Articles | Volume 24, issue 4
https://doi.org/10.5194/npg-24-581-2017
© 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-24-581-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
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09 Oct 2017
Research article | Highlight paper |
| 09 Oct 2017
Balanced source terms for wave generation within the Hasselmann equation
Vladimir Zakharov
Department of Mathematics, University of Arizona, Tucson, AZ 85721,
USA
Lebedev Physical Institute RAS, Leninsky 53, Moscow 119991,
Russia
Novosibirsk State University, Novosibirsk, 630090, Russia
Waves and Solitons LLC, 1719 W. Marlette Ave., Phoenix, AZ 85015,
USA
Donald Resio
Taylor Engineering Research Institute, University of North
Florida, Jacksonville, FL, USA
Andrei Pushkarev
CORRESPONDING AUTHOR
Department of Mathematics, University of Arizona, Tucson, AZ 85721,
USA
Lebedev Physical Institute RAS, Leninsky 53, Moscow 119991,
Russia
Novosibirsk State University, Novosibirsk, 630090, Russia
Waves and Solitons LLC, 1719 W. Marlette Ave., Phoenix, AZ 85015,
USA
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In our simulations of sea swell, we show that its evolution exhibits remarkable features of universality. At long stretches the swell ``forgets'' initial conditions and keeps its specific distribution of wave energy in scales and directions. Slow evolution of swell in time and space can be related to fundamental relationships of the so-called theory of weak turbulence that gives a solid basis for the swell prediction.
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In our simulations of sea swell, we show that its evolution exhibits remarkable features of universality. At long stretches the swell ``forgets'' initial conditions and keeps its specific distribution of wave energy in scales and directions. Slow evolution of swell in time and space can be related to fundamental relationships of the so-called theory of weak turbulence that gives a solid basis for the swell prediction.
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The work aims to check one of the assumptions under which the kinetic equation for water waves was derived in order to understand whether it can be applied to situations described by the Phillips spectrum, which includes rough sea. We evaluated a spectral line width of the spectrum from the simulations in the framework of primordial dynamical equations at different levels of nonlinearity in the system, and showed that it remains narrow even for the situations described by the Phillips spectrum.
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Oxana Kurkina, Tatyana Talipova, Tarmo Soomere, Ayrat Giniyatullin, and Andrey Kurkin
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Pedro Monroy, Emilio Hernández-García, Vincent Rossi, and Cristóbal López
Nonlin. Processes Geophys., 24, 293–305, https://doi.org/10.5194/npg-24-293-2017, https://doi.org/10.5194/npg-24-293-2017, 2017
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We study the problem of sinking particles in a realistic oceanic flow, with major energetic structures in the mesoscale, focussing on marine biogenic particles. By using a simplified equation of motion for small particles in a mesoscale velocity field, we estimate the influence of physical processes such as the Coriolis force and the particle's inertia, and we conclude that they represent negligible corrections to passive transport by the flow, with added vertical velocity due to gravity.
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
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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.
Sergei I. Badulin and Vladimir E. Zakharov
Nonlin. Processes Geophys., 24, 237–253, https://doi.org/10.5194/npg-24-237-2017, https://doi.org/10.5194/npg-24-237-2017, 2017
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In our simulations of sea swell, we show that its evolution exhibits remarkable features of universality. At long stretches the swell ``forgets'' initial conditions and keeps its specific distribution of wave energy in scales and directions. Slow evolution of swell in time and space can be related to fundamental relationships of the so-called theory of weak turbulence that gives a solid basis for the swell prediction.
Anatoly Abrashkin and Efim Pelinovsky
Nonlin. Processes Geophys., 24, 255–264, https://doi.org/10.5194/npg-24-255-2017, https://doi.org/10.5194/npg-24-255-2017, 2017
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The nonlinear Schrödinger equation describing weakly rotational wave packets in a fluid in the Lagrangian coordinates is derived. Rogue effects are possible in low-vorticity waves, and the effect of vorticity is manifested in a shift of the wave number in the carrier wave. Special attention is paid to Gouyon and Gerstner waves. It is shown that this equation in the Eulerian variables can be obtained from the Lagrangian solution with an ordinary change in the horizontal coordinates.
Irina I. Rypina and Lawrence J. Pratt
Nonlin. Processes Geophys., 24, 189–202, https://doi.org/10.5194/npg-24-189-2017, https://doi.org/10.5194/npg-24-189-2017, 2017
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Fluid parcels exchange water properties when coming into contact with each other, leading to mixing. The trajectory encounter volume, defined here as the volume of fluid that passes close to a reference trajectory over a finite time interval, is introduced as a measure of the mixing potential of a flow. Regions with a low encounter volume (the cores of coherent eddies) have a low mixing potential. Regions with a large encounter volume (turbulent or chaotic regions) have a high mixing potential.
Nizar Abcha, Tonglei Zhang, Alexander Ezersky, Efim Pelinovsky, and Ira Didenkulova
Nonlin. Processes Geophys., 24, 157–165, https://doi.org/10.5194/npg-24-157-2017, https://doi.org/10.5194/npg-24-157-2017, 2017
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Parametric excitation of edge waves with a frequency 2 times less than the frequency of surface waves propagating perpendicular to the inclined bottom are investigated in laboratory experiments. The domain of instability on the plane of surface wave parameters (amplitude–frequency) is found. The subcritical instability is observed in the system of parametrically excited edge waves. It is shown that breaking of surface waves initiates turbulent effects and can suppress the parametric generation.
Sergey V. Prants, Maxim V. Budyansky, and Michael Yu. Uleysky
Nonlin. Processes Geophys., 24, 89–99, https://doi.org/10.5194/npg-24-89-2017, https://doi.org/10.5194/npg-24-89-2017, 2017
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Transport of subtropical waters in the Japan Sea is simulated based on altimeter data. Preferred transport pathways across the Subpolar Front are found.
The cross-frontal transport is shown to be inhomogeneous with gates and barriers whose locations are determined by a local velocity field. The gates open due to suitable dispositions of mesoscale eddies facilitating propagation of subtropical waters to the north. There are forbidden zones where the northward transport has not been observed.
Aaron Coutino and Marek Stastna
Nonlin. Processes Geophys., 24, 61–75, https://doi.org/10.5194/npg-24-61-2017, https://doi.org/10.5194/npg-24-61-2017, 2017
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We have re-examined the classical geostrophic adjustment problem, where a disturbance of a density stratification is released from rest in a rotating frame of reference, from a numerical point of view. This has enabled us to consider the governing equations without approximations. We show that both the waves generated and the remaining state exhibit nonlinear effects. Due to advances in available computational power, we can now revisit classical problems and solve them completely.
Floriane Gidel, Onno Bokhove, and Anna Kalogirou
Nonlin. Processes Geophys., 24, 43–60, https://doi.org/10.5194/npg-24-43-2017, https://doi.org/10.5194/npg-24-43-2017, 2017
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Extreme water waves impacting ships and offshore structures can not only cause severe structural damage, but also threaten the safety of passengers and crew. Accordingly, the motivation for the present work is to better understand the dynamics of extreme waves in two cases: the case of "green water" and the case of "freak waves". Our methodology can simulate those two events in order to estimate the forces of such extreme waves and thus aid engineers in the design of safer maritime structures.
Claudia Cherubini, Nicola Pastore, Concetta I. Giasi, and Nicoletta Maria Allegretti
Nonlin. Processes Geophys., 24, 23–42, https://doi.org/10.5194/npg-24-23-2017, https://doi.org/10.5194/npg-24-23-2017, 2017
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Aquifers offer the possibility of exploiting geothermal energy. Especially in fractured aquifers, in order to increase the optimal efficiency of installations which use groundwater as a geothermal resource, flow and heat transport dynamics need to be well understood. This study is aimed at deepening the understanding of this topic through heat transport experiments in fractured networks and their interpretation.
Konstantin V. Koshel and Eugene A. Ryzhov
Nonlin. Processes Geophys., 24, 1–8, https://doi.org/10.5194/npg-24-1-2017, https://doi.org/10.5194/npg-24-1-2017, 2017
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The paper deals with the dynamics of an isolated vortex that evolves in a time-dependent strain environment. We establish parameters leading to parametric instability of stationary steady-state configuration using a combination of analytical and numerical techniques. Our findings may contribute to a deeper understanding of the coherent vortex dynamics in the ocean.
Arnida L. Latifah and E. van Groesen
Nonlin. Processes Geophys., 23, 341–359, https://doi.org/10.5194/npg-23-341-2016, https://doi.org/10.5194/npg-23-341-2016, 2016
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This paper showed the relevance of phase coherence by illustrations of signals with increasingly less restrictions on the phase function. Then the wavelet transform was used to determined the time–frequency spectrum of a time signal. We used the wavelet transform to identify critical group events of the influx signal and it is shown that the group event with the largest local energy signal is the most probable group to generate a freak wave. It gives a local mechanism of a freak wave appearance.
Jean-Louis Le Mouël, Vladimir G. Kossobokov, Frederic Perrier, and Pierre Morat
Nonlin. Processes Geophys., 23, 319–330, https://doi.org/10.5194/npg-23-319-2016, https://doi.org/10.5194/npg-23-319-2016, 2016
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Heating experiments carried out in a limestone quarry close to Paris have shown a classical shape of temperature distribution in steady-state plumes in averages over 24 h, along with rich dynamics of heat flow with intermittent trains of oscillations, spatially coherent, of large amplitudes and a ~ 400 s period, separated by relative quiescence whose duration can reach several hours. The observed behavior could be a universal feature of some turbulent plumes in real geophysical environments.
Borja Aguiar-González and Theo Gerkema
Nonlin. Processes Geophys., 23, 285–305, https://doi.org/10.5194/npg-23-285-2016, https://doi.org/10.5194/npg-23-285-2016, 2016
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We derive a new two-fluid layer model consisting of forced rotation-modified Boussinesq equations for studying the limiting amplitudes of tidally generated fully nonlinear, weakly nonhydrostatic dispersive interfacial tides and solitons. Numerical solutions show that solitons attain in some cases a limiting table-shaped form, but may also be limited well below that state by saturation of the underlying quasi-linear internal tide under increasing barotropic forcing.
Manel Grifoll, Jorge Navarro, Elena Pallares, Laura Ràfols, Manuel Espino, and Ana Palomares
Nonlin. Processes Geophys., 23, 143–158, https://doi.org/10.5194/npg-23-143-2016, https://doi.org/10.5194/npg-23-143-2016, 2016
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In this contribution the wind jet dynamics in the northern margin of the Ebro River shelf (NW Mediterranean Sea) are investigated using coupled numerical models. The study area is characterized by persistent and energetic offshore winds during autumn and winter. However, the coupling effect in the wind resource assessment may be relevant due to the cubic relation between the wind intensity and power.
Vassili Kitsios, Jorgen S. Frederiksen, and Meelis J. Zidikheri
Nonlin. Processes Geophys., 23, 95–105, https://doi.org/10.5194/npg-23-95-2016, https://doi.org/10.5194/npg-23-95-2016, 2016
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To numerically simulate the atmosphere and ocean, the large eddies are resolved on a grid, and the effect the small unresolved eddies have on the large ones is modelled. Improper modelling leads to resolution-dependent results. We solve this long-standing problem by calculating the model coefficients from high-resolution simulations, and characterise the coefficients with a set of scaling laws. Low-resolution simulations adopting these laws reproduce the statistics of the high-resolution cases.
Gavita S. Regunath, William B. Zimmerman, and Julia M. Rees
Nonlin. Processes Geophys., 23, 83–89, https://doi.org/10.5194/npg-23-83-2016, https://doi.org/10.5194/npg-23-83-2016, 2016
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Helical structures are commonplace in geophysical flows, but their effect on turbulence is still enigmatic. A novel PIV laser technique has been used to analyze helical structures in a turbulent swirling jet where the underlying shear flow is subjected to external acoustic forcing. Although the acoustic excitation had an effect on the flow field, no evidence for the existence of large-scale helical structures with maximal helicity was found.
Pilar López and José L. Cano
Nonlin. Processes Geophys., 23, 75–82, https://doi.org/10.5194/npg-23-75-2016, https://doi.org/10.5194/npg-23-75-2016, 2016
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The focus of this paper is to improve our studies related to the novel use of the Thorpe method applied to atmospheric boundary layer (ABL) using new data from Spanish field experiments. We analyse the time behaviour of the maximum Thorpe displacement (dT)max and the Thorpe-scale LT during a day cycle. We also analyse the relation between (dT)max and LT. We deduce that they confirm a power law statistically significant, with differences between convective conditions and shear-driven conditions.
A. M. Matulka, Y. Zhang, and Y. D. Afanasyev
Nonlin. Processes Geophys., 23, 21–29, https://doi.org/10.5194/npg-23-21-2016, https://doi.org/10.5194/npg-23-21-2016, 2016
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In this paper, a turbulent ocean is modelled in the laboratory. The rotation of the Earth around its axis is represented by the rotation of a turntable. Similar to that in the Earth's ocean, the currents in the laboratory "ocean" are created by density effects when the water is heated or made salty. The laboratory currents are measured by a system which is not unlike the satellite altimetry system used by oceanographers to create "topographic" maps of the elevation of the water surface.
L. Shemer and B. K. Ee
Nonlin. Processes Geophys., 22, 737–747, https://doi.org/10.5194/npg-22-737-2015, https://doi.org/10.5194/npg-22-737-2015, 2015
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
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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.
P. R. Renosh, F. G. Schmitt, and H. Loisel
Nonlin. Processes Geophys., 22, 633–643, https://doi.org/10.5194/npg-22-633-2015, https://doi.org/10.5194/npg-22-633-2015, 2015
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Intermittent dynamics of particle size distribution in coastal waters is studied. Particle sizes are separated into four size classes: silt, fine, coarse and macro particles. The time series of each size class is derived, and their multiscaling properties studied. Similar analysis has been done for suspended particulate matter and total volume concentration. All quantities display a nonlinear moment function and a negative Hurst scaling exponent.
D. Garaboa-Paz and V. Pérez-Muñuzuri
Nonlin. Processes Geophys., 22, 571–577, https://doi.org/10.5194/npg-22-571-2015, https://doi.org/10.5194/npg-22-571-2015, 2015
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The present study aims to improve the calculus of finite-time Lyapunov exponents (FTLEs) applied to describe the transport of inertial particles in a fluid flow. To this aim, the deformation tensor is modified to take into account that the stretching rate between particles separated by a certain distance is influenced by the initial velocity of the particles. Results are presented for two different flows and compared with the classical method by Shadden (2005).
P. He and S. Basu
Nonlin. Processes Geophys., 22, 447–471, https://doi.org/10.5194/npg-22-447-2015, https://doi.org/10.5194/npg-22-447-2015, 2015
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The present work, to the best of our knowledge, is the first DNS study reporting temporal (long-term) statistics of intermittent turbulence (a.k.a. bursting events) in stably stratified flows. The present paper not only accurately reproduces recently published key spatial statistics of intermittent turbulence but also reports some intriguing features, e.g., the coexistence of internal waves and intermittent turbulence.
S. R. Ramp, Y. J. Yang, D. B. Reeder, M. C. Buijsman, and F. L. Bahr
Nonlin. Processes Geophys., 22, 413–431, https://doi.org/10.5194/npg-22-413-2015, https://doi.org/10.5194/npg-22-413-2015, 2015
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Highly energetic mode-2 nonlinear internal waves were found to be generated at several sites near the northern Heng-Chun (western) Ridge south of Taiwan. The local environment however was highly dissipative, and the energy budget suggests that little wave energy escapes the ridge to contribute to the large transbasin waves that have been previously observed in other studies.
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.
I. V. Shugan, H. H. Hwung, and R. Y. Yang
Nonlin. Processes Geophys., 22, 313–324, https://doi.org/10.5194/npg-22-313-2015, https://doi.org/10.5194/npg-22-313-2015, 2015
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An analytical weakly nonlinear model of Benjamin–Feir instability of a Stokes wave on nonuniform unidirectional current is presented. In contrast to the models based on versions of the cubic Schrodinger equation the current variations could be strong, which allows us to examine the blockage of waves. Waves may overpass the blocking barrier produced by strong adverse current. We find reasonable correspondence between the results of model simulations and available experimental results.
K. G. Lamb and A. Warn-Varnas
Nonlin. Processes Geophys., 22, 289–312, https://doi.org/10.5194/npg-22-289-2015, https://doi.org/10.5194/npg-22-289-2015, 2015
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Two-dimensional numerical simulations of the shoaling of an internal solitary wave (ISW) in the South China Sea have been undertaken. Peak amplitudes are attained at depths of 250 and 600m. Horizontal resolutions of 50m are required to simulate the formation of a pedestal in shallow water behind the shoaling wave. At a depth of 200m, waves can exceed maximum ISW amplitudes by 50%. Sensitivity to the bathymetry and stratification and the effects of rotation are considered.
J. P. McHugh
Nonlin. Processes Geophys., 22, 259–274, https://doi.org/10.5194/npg-22-259-2015, https://doi.org/10.5194/npg-22-259-2015, 2015
M. Humi
Nonlin. Processes Geophys., 22, 133–138, https://doi.org/10.5194/npg-22-133-2015, https://doi.org/10.5194/npg-22-133-2015, 2015
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Long's equation models the steady state of two-dimensional stratified
flow over terrain. It has been used extensively to investigate the generation
and properties of gravity waves and their impact on the structure
constants of the atmosphere. In this paper we derive a time-dependent version
of this equation which might be useful in the analysis of experimental data about gravity waves.
O. E. Kurkina, A. A. Kurkin, E. A. Rouvinskaya, and T. Soomere
Nonlin. Processes Geophys., 22, 117–132, https://doi.org/10.5194/npg-22-117-2015, https://doi.org/10.5194/npg-22-117-2015, 2015
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We have derived exact analytical expressions for the coefficients of evolution equations of long wave motion in the three-layer fluid with arbitrary parameters of the layers and established interrelations of these equations for different interfaces. To our understanding, the core advancement is the clarification and mapping of the regimes of soliton appearance and propagation in this environment that is much more realistic for the description of ocean internal waves.
J. C. Harris and S. T. Grilli
Nonlin. Processes Geophys., 21, 1169–1184, https://doi.org/10.5194/npg-21-1169-2014, https://doi.org/10.5194/npg-21-1169-2014, 2014
W. Kristina, O. Bokhove, and E. van Groesen
Nonlin. Processes Geophys., 21, 987–1005, https://doi.org/10.5194/npg-21-987-2014, https://doi.org/10.5194/npg-21-987-2014, 2014
L. M. Ivanov, C. A. Collins, and T. M. Margolina
Nonlin. Processes Geophys., 21, 887–900, https://doi.org/10.5194/npg-21-887-2014, https://doi.org/10.5194/npg-21-887-2014, 2014
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Short summary
The Hasselmann equation (HE) is the basis of modern surface ocean wave prediction models. Currently, they operate in the
black box with the tuning knobsmodes, since there is no consensus on universal wind input and wave-breaking dissipation source terms, and require re-tuning for different boundary and external conditions. We offer a physically justified framework able to reproduce theoretical properties of the HE and experimental field data without re-tuning of the model.
The Hasselmann equation (HE) is the basis of modern surface ocean wave prediction models....
