Articles | Volume 31, issue 2
https://doi.org/10.5194/npg-31-219-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-31-219-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
23 Apr 2024
Research article |
| 23 Apr 2024
| 23 Apr 2024
Evolution of small-scale turbulence at large Richardson numbers
Dept. of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA
Irina Soustova
Institute of Applied Physics, Russian Academy of Sciences, 603950 Nizhny Novgorod, Russia
Yuliya Troitskaya
Institute of Applied Physics, Russian Academy of Sciences, 603950 Nizhny Novgorod, Russia
Daria Gladskikh
Institute of Applied Physics, Russian Academy of Sciences, 603950 Nizhny Novgorod, Russia
Moscow Center for Fundamental and Applied Mathematics, 119991 Moscow, Russia
Research Computing Center, Moscow State University, 119991 Moscow, Russia
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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
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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.
O. A. Druzhinin and L. A. Ostrovsky
Nonlin. Processes Geophys., 22, 337–348, https://doi.org/10.5194/npg-22-337-2015, https://doi.org/10.5194/npg-22-337-2015, 2015
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The objective of this paper is to study the dynamics of turbulence near a pycnocline, both in the free regime and under the action of an internal wave (IW) propagating along a pycnocline by direct numerical simulation (DNS). Turbulence is initially induced in a horizontal layer above the pycnocline. The DNS results show that turbulence kinetic energy (TKE) is significantly enhanced as compared to the TKE in the absence of IW, and most of the TKE is localized in the vicinity of the pycnocline.
O. A. Druzhinin, L. A. Ostrovsky, and S. S. Zilitinkevich
Nonlin. Processes Geophys., 20, 977–986, https://doi.org/10.5194/npg-20-977-2013, https://doi.org/10.5194/npg-20-977-2013, 2013
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.
Naohisa Takagaki, Naoya Suzuki, Yuliya Troitskaya, Chiaki Tanaka, Alexander Kandaurov, and Maxim Vdovin
Ocean Sci., 16, 1033–1045, https://doi.org/10.5194/os-16-1033-2020, https://doi.org/10.5194/os-16-1033-2020, 2020
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Currents are high-speed continuous ocean flows. In general, currents accelerate surface waves. However, studies are performed at normal wind speeds only, with few studies at extremely high wind speeds. We investigate the effects of current on surface waves at extremely high wind speeds and use three wind-wave tanks to demonstrate surface waves and currents. As a result, at extremely high wind speeds, a similar acceleration effect is observed as under the conditions of normal wind speeds.
Sergej Zilitinkevich, Oleg Druzhinin, Andrey Glazunov, Evgeny Kadantsev, Evgeny Mortikov, Iryna Repina, and Yulia Troitskaya
Atmos. Chem. Phys., 19, 2489–2496, https://doi.org/10.5194/acp-19-2489-2019, https://doi.org/10.5194/acp-19-2489-2019, 2019
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We consider the budget of turbulent kinetic energy (TKE) in stably stratified flows. TKE is generated by velocity shear, then partially converted to potential energy, but basically cascades towards very small eddies and dissipates into heat. The TKE dissipation rate is vital for comprehending and modelling turbulent flows in geophysics, astrophysics, and engineering. Until now its dependence on static stability remained unclear. We define it theoretically and validate against experimental data.
Hanna K. Lappalainen, Veli-Matti Kerminen, Tuukka Petäjä, Theo Kurten, Aleksander Baklanov, Anatoly Shvidenko, Jaana Bäck, Timo Vihma, Pavel Alekseychik, Meinrat O. Andreae, Stephen R. Arnold, Mikhail Arshinov, Eija Asmi, Boris Belan, Leonid Bobylev, Sergey Chalov, Yafang Cheng, Natalia Chubarova, Gerrit de Leeuw, Aijun Ding, Sergey Dobrolyubov, Sergei Dubtsov, Egor Dyukarev, Nikolai Elansky, Kostas Eleftheriadis, Igor Esau, Nikolay Filatov, Mikhail Flint, Congbin Fu, Olga Glezer, Aleksander Gliko, Martin Heimann, Albert A. M. Holtslag, Urmas Hõrrak, Juha Janhunen, Sirkku Juhola, Leena Järvi, Heikki Järvinen, Anna Kanukhina, Pavel Konstantinov, Vladimir Kotlyakov, Antti-Jussi Kieloaho, Alexander S. Komarov, Joni Kujansuu, Ilmo Kukkonen, Ella-Maria Duplissy, Ari Laaksonen, Tuomas Laurila, Heikki Lihavainen, Alexander Lisitzin, Alexsander Mahura, Alexander Makshtas, Evgeny Mareev, Stephany Mazon, Dmitry Matishov, Vladimir Melnikov, Eugene Mikhailov, Dmitri Moisseev, Robert Nigmatulin, Steffen M. Noe, Anne Ojala, Mari Pihlatie, Olga Popovicheva, Jukka Pumpanen, Tatjana Regerand, Irina Repina, Aleksei Shcherbinin, Vladimir Shevchenko, Mikko Sipilä, Andrey Skorokhod, Dominick V. Spracklen, Hang Su, Dmitry A. Subetto, Junying Sun, Arkady Y. Terzhevik, Yuri Timofeyev, Yuliya Troitskaya, Veli-Pekka Tynkkynen, Viacheslav I. Kharuk, Nina Zaytseva, Jiahua Zhang, Yrjö Viisanen, Timo Vesala, Pertti Hari, Hans Christen Hansson, Gennady G. Matvienko, Nikolai S. Kasimov, Huadong Guo, Valery Bondur, Sergej Zilitinkevich, and Markku Kulmala
Atmos. Chem. Phys., 16, 14421–14461, https://doi.org/10.5194/acp-16-14421-2016, https://doi.org/10.5194/acp-16-14421-2016, 2016
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After kick off in 2012, the Pan-Eurasian Experiment (PEEX) program has expanded fast and today the multi-disciplinary research community covers ca. 80 institutes and a network of ca. 500 scientists from Europe, Russia, and China. Here we introduce scientific topics relevant in this context. This is one of the first multi-disciplinary overviews crossing scientific boundaries, from atmospheric sciences to socio-economics and social sciences.
O. A. Druzhinin and L. A. Ostrovsky
Nonlin. Processes Geophys., 22, 337–348, https://doi.org/10.5194/npg-22-337-2015, https://doi.org/10.5194/npg-22-337-2015, 2015
Short summary
Short summary
The objective of this paper is to study the dynamics of turbulence near a pycnocline, both in the free regime and under the action of an internal wave (IW) propagating along a pycnocline by direct numerical simulation (DNS). Turbulence is initially induced in a horizontal layer above the pycnocline. The DNS results show that turbulence kinetic energy (TKE) is significantly enhanced as compared to the TKE in the absence of IW, and most of the TKE is localized in the vicinity of the pycnocline.
O. A. Druzhinin, L. A. Ostrovsky, and S. S. Zilitinkevich
Nonlin. Processes Geophys., 20, 977–986, https://doi.org/10.5194/npg-20-977-2013, https://doi.org/10.5194/npg-20-977-2013, 2013
Yu. I. Troitskaya, E. V. Ezhova, and S. S. Zilitinkevich
Nonlin. Processes Geophys., 20, 825–839, https://doi.org/10.5194/npg-20-825-2013, https://doi.org/10.5194/npg-20-825-2013, 2013
Yu. I. Troitskaya, E. V. Ezhova, D. A. Sergeev, A. A. Kandaurov, G. A. Baidakov, M. I. Vdovin, and S. S. Zilitinkevich
Nonlin. Processes Geophys., 20, 841–856, https://doi.org/10.5194/npg-20-841-2013, https://doi.org/10.5194/npg-20-841-2013, 2013
Related subject area
Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
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Nonlin. Processes Geophys., 30, 289–297, https://doi.org/10.5194/npg-30-289-2023, https://doi.org/10.5194/npg-30-289-2023, 2023
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Eugenia Kalnay, Travis Sluka, Takuma Yoshida, Cheng Da, and Safa Mote
Nonlin. Processes Geophys., 30, 217–236, https://doi.org/10.5194/npg-30-217-2023, https://doi.org/10.5194/npg-30-217-2023, 2023
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Strongly coupled data assimilation (SCDA) generates coherent integrated Earth system analyses by assimilating the full Earth observation set into all Earth components. We describe SCDA based on the ensemble Kalman filter with a hierarchy of coupled models, from a coupled Lorenz to the Climate Forecast System v2. SCDA with a sufficiently large ensemble can provide more accurate coupled analyses compared to weakly coupled DA. The correlation-cutoff method can compensate for a small ensemble size.
Antoine Perrot, Olivier Pannekoucke, and Vincent Guidard
Nonlin. Processes Geophys., 30, 139–166, https://doi.org/10.5194/npg-30-139-2023, https://doi.org/10.5194/npg-30-139-2023, 2023
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This work is a theoretical contribution that provides equations for understanding uncertainty prediction applied in air quality where multiple chemical species can interact. A simplified minimal test bed is introduced that shows the ability of our equations to reproduce the statistics estimated from an ensemble of forecasts. While the latter estimation is the state of the art, solving equations is numerically less costly, depending on the number of chemical species, and motivates this research.
Pierre Tandeo, Pierre Ailliot, and Florian Sévellec
Nonlin. Processes Geophys., 30, 129–137, https://doi.org/10.5194/npg-30-129-2023, https://doi.org/10.5194/npg-30-129-2023, 2023
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The goal of this paper is to obtain probabilistic predictions of a partially observed dynamical system without knowing the model equations. It is illustrated using the three-dimensional Lorenz system, where only two components are observed. The proposed data-driven procedure is low-cost, is easy to implement, uses linear and Gaussian assumptions and requires only a small amount of data. It is based on an iterative linear Kalman smoother with a state augmentation.
Elia Gorokhovsky and Jeffrey L. Anderson
Nonlin. Processes Geophys., 30, 37–47, https://doi.org/10.5194/npg-30-37-2023, https://doi.org/10.5194/npg-30-37-2023, 2023
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Older observations of the Earth system sometimes lack information about the time they were taken, posing problems for analyses of past climate. To begin to ameliorate this problem, we propose new methods of varying complexity, including methods to estimate the distribution of the offsets between true and reported observation times. The most successful method accounts for the nonlinearity in the system, but even the less expensive ones can improve data assimilation in the presence of time error.
Chu-Chun Chang and Eugenia Kalnay
Nonlin. Processes Geophys., 29, 317–327, https://doi.org/10.5194/npg-29-317-2022, https://doi.org/10.5194/npg-29-317-2022, 2022
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This study introduces a new approach for enhancing the ensemble data assimilation (DA), a technique that combines observations and forecasts to improve numerical weather predictions. Our method uses the prescribed correlations to suppress spurious errors, improving the accuracy of DA. The experiments on the simplified atmosphere model show that our method has comparable performance to the traditional method but is superior in the early stage and is more computationally efficient.
Andrey A. Popov, Amit N. Subrahmanya, and Adrian Sandu
Nonlin. Processes Geophys., 29, 241–253, https://doi.org/10.5194/npg-29-241-2022, https://doi.org/10.5194/npg-29-241-2022, 2022
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Numerical weather prediction requires the melding of both computational model and data obtained from sensors such as satellites. We focus on one algorithm to accomplish this. We aim to aid its use by additionally supplying it with data obtained from separate models that describe the average behavior of the computational model at any given time. We show that our approach outperforms the standard approaches to this problem.
Sagar K. Tamang, Ardeshir Ebtehaj, Peter Jan van Leeuwen, Gilad Lerman, and Efi Foufoula-Georgiou
Nonlin. Processes Geophys., 29, 77–92, https://doi.org/10.5194/npg-29-77-2022, https://doi.org/10.5194/npg-29-77-2022, 2022
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The outputs from Earth system models are optimally combined with satellite observations to produce accurate forecasts through a process called data assimilation. Many existing data assimilation methodologies have some assumptions regarding the shape of the probability distributions of model output and observations, which results in forecast inaccuracies. In this paper, we test the effectiveness of a newly proposed methodology that relaxes such assumptions about high-dimensional models.
Yumeng Chen, Alberto Carrassi, and Valerio Lucarini
Nonlin. Processes Geophys., 28, 633–649, https://doi.org/10.5194/npg-28-633-2021, https://doi.org/10.5194/npg-28-633-2021, 2021
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Chaotic dynamical systems are sensitive to the initial conditions, which are crucial for climate forecast. These properties are often used to inform the design of data assimilation (DA), a method used to estimate the exact initial conditions. However, obtaining the instability properties is burdensome for complex problems, both numerically and analytically. Here, we suggest a different viewpoint. We show that the skill of DA can be used to infer the instability properties of a dynamical system.
Zofia Stanley, Ian Grooms, and William Kleiber
Nonlin. Processes Geophys., 28, 565–583, https://doi.org/10.5194/npg-28-565-2021, https://doi.org/10.5194/npg-28-565-2021, 2021
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In weather forecasting, observations are incorporated into a model of the atmosphere through a process called data assimilation. Sometimes observations in one location may impact the weather forecast in another faraway location in undesirable ways. The impact of distant observations on the forecast is mitigated through a process called localization. We propose a new method for localization when a model has multiple length scales, as in a model spanning both the ocean and the atmosphere.
Stephen Jewson, Giuliana Barbato, Paola Mercogliano, Jaroslav Mysiak, and Maximiliano Sassi
Nonlin. Processes Geophys., 28, 329–346, https://doi.org/10.5194/npg-28-329-2021, https://doi.org/10.5194/npg-28-329-2021, 2021
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Climate model simulations are uncertain. In some cases this makes it difficult to know how to use them. Significance testing is often used to deal with this issue but has various shortcomings. We describe two alternative ways to manage uncertainty in climate model simulations that avoid these shortcomings. We test them on simulations of future rainfall over Europe and show they produce more accurate projections than either using unadjusted climate model output or statistical testing.
Sagar K. Tamang, Ardeshir Ebtehaj, Peter J. van Leeuwen, Dongmian Zou, and Gilad Lerman
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Abd AlRahman AlMomani and Erik Bollt
Nonlin. Processes Geophys., 28, 153–166, https://doi.org/10.5194/npg-28-153-2021, https://doi.org/10.5194/npg-28-153-2021, 2021
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This paper introduces a tool for data-driven discovery of early warning signs of critical transitions in ice shelves from remote sensing data. Our directed spectral clustering method considers an asymmetric affinity matrix along with the associated directed graph Laplacian. We applied our approach to reprocessing the ice velocity data and remote sensing satellite images of the Larsen C ice shelf.
Shin'ya Nakano
Nonlin. Processes Geophys., 28, 93–109, https://doi.org/10.5194/npg-28-93-2021, https://doi.org/10.5194/npg-28-93-2021, 2021
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The ensemble-based variational method is a method for solving nonlinear data assimilation problems by using an ensemble of multiple simulation results. Although this method is derived based on a linear approximation, highly uncertain problems, in which system nonlinearity is significant, can also be solved by applying this method iteratively. This paper reformulated this iterative algorithm to analyze its behavior in high-dimensional nonlinear problems and discuss the convergence.
Olivier Pannekoucke, Richard Ménard, Mohammad El Aabaribaoune, and Matthieu Plu
Nonlin. Processes Geophys., 28, 1–22, https://doi.org/10.5194/npg-28-1-2021, https://doi.org/10.5194/npg-28-1-2021, 2021
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Numerical weather prediction involves numerically solving the mathematical equations, which describe the geophysical flow, by transforming them so that they can be computed. Through this transformation, it appears that the equations actually solved by the machine are then a modified version of the original equations, introducing an error that contributes to the model error. This work helps to characterize the covariance of the model error that is due to this modification of the equations.
Pengcheng Yan, Guolin Feng, Wei Hou, and Ping Yang
Nonlin. Processes Geophys., 27, 489–500, https://doi.org/10.5194/npg-27-489-2020, https://doi.org/10.5194/npg-27-489-2020, 2020
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A system transiting from one stable state to another has to experience a period. Can we predict the end moment (state) if the process has not been completed? This paper presents a method to solve this problem. This method is based on the quantitative relationship among the parameters, which is used to describe the transition process of the abrupt change. By using the historical data, we extract some parameters for predicting the uncompleted climate transition process.
Reinhold Hess
Nonlin. Processes Geophys., 27, 473–487, https://doi.org/10.5194/npg-27-473-2020, https://doi.org/10.5194/npg-27-473-2020, 2020
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Forecasts of ensemble systems are statistically aligned to synoptic observations at DWD in order to provide support for warning decision management. Motivation and design consequences for extreme and rare meteorological events are presented. Especially for probabilities of severe wind gusts global logistic parameterisations are developed that generate robust statistical forecasts for extreme events, while local characteristics are preserved.
Jonathan Demaeyer and Stéphane Vannitsem
Nonlin. Processes Geophys., 27, 307–327, https://doi.org/10.5194/npg-27-307-2020, https://doi.org/10.5194/npg-27-307-2020, 2020
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Postprocessing schemes used to correct weather forecasts are no longer efficient when the model generating the forecasts changes. An approach based on response theory to take the change into account without having to recompute the parameters based on past forecasts is presented. It is tested on an analytical model and a simple model of atmospheric variability. We show that this approach is effective and discuss its potential application for an operational environment.
Carlos Osácar, Manuel Membrado, and Amalio Fernández-Pacheco
Nonlin. Processes Geophys., 27, 235–237, https://doi.org/10.5194/npg-27-235-2020, https://doi.org/10.5194/npg-27-235-2020, 2020
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We deduce that after a global thermal perturbation, the Earth's
atmosphere would need about a couple of months to come back to equilibrium.
André Düsterhus
Nonlin. Processes Geophys., 27, 121–131, https://doi.org/10.5194/npg-27-121-2020, https://doi.org/10.5194/npg-27-121-2020, 2020
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Seasonal prediction of the of the North Atlantic Oscillation (NAO) has been improved in recent years by improving dynamical models and ensemble predictions. One step therein was the so-called sub-sampling, which combines statistical and dynamical predictions. This study generalises this approach and makes it much more accessible. Furthermore, it presents a new verification approach for such predictions.
Courtney Quinn, Terence J. O'Kane, and Vassili Kitsios
Nonlin. Processes Geophys., 27, 51–74, https://doi.org/10.5194/npg-27-51-2020, https://doi.org/10.5194/npg-27-51-2020, 2020
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This study presents a novel method for reduced-rank data assimilation of multiscale highly nonlinear systems. Time-varying dynamical properties are used to determine the rank and projection of the system onto a reduced subspace. The variable reduced-rank method is shown to succeed over other fixed-rank methods. This work provides implications for performing strongly coupled data assimilation with a limited number of ensemble members on high-dimensional coupled climate models.
Nina Schuhen
Nonlin. Processes Geophys., 27, 35–49, https://doi.org/10.5194/npg-27-35-2020, https://doi.org/10.5194/npg-27-35-2020, 2020
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We present a new way to adaptively improve weather forecasts by incorporating last-minute observation information. The recently measured error, together with a statistical model, gives us an indication of the expected future error of wind speed forecasts, which are then adjusted accordingly. This new technique can be especially beneficial for customers in the wind energy industry, where it is important to have reliable short-term forecasts, as well as providers of extreme weather warnings.
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Short summary
The nonstationary kinetic model of turbulence is used to describe the evolution and structure of the upper turbulent layer with the parameters taken from in situ observations. As an example, we use a set of data for three cruises made in different areas of the world ocean. With the given profiles of current shear and buoyancy frequency, the theory yields results that satisfactorily agree with the measurements of the turbulent dissipation rate.
The nonstationary kinetic model of turbulence is used to describe the evolution and structure of...
