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Symmetry
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Geophysical Fluid Dynamics and Symmetry
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Special Issue "Geophysical Fluid Dynamics and Symmetry"

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: 31 December 2023 | Viewed by 7284

Special Issue Editors

Dr. Mikhail A. Sokolovskiy

E-Mail Website
Guest Editor
Institute of Water Problems, Russian Academy of Science, 3 Gubkina Street, 119333 Moscow, Russia
Interests: vortex dynamics in stratified/homogeneous rotating fluid; application to the geophysical environs
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Xavier Carton

E-Mail Website
Guest Editor
Laboratoire d’Océanographie Physique et Spatiale, Institut Universitaire Européen de la Mer, Universite de Bretagne Occidentale, 29280 Plouzané, France
Interests: ocean dynamics; mesoscale vortex stability and interactions; continental slope currents; outflows from marginal seas
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue, “Geophysical Fluid Dynamics and Symmetry”, is dedicated to the publication of novel results on the symmetry in three/two-dimensional vortex and/or wave structures and their dynamics in rotating stratified/barotropic flows. Papers on layer-wise models of vortex and wave dynamics are also invited. Papers focusing on their generation mechanism, stability, evolution, and interactions; on their relationship with smaller-scale flows; and on their effects on tracer transport are solicited. Papers should preferably provide elements of mathematical theories in these contexts, but can also rely on extensive numerical modelling or data analysis.

The aim of this Issue is to provide readers with an overview of recent progress in this field, with application to the dynamics of planetary oceans and atmospheres.

Dr. Mikhail A. Sokolovskiy
Prof. Dr. Xavier Carton
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • theoretical and numerical studies of symmetric vortex and wave dynamics
  • role of potential vorticity concentrations in rotating and stratified flow dynamics
  • vortex/wave stability and/or evolution under external forcing
  • nonlinear interaction between vortices/waves
  • instability of flows with initial symmetry or developing symmetry

Published Papers (5 papers)

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Article
Dynamics of a Circular Foil and Two Pairs of Point Vortices: New Relative Equilibria and a Generalization of Helmholtz Leapfrogging
by
Ivan A. Bizyaev
and
Ivan S. Mamaev
Symmetry 2023, 15(3), 698; https://doi.org/10.3390/sym15030698 - 10 Mar 2023
Viewed by 695
Abstract
In this paper, we study the plane-parallel motion of a circular foil interacting with two vortex pairs in an infinite volume of an ideal fluid. We assumed that the circulation of the velocity of the fluid around the foil was zero. We showed [...] Read more.
In this paper, we study the plane-parallel motion of a circular foil interacting with two vortex pairs in an infinite volume of an ideal fluid. We assumed that the circulation of the velocity of the fluid around the foil was zero. We showed that the equations of motion possess an invariant submanifold such that the foil performed translational motion and the vortices were symmetric relative to the foil’s direction of motion. A qualitative analysis of the motion on this invariant submanifold was made. New relative equilibria were found, a bifurcation diagram was constructed, and a stability analysis is given. In addition, trajectories generalizing Helmholtz leapfrogging were found where the vortices passed alternately through each other, while remaining at a finite distance from the foil. Full article
(This article belongs to the Special Issue Geophysical Fluid Dynamics and Symmetry)
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Article
Eady Baroclinic Instability of a Circular Vortex
by
Armand Vic
,
Xavier Carton
and
Jonathan Gula
Symmetry 2022, 14(7), 1438; https://doi.org/10.3390/sym14071438 - 13 Jul 2022
Viewed by 871
Abstract
The stability of two superposed buoyancy vortices is studied linearly in a two-level Surface Quasi-Geostrophic (SQG) model. The basic flow is chosen as two circular vortices with uniform buoyancy, coaxial, and the same radius. A perturbation with a single angular mode is added [...] Read more.
The stability of two superposed buoyancy vortices is studied linearly in a two-level Surface Quasi-Geostrophic (SQG) model. The basic flow is chosen as two circular vortices with uniform buoyancy, coaxial, and the same radius. A perturbation with a single angular mode is added to this mean flow. The SQG equations linearized in perturbation around this basic flow form a two-dimensional ODE for which the normal and singular mode solutions are numerically computed. The instability of these two vortices depends on several parameters. The parameters varied here are: the vertical distance between the two levels and the two values of the vortex buoyancies (called vortex intensity hereafter); the other parameters remain fixed. For normal modes, the system is stable if the levels are sufficiently far from each other vertically, to prevent vertical interactions of the buoyancy patches. Stability is also reached if the layers are close to each other, but if the vortices have very different intensities, again preventing the resonance of Rossby waves around their contours. The system is unstable if the vortex intensities are similar and if the two levels are close to each other. The growth rates of the normal modes increase with the angular wave-number, also corresponding to shorter vertical distances. The growth rates of the singular modes depend more on the distance between the levels than on the ratio of the vortex intensities, at a short time; as expected, they converge towards the growth rates of the normal modes. This study remaining linear does not predict the final evolution of such unstable vortices. This nonlinear evolution will be studied in a sequel of this work. Full article
(This article belongs to the Special Issue Geophysical Fluid Dynamics and Symmetry)
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Article
On (n,1) Wave Attractors: Coordinates and Saturation Time
by
Ilias Sibgatullin
,
Alexandr Petrov
,
Xiulin Xu
and
Leo Maas
Symmetry 2022, 14(2), 319; https://doi.org/10.3390/sym14020319 - 04 Feb 2022
Cited by 2 | Viewed by 1128
Abstract
The simplest geometry of the domain, for which internal wave attractors were for the first time investigated both experimentally and numerically, has the shape of a trapezium with one vertical wall and one inclined lateral wall, characterized by two parameters. Using the symmetries [...] Read more.
The simplest geometry of the domain, for which internal wave attractors were for the first time investigated both experimentally and numerically, has the shape of a trapezium with one vertical wall and one inclined lateral wall, characterized by two parameters. Using the symmetries of such a geometry we give an exact solution for the coordinates of the wave attractors with one reflection from each of the lateral boundaries and an integer amount n of reflections from each of the horizontal boundaries. The area of existence for each (n,1) attractor has the form of a triangle in the (d,τ) parameter plane, and the shape of this triangle is explicitly given with the help of inequalities or vertices. The expression for the Lyapunov exponents and their connection to the focusing parameters is given analytically. The corresponding direct numerical simulations with low viscosity fully support the analytical results and demonstrate that in bounded domains (n,1) wave attractors can be effective transformers of the global forcing into traveling waves. The saturation time from the state of rest to the final wave regime depends almost linearly on the number of cells, n. Full article
(This article belongs to the Special Issue Geophysical Fluid Dynamics and Symmetry)
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Article
Vertical Shear Processes in River Plumes: Instabilities and Turbulent Mixing
by
Adam Ayouche
,
Xavier Carton
and
Guillaume Charria
Symmetry 2022, 14(2), 217; https://doi.org/10.3390/sym14020217 - 23 Jan 2022
Cited by 3 | Viewed by 1864
Abstract
In this paper, the problem of vertical shear flow instabilities at the base of a river plume and their consequences in terms of turbulent energy production and mixing is addressed. This study was carried out using 2D non-hydrostatic simulations and a linear stability [...] Read more.
In this paper, the problem of vertical shear flow instabilities at the base of a river plume and their consequences in terms of turbulent energy production and mixing is addressed. This study was carried out using 2D non-hydrostatic simulations and a linear stability analysis. The initial conditions used in these simulations were similar to those observed in river plumes near estuaries. Unstable stratified sheared flows follow three stages of evolution: (i) the generation of billows induced by vertical shear instabilities, (ii) intensification, and (iii) elongation. The elongation of the generated billows is related to the strain intensity, which depends on the physical setting involved (velocity shear, stratification thickness, and bottom slope). Two vertical shear instabilities were found in our study: the Holmboe and Kelvin–Helmholtz instabilities. The Kelvin–Helmholtz instability has a smaller growth time and longer wavelengths; the Holmboe instability is characterized by a longer growth time and shorter wavelengths. The Kelvin–Helmholtz instability is intensified when the bottom is sloped and for large shears. The Holmboe instability is stronger when the stratification thickness is reduced compared to the shear thickness and when the bottom is sloped. For mixing, the flow can be: (i) pre-turbulent, (ii) quasi-turbulent, or (iii) turbulent. The pre-turbulent flow corresponds to more mass mixing than momentum mixing and to more Eddy Kinetic Energy dissipation than Eddy Available Potential Energy dissipation. Such a flow is encountered over a flat bottom whatever the initial shear is. The quasi-turbulent and turbulent flows are reached when the bottom is sloped and when the stratification thickness is reduced. Using turbulent mixing statistics (mixing coefficients, mixing efficiency, Eddy Kinetic Energy, and Eddy Available Potential Energy dissipation rates), we showed that, despite their slow growth, Holmboe instabilities contribute more efficiently to turbulent mixing than Kelvin–Helmholtz instabilities. Holmboe instabilities are the only source of turbulent mixing when sharp density gradients are observed (small buoyancy thickness experiment). Our simulations highlight the contribution of the Holmboe instability to turbulent mixing. Full article
(This article belongs to the Special Issue Geophysical Fluid Dynamics and Symmetry)
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Article
The Symmetry and Stability of the Flow Separation around a Sphere at Low and Moderate Reynolds Numbers
by
Junwei Li
and
Benmou Zhou
Symmetry 2021, 13(12), 2286; https://doi.org/10.3390/sym13122286 - 01 Dec 2021
Cited by 7 | Viewed by 1865
Abstract
The flow separation state reflects the symmetry and stability of flow around spheres. The three-dimensional structures of flow around a rigid sphere at moderate Reynolds number (Re) between 20 and 400 by using finite volume method with adaptive mesh refinement are [...] Read more.
The flow separation state reflects the symmetry and stability of flow around spheres. The three-dimensional structures of flow around a rigid sphere at moderate Reynolds number (Re) between 20 and 400 by using finite volume method with adaptive mesh refinement are presented, and the process of separation angles changing from stable to oscillating state with increasing of Re is analyzed. The results show that the flow is steady, and the separation angles are stable and axisymmetric at Re in less than 200. The flow is unsteady and time-periodic, and the flow separation becomes regular fluctuations and asymmetric at Re = 300, which leads to the nonzero value of lateral force and the phase difference between lift and lateral force. At Re = 400, the flow is unsteady, non-periodic, and asymmetric, as is the flow separation. It’s concluded that the flow separation angle increases when Re increases within a range between 40 and 200. With Re continues to increase, the flow separation state changes from stable to periodically regular until quasi-periodically irregular. The vortex structure changes from no shedding to asymmetric periodic shedding, and finally to asymmetric and intermittently periodic vortex shedding. These results have important implications for the stability of flow around spheres. Full article
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Transport barriers in geophysical flows
Authors: Sergey Prants
Affiliation: Pacific Oceanological Institute of the Russian Academy of Sciences
Abstract: In the Lagrangian approach, the transport processes in the ocean and atmosphere are studied by tracking water or air parcels, each of which may carry different tracers. In the ocean, they are salt, nutrients, heat, and particulate matter such as plankters, oil, radionuclides and microplastic. In the atmosphere, the tracers are water vapor, ozone and various chemicals.The observation and simulation reveal highly complex patterns of advection of tracers in turbulent-like geophysical flows. Transport barriers are material surfaces across which the transport is minimal. They can be classified into elliptic, parabolic and hyperbolic barriers. Different diagnostics in detecting transport barriers and analysis of their role in dynamics of oceanic and atmospheric flows are reviewed. We discuss the mathematical tools, borrowed from dynamical systems theory, for detecting transport barriers in simple kinematic and dynamic models of vortical and jet-like flows. It is shown how the ideas and methods, developed for simple model flows, can be successfully applied for studying the role of barriers in oceanic and atmospheric flows. Special attention is paid to discussion of the role of transport barriers for important practical issues: anthropogenic and natural pollutants, advection of plankton, cross-shelf exchange and propagation of upwelling fronts in coastal zones.

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