly regulating the intensity and spatial inhomogeneity of tidal mixing.
David Wichmann, Christian Kehl, Henk A. Dijkstra, and Erik van Sebille
Nonlin. Processes Geophys., 27, 501–518, https://doi.org/10.5194/npg-27-501-2020, https://doi.org/10.5194/npg-27-501-2020, 2020
Short summary
Short summary
The surface transport of heat, nutrients and plastic in the North Atlantic Ocean is organized into large-scale flow structures. We propose a new and simple method to detect such features in ocean drifter data sets by identifying groups of trajectories with similar dynamical behaviour using network theory. We successfully detect well-known regions such as the Subpolar and Subtropical gyres, the Western Boundary Current region and the Caribbean Sea.
Michael Ghil
Nonlin. Processes Geophys., 27, 429–451, https://doi.org/10.5194/npg-27-429-2020, https://doi.org/10.5194/npg-27-429-2020, 2020
Short summary
Short summary
The scientific questions posed by the climate sciences are central to socioeconomic concerns today. This paper revisits several crucial questions, starting with
What can we predict beyond 1 week, for how long, and by what methods?, and ending with
Can we achieve enlightened climate control of our planet by the end of the century?We review the progress in dealing with the nonlinearity and stochasticity of the Earth system and emphasize major strides in coupled climate–economy modeling.
Kolja Leon Kypke, William Finlay Langford, and Allan Richard Willms
Nonlin. Processes Geophys., 27, 391–409, https://doi.org/10.5194/npg-27-391-2020, https://doi.org/10.5194/npg-27-391-2020, 2020
Short summary
Short summary
The climate of Earth is governed by nonlinear processes of geophysics. This paper presents energy balance models (EBMs) embracing these nonlinear processes which lead to positive feedback, amplifying the effects of anthropogenic forcing and leading to bifurcations. We define bifurcation as a change in the topological equivalence class of the system. We initiate a bifurcation analysis of EBMs of Anthropocene climate, which shows that a catastrophic climate change may occur in the next century.
João H. Bettencourt, Vincent Rossi, Lionel Renault, Peter Haynes, Yves Morel, and Véronique Garçon
Nonlin. Processes Geophys., 27, 277–294, https://doi.org/10.5194/npg-27-277-2020, https://doi.org/10.5194/npg-27-277-2020, 2020
Short summary
Short summary
The oceans are losing oxygen, and future changes may worsen this problem. We performed computer simulations of an idealized Iberian Peninsula upwelling system to identify the main fine-scale processes driving dissolved oxygen variability as well as study the response of oxygen levels to changes in wind patterns and phytoplankton species. Our results suggest that oxygen levels would decrease if the wind blows for long periods of time or if phytoplankton is dominated by species that grow slowly.
Peter Read, Daniel Kennedy, Neil Lewis, Hélène Scolan, Fachreddin Tabataba-Vakili, Yixiong Wang, Susie Wright, and Roland Young
Nonlin. Processes Geophys., 27, 147–173, https://doi.org/10.5194/npg-27-147-2020, https://doi.org/10.5194/npg-27-147-2020, 2020
Short summary
Short summary
Baroclinic and barotropic instabilities are well known as the processes responsible for the production of the most important energy-containing eddies in the atmospheres and oceans of Earth and other planets. Linear and nonlinear instability theories provide insights into when such instabilities may occur, grow to a large amplitude and saturate, with examples from the laboratory, simplified numerical models and planetary atmospheres. We conclude with a number of open issues for future research.
Henk A. Dijkstra
Nonlin. Processes Geophys., 26, 359–369, https://doi.org/10.5194/npg-26-359-2019, https://doi.org/10.5194/npg-26-359-2019, 2019
Short summary
Short summary
I provide a personal view on the role of bifurcation analysis of climate models in the development of a theory of variability in the climate system. By outlining the state of the art of the methodology and by discussing what has been done and what has been learned from a hierarchy of models, I will argue that there are low-order phenomena of climate variability, such as El Niño and the Atlantic Multidecadal Oscillation.
Mallory Carlu, Francesco Ginelli, Valerio Lucarini, and Antonio Politi
Nonlin. Processes Geophys., 26, 73–89, https://doi.org/10.5194/npg-26-73-2019, https://doi.org/10.5194/npg-26-73-2019, 2019
Short summary
Short summary
We explore the nature of instabilities in a well-known meteorological toy model, the Lorenz 96, to unravel key mechanisms of interaction between scales of different resolutions and time scales. To do so, we use a mathematical machinery known as Lyapunov analysis, allowing us to capture the degrees of chaoticity associated with fundamental directions of instability. We find a non-trivial group of such directions projecting significantly on slow variables, associated with long term dynamics.
Genevieve Jay Brett, Larry Pratt, Irina Rypina, and Peng Wang
Nonlin. Processes Geophys., 26, 37–60, https://doi.org/10.5194/npg-26-37-2019, https://doi.org/10.5194/npg-26-37-2019, 2019
Short summary
Short summary
The relative importance of chaotic stirring and smaller-scale turbulent mixing for the distribution of dye in an idealized ocean flow feature is quantified using three different methods. We find that stirring is the dominant process in large areas with fast stirring, while mixing dominates in small fast-stirring regions and all slow-stirring regions. This quantification of process dominance can help oceanographers think about when to model stirring accurately, which can be costly.
Catherine Nicolis
Nonlin. Processes Geophys., 25, 649–658, https://doi.org/10.5194/npg-25-649-2018, https://doi.org/10.5194/npg-25-649-2018, 2018
Short summary
Short summary
Ordinarily the climatic impact of systematic variations of parameters arising from anthropogenic effects is addressed on the basis of large numerical models, where parameters are set to a prescribed level and the system is subsequently left to relax. We have revisited the problem from a nonlinear dynamics perspective in which the time variation of parameters is fully incorporated into the evolution laws. Some universal trends of the response have been identified.
Gabriele Vissio and Valerio Lucarini
Nonlin. Processes Geophys., 25, 413–427, https://doi.org/10.5194/npg-25-413-2018, https://doi.org/10.5194/npg-25-413-2018, 2018
Short summary
Short summary
Constructing good parametrizations is key when studying multi-scale systems. We consider a low-order model and derive a parametrization via a recently developed statistical mechanical approach. We show how the method allows for seamlessly treating the case when the unresolved dynamics is both faster and slower than the resolved one. We test the skill of the parametrization by using the formalism of the Wasserstein distance, which allows for measuring how different two probability measures are.
Dirk L. van Kekem and Alef E. Sterk
Nonlin. Processes Geophys., 25, 301–314, https://doi.org/10.5194/npg-25-301-2018, https://doi.org/10.5194/npg-25-301-2018, 2018
Short summary
Short summary
In this paper we investigate the spatiotemporal properties of waves in the Lorenz-96 model. In particular, we explain how these properties are related to the presence of Hopf and pitchfork bifurcations. We also explain bifurcation scenarios by which multiple stable waves can coexist for the same parameter values.
Davide Faranda, Gabriele Messori, M. Carmen Alvarez-Castro, and Pascal Yiou
Nonlin. Processes Geophys., 24, 713–725, https://doi.org/10.5194/npg-24-713-2017, https://doi.org/10.5194/npg-24-713-2017, 2017
Short summary
Short summary
We study the dynamical properties of the Northern Hemisphere atmospheric circulation by analysing the sea-level pressure, 2 m temperature, and precipitation frequency field over the period 1948–2013. The metrics are linked to the predictability and the persistence of the atmospheric flows. We study the dependence on the seasonal cycle and the fields corresponding to maxima and minima of the dynamical indicators.
Sylwester Arabas and Shin-ichiro Shima
Nonlin. Processes Geophys., 24, 535–542, https://doi.org/10.5194/npg-24-535-2017, https://doi.org/10.5194/npg-24-535-2017, 2017
Short summary
Short summary
The paper bridges cloud/aerosol modelling with bifurcation analysis. It identifies two nonlinear peculiarities in the differential equations describing formation of atmospheric clouds through vapour condensation on a population of aerosol particles. A key finding of the paper is an analytic estimate for the timescale of the process. The study emerged from discussions on the causes of hysteretic behaviour of the system that we observed in the results of numerical simulations.
Yoann Robin, Pascal Yiou, and Philippe Naveau
Nonlin. Processes Geophys., 24, 393–405, https://doi.org/10.5194/npg-24-393-2017, https://doi.org/10.5194/npg-24-393-2017, 2017
Short summary
Short summary
If climate is viewed as a chaotic dynamical system, its trajectories yield on an object called an attractor. Being perturbed by an external forcing, this attractor could be modified. With Wasserstein distance, we estimate on a derived Lorenz model the impact of a forcing similar to climate change. Our approach appears to work with small data sizes. We have obtained a methodology quantifying the deformation of well-known attractors, coherent with the size of data available.
Elisa Johanna Spreitzer, Manuel Patrik Marschalik, and Peter Spichtinger
Nonlin. Processes Geophys., 24, 307–328, https://doi.org/10.5194/npg-24-307-2017, https://doi.org/10.5194/npg-24-307-2017, 2017
Short summary
Short summary
We developed a simple analytical model for describing subvisible cirrus clouds qualitatively. Using theory of dynamical systems we found two different states for the long-term behaviour of subvisible cirrus clouds, i.e. an attractor case (stable equilibrium point) and a limit cycle scenario. The transition between the states constitutes a Hopf bifurcation and is determined by environmental conditions such as vertical updraughts and temperature.
Daniel Garaboa-Paz, Nieves Lorenzo, and Vicente Pérez-Muñuzuri
Nonlin. Processes Geophys., 24, 227–235, https://doi.org/10.5194/npg-24-227-2017, https://doi.org/10.5194/npg-24-227-2017, 2017
Short summary
Short summary
This paper evaluates the connection between winter precipitation over the Iberian Peninsula and the large-scale tropospheric mixing over the eastern Atlantic Ocean. Finite-time Lyapunov exponents (FTLEs) have been calculated from 1979 to 2008 to evaluate this mixing. Our study suggests that significant negative correlations exist between summer FTLE anomalies and winter precipitation over Portugal and Spain.
Nazario Tartaglione
Nonlin. Processes Geophys., 24, 167–178, https://doi.org/10.5194/npg-24-167-2017, https://doi.org/10.5194/npg-24-167-2017, 2017
Short summary
Short summary
This paper aims to show how the tropical circulation responds to changes of the vertical stratification of the imposed temperature that drives the model. These changes mimic the presence of water vapor cycles. Thus, for simplicity's sake we impose a periodic change of this stratification with variable periods of 10–90 days. The model responds with quasi-periodic oscillations having two or more dominant frequencies. After a long forcing time period, chaotic behavior starts to appear cyclically.
Rahel Vortmeyer-Kley, Ulf Gräwe, and Ulrike Feudel
Nonlin. Processes Geophys., 23, 159–173, https://doi.org/10.5194/npg-23-159-2016, https://doi.org/10.5194/npg-23-159-2016, 2016
Short summary
Short summary
Since eddies play a major role in the dynamics of oceanic flows, it is of great interest to gain information about their tracks, lifetimes and shapes. We develop an eddy tracking tool based on structures in the flow with collecting (attracting) or separating (repelling) properties. In test cases mimicking oceanic flows it yields eddy lifetimes close to the analytical ones. It even provides a detailed view of the dynamics that can be useful to gain more insight into eddy dynamics in oceanic flows.
J. Rombouts and M. Ghil
Nonlin. Processes Geophys., 22, 275–288, https://doi.org/10.5194/npg-22-275-2015, https://doi.org/10.5194/npg-22-275-2015, 2015
Short summary
Short summary
Our conceptual model describes global temperature and vegetation extent. We use elements from Daisyworld and classical energy balance models and add an ocean with sea ice. The model exhibits oscillatory behavior within a plausible range of parameter values.
Its periodic solutions have sawtooth behavior that is characteristic of relaxation oscillations, as well as suggestive of Quaternary glaciation cycles. The model is one of the simplest of its kind to produce such oscillatory behavior.
P. C. Yan, G. L. Feng, and W. Hou
Nonlin. Processes Geophys., 22, 249–258, https://doi.org/10.5194/npg-22-249-2015, https://doi.org/10.5194/npg-22-249-2015, 2015
Short summary
Short summary
A novel method is created to detect the process of the abrupt change, which has not been mentioned yet in traditional research. By building an ideal time series with a transition process, the results show that the process could be detected clearly. When applied to a climate index, this method detects five processes, and all of them have reappeared via the “start-end states” phase diagram. Additionally, it is detectable that the persist time of the process is related to global warming.
N. Tartaglione
Nonlin. Processes Geophys., 22, 173–185, https://doi.org/10.5194/npg-22-173-2015, https://doi.org/10.5194/npg-22-173-2015, 2015
Short summary
Short summary
At the Equator, where the heating is larger than that at other latitudes, air rises and diverges poleward in the upper troposphere, descending more or less at 30° latitude; this circulation is the Hadley cell.
We studied the impact of different meridional and vertical temperature distributions on a few features of the Hadley cell. Some parameters show a regular dependence on these distributions; others remain rather stable with distributions, but when they change, they do it in an abrupt way.
Cited articles
Aref, H.: Stirring by chaotic advection, J. Fluid Mech., 143, 1–21, 1984.
Bettencourt, J. H., López, C., Hernández-García, E., Montes, I., Sudre, J., Dewitte, B., Paulmier, A., and Garçon, V.: Boundaries of the Peruvian oxygen minimum zone shaped by coherent mesoscale dynamics, Nat. Geosci., 8, 937–940, 2014.
Bowman, K. P.: Large-scale isentropic mixing properties of the Antarctic polar vortex from analyzed winds, J. Geophys. Res., 98, 23013–23027, https://doi.org/10.1029/93JD02599, 1993.
Branicki, M. and Kirwan Jr., A. D.: Stirring: The Eckart paradigm revisited, Int. J. Eng. Sci., 48, 1027–1042, 2010.
Branicki, M. and Wiggins, S.: An adaptive method for computing invariant manifolds in non-autonomous, three-dimensional dynamical systems, Physica D, 238, 1625–1657, 2009.
Branicki, M., Mancho, A. M., and Wiggins, S.: A Lagrangian description of transport associated with a Front-Eddy interaction: application to data from the North-Western Mediterranean Sea, Physica D, 240, 282–304, 2011.
Cartwright, J. H. E., Feingold, M., and Piro, O.: Chaotic adection in three-dimensional unsteady incompressible laminar flow, J. Fluid Mech., 316, 259–284, 1996.
Dee, D. P., Uppala, S. M., Simmons, A. J., Berrisford, P., Poli, P., Kobayashi, S., Andrae, U., Balmaseda, M. A., Balsamo, G., Bauer, P., Bechtold, P., Beljaars, A. C. M., van de Berg, L., Bidlot, J., Bormann, N., Delsol, C., Dragani, R., Fuentes, M., Geer, A. J., Haimberger, L., Healy, S. B., Hersbach, H., Hólm, E. V.,Isaksen, L., Kållberg, P., Köhler, M., Matricardi, M., McNally, A. P., Monge-Sanz, B. M., Morcrette, J.-J., Park, B.-K., Peubey, C., de Rosnay, P., Tavolato, C., Thépaut, J.-N., and Vitart, F.: The ERA-Interim reanalysis: configuration and performance of the data assimilation system, Q. J. Roy. Meteor. Soc., 137, 553–597, https://doi.org/10.1002/qj.828, 2011.
de la Cámara, A., Mancho, A. M., Ide, K., Serrano, E., and Mechoso, C.: Routes of transport across the Antarctic polar vortex in the southern spring., J. Atmos. Sci., 69, 753–767, 2012.
de la Cámara, A., Mechoso, R., Mancho, A. M., Serrano, E., and Ide., K.: Isentropic transport within the Antarctic polar night vortex: Rossby wave breaking evidence and Lagrangian structures, J. Atmos. Sci., 70, 2982–3001, 2013.
d'Ovidio, F., Isern-Fontanet, J., López, C., Hernández-García, E., and García-Ladona, E.: Comparison between Eulerian diagnostics and finite-size Lyapunov exponents computed from altimetry in the Algerian basin, Deep-Sea Res. Pt. I, 56, 15–31, 2009.
du Toit, P. C. and Marsden, J. E.: Horseshoes in hurricanes, J. Fix. Point Theory A., 7, 351–384, 2010.
García-Garrido, V. J., Mancho, A. M., Wiggins, S., and Mendoza, C.: A dynamical systems approach to the surface search for debris associated with the disappearance of flight MH370, Nonlin. Processes Geophys., 22, 701–712, https://doi.org/10.5194/npg-22-701-2015, 2015.
García-Garrido, V. J., Ramos, A., Mancho, A. M., Coca, J., and Wiggins, S.: A dynamical systems perspective for a real-time response to a marine oil spill, Mar. Pollut. Bull., 112, 201–210, https://doi.org/10.1016/j.marpolbul.2016.08.018, 2016.
García-Garrido, V. J., Curbelo, J., Mechoso, C. R., Mancho, A. M., and Wiggins, S.: A simple kinematic model for the Lagrangian description of relevant nonlinear processes in the stratospheric polar vortex, Nonlin. Processes Geophys., 24, 265–278, https://doi.org/10.5194/npg-24-265-2017, 2017.
Guha, A., Mechoso, C. R., Konor, C. S., and Heikes, R. P.: Modeling Rossby Wave Breaking in the Southern Spring Stratosphere, J. Atmos. Sci., 73, 393–406, 2016.
Haller, G. and Yuan, G.: Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D, 147, 352–370, 2000.
Joseph, B. and Legras, B.: Relation between Kinematic Boundaries, Stirring, and Barriers for the Antarctic Polar Vortex, J. Atmos. Sci., 59, 1198–1212, 2002.
Lekien, F. and Ross, S. D.: The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds, Chaos, 20, 017505, https://doi.org/10.1063/1.3278516, 2010.
Lopesino, C., Balibrea-Iniesta, F., García-Garrido, V. J., Wiggins, S., and Mancho, A. M.: A theoretical framework for lagrangian descriptors, Int. J. Bifurcat. Chaos, 27, 1730001, https://doi.org/10.1142/S0218127417300014, 2017.
Madrid, J. A. J. and Mancho, A. M.: Distinguished trajectories in time dependent vector fields, Chaos, 19, 013111, https://doi.org/10.1063/1.3056050, 2009.
Mancho, A. M., Hernández-García, E., Small, D., Wiggins, S., and Fernández, V.: Lagrangian transport through an ocean front in the North-Western Mediterranean Sea, J. Phys. Oceanogr., 38, 1222–1237, 2006.
Mancho, A. M., Wiggins, S., Curbelo, J., and Mendoza, C.: Lagrangian descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems, Commun. Nonlinear Sci., 18, 3530–3557, 2013.
Manney, G. L. and Lawrence, Z. D.: The major stratospheric final warming in 2016: dispersal of vortex air and termination of Arctic chemical ozone loss, Atmos. Chem. Phys., 16, 15371–15396, https://doi.org/10.5194/acp-16-15371-2016, 2016.
Manney, G. L., Farrara, J. D., and Mechoso, C. R.: The behavior of wave 2 in the southern hemisphere stratosphere during late winter and early spring., J. Atmos. Sci., 48, 976–998, 1991.
Mechoso, C. R. and Hartmann, D. L.: An Observational Study of Traveling Planetary Waves in the Southern Hemisphere, J. Atmos. Sci., 39, 1921–1935, https://doi.org/10.1175/1520-0469(1982)039<1921:AOSOTP>2.0.CO;2, 1982.
Mechoso, C. R., O'Neill, A., Pope, V. D., and Farrara, J. D.: A study of the stratospheric final warming of 1982 in the Southern Hemisphere, Q. J. Roy. Meteor. Soc., 114, 1365–1384, 1988.
Mendoza, C. and Mancho, A. M.: The hidden geometry of ocean flows, Phys. Rev. Lett., 105, 038501, https://doi.org/10.1103/PhysRevLett.105.038501, 2010.
Mendoza, C., Mancho, A. M., and Wiggins, S.: Lagrangian descriptors and the assessment of the predictive capacity of oceanic data sets, Nonlin. Processes Geophys., 21, 677–689, https://doi.org/10.5194/npg-21-677-2014, 2014.
Mezić, I. and Wiggins, S.: On the integrability and perturbation of three-dimensional fluid flows with symmetry, J. Nonlinear Sci., 4, 157–194, 1994.
Mezic, I. and Wiggins, S.: A method for visualization of invariant sets of dynamical systems based on the ergodic partition, Chaos, 9, 213–218, 1999.
Moharana, N. R., Speetjens, M. F. M., Trieling, R. R., and Clercx, H. J. H.: Three-dimensional Lagrangian transport phenomena in unsteady laminar flows driven by a rotating sphere, Phys. Fluids, 25, 093602, https://doi.org/10.1063/1.4819901, 2013.
Pouransari, Z., Speetjens, M. F. M., and Clercx, H. J. H.: Formation of coherent structures by fluid inertia in three-dimensional laminar flows, J. Fluid Mech., 654, 5–34, 2010.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P.: Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, New York, NY, USA, 1992.
Quintanar, A. I. and Mechoso, C. R.: Quasi-stationary waves in the Southern Hemisphere. Part I: Observational data, J. Climate, 4, 2659–2672, 1995.
Rabier, F., Bouchard, A., Brun, E., Doerenbecher, A., Guedj, S., Guidard, V., Karbou, F., Peuch, V., El Amraoui, L., Puech, D., Genthon, C., Picard, G., Town, M., Hertzog, A., Vial, F., Cocquerez, P., Cohn, S. A., Hock, T., Fox, J., Cole, H., Parsons, D., Powers, J., Romberg, K., VanAndel, J., Deshler, T., Mercer, J., Haase, J. S., Avallone, L., Kalnajs, L., Mechoso, C. R., Tangborn, A., Pellegrini, A., Frenot, Y., Thépaut, J., McNally, A., Balsamo, G., and Steinle, P.: The Concordiasi Project in Antarctica, B. Am. Meteorol. Soc., 91, 69–86, https://doi.org/10.1175/2009BAMS2764.1, 2010.
Rempel, E. L., Chian, A. C.-L., Brandenburg, A., Munuz, P. R., and Shadden, S. C.: Coherent structures and the saturation of a nonlinear dynamo, J. Fluid Mech., 729, 309–329, 2013.
Rutherford, B. and Dangelmayr, G.: A three-dimensional Lagrangain hurricane eyewall computation, Q. J. Roy. Meteor. Soc., 136, 1931–1944, 2010.
Rutherford, B., Dangelmayr, G., and Montgomery, M. T.: Lagrangian coherent structures in tropical cyclone intensification, Atmos. Chem. Phys., 12, 5483–5507, https://doi.org/10.5194/acp-12-5483-2012, 2012.
Rypina, I. I., Pratt, L. J., Wang, P., Özgökmen, T. M., and Mezic, I.: Resonanace phenomena in a time-dependent, three-dimensional model of an idealized eddy, Chaos, 25, 087401, https://doi.org/10.1063/1.4916086, 2015.
Shadden, S. C., Lekien, F., and Marsden, J. E.: Definition and properties of Lagrangian Coherent Structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows, Physica D, 212, 271–304, 2005.
Simmons, A., Uppala, S., Dee, D., and Kobayashi, S.: ERA-Interim: New ECMWF reanalysis products from 1989 onwards, ECMWF Newsletter, 110, 25–35, 2007.
Smith, M. L. and McDonald, A. J.: A quantitative measure of polar vortex strength using the function M, J. Gephys. Res.-Atmos., 119, 5966–5985, 2014.
Wiggins, S.: Global bifurcations and chaos: analytical methods, vol. 73, Springer Verlag, New York, USA, 1988.
Wiggins, S.: Coherent structures and chaotic advection in three dimensions, J. Fluid Mech., 654, 1–4, https://doi.org/10.1017/S0022112010002569, 2010.
Yamazaki, K. and Mechoso, C. R.: Observations of the Final Warming in the Stratosphere of the Southern Hemisphere during 1979, J. Atmos. Sci., 42, 1198–1205, 1985.
Short summary
Lagrangian coherent structures have supported the description of transport processes in fluid dynamics. In this work we use the M function to provide new insights into the 3-D Lagrangian structure of the southern stratosphere. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied to describe the vertical extension of the stratospheric polar vortex and its evolution.
Lagrangian coherent structures have supported the description of transport processes in fluid...
