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Fluids
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Instabilities and Nonlinear Dynamics in Oceanic Flows
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Instabilities and Nonlinear Dynamics in Oceanic Flows

A special issue of Fluids (ISSN 2311-5521). This special issue belongs to the section "Geophysical and Environmental Fluid Mechanics".

Deadline for manuscript submissions: closed (15 January 2023) | Viewed by 13698

Special Issue Editors

Prof. Dr. Xavier Carton

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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
Prof. Dr. Sabrina Speich

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Guest Editor
Laboratoire de Météorologie Dynamique – IPSL, Ecole Normale Supérieure — PSL, Paris, France
Interests: climate sciences; physical oceanography; ocean changes and impact on climate at regional and global scale; air–sea exchanges and changes; shaping of the ocean dynamics and climate change on marine ecosystems

Special Issue Information

Dear Colleagues,

This Special Issue will concentrate on nonlinear ocean dynamics (in particular at mesoscale and sub-mesoscale) and on the mechanisms inherent to these nonlinearities, in particular, flow instabilities and interactions of coherent structures.

Theoretical contributions and process studies lie at the core of this topic. Studies based on observations or on more general numerical modeling are welcome, provided they concentrate on the mechanisms of nonlinear ocean dynamics. Purely descriptive regional studies should be avoided. Mechanisms involving coupled atmospheric and oceanic flows will be considered.

Prof. Dr. Xavier Carton
Prof. Dr. Sabrina Speich
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. Fluids 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 1800 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

  • process studies (theory and modeling)
  • mesoscale and sub-mesoscale oceanic structures
  • nonlinear dynamics
  • flow characterization, stability, and evolution
  • oceanic eddies and filaments
  • eddy interactions (mutual and with a surrounding)

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Published Papers (5 papers)

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Research

15 pages, 7053 KiB  
Article
Simulation of Winter Deep Slope Convection in Peter the Great Bay (Japan Sea)
by Sergey V. Prants, Pavel A. Fayman, Maxim V. Budyansky and Michael Yu. Uleysky
Fluids 2022, 7(4), 134; https://doi.org/10.3390/fluids7040134 - 12 Apr 2022
Cited by 8 | Viewed by 2424
Abstract
In wintertime, a high-density water forms on the shallow shelf in the vast Peter the Great Bay (Japan Sea). The steep continental slope with deep canyons and cold winters in the area provide suitable conditions for the implementation of deep slope convection—an important [...] Read more.
In wintertime, a high-density water forms on the shallow shelf in the vast Peter the Great Bay (Japan Sea). The steep continental slope with deep canyons and cold winters in the area provide suitable conditions for the implementation of deep slope convection—an important phenomenon in the formation of intermediate and bottom waters that occurs at a few locations in some semi-enclosed seas, including the Japan Sea. The descent of dense shelf water down the continental slope of Peter the Great Bay usually occurs to 1000–1200 m; however, in anomalously cold winters, it has been observed at greater than 2000 m depth supporting renewal and deep ventilation of intermediate and bottom waters in the Japan Sea. The deep slope convection is a rare episodic phenomenon with durations ranging from several hours to several days, that has never been simulated in Peter the Great Bay with a realistic numerical model of circulation. We apply the Regional Ocean Modeling System (ROMS) with a 600 m horizontal resolution to simulate the deep slope convection in the anomalously cold winter of 2001 when it has been observed in cruises. The results are compared with propagation of deep shelf water in the regular winter of 2010 when hydrological characteristics of this water were recorded by a profiler “Aqualog” installed at the shelf break. Using Lagrangian methods, we track and analyze the formation of dense shelf water, its advection to the slope edge in the bottom layer and descent down the slope. Special attention is payed to the role of coastal eddies arising due to a symmetric instability. These eddies promote the cross-shelf transport of the dense shelf water towards the continental slope edge. The simulation results are compared with rare observations of the deep slope convection in Peter the Great Bay. Full article
(This article belongs to the Special Issue Instabilities and Nonlinear Dynamics in Oceanic Flows)
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18 pages, 2113 KiB  
Article
Volume Transport by a 3D Quasigeostrophic Heton
by Adhithiya Sivakumar and Jeffrey B. Weiss
Fluids 2022, 7(3), 92; https://doi.org/10.3390/fluids7030092 - 2 Mar 2022
Viewed by 2546
Abstract
Oceanic flows self-organize into coherent vortices, which strongly influence their transport and mixing properties. Counter-rotating vortex pairs can travel long distances and carry trapped fluid as they move. These structures are often modeled as hetons, viz. counter-rotating quasigeostrophic point vortex pairs with equal [...] Read more.
Oceanic flows self-organize into coherent vortices, which strongly influence their transport and mixing properties. Counter-rotating vortex pairs can travel long distances and carry trapped fluid as they move. These structures are often modeled as hetons, viz. counter-rotating quasigeostrophic point vortex pairs with equal circulations. Here, we investigate the structure of the transport induced by a single three-dimensional heton. The transport is determined by the Hamiltonian structure of the velocity field induced by the heton’s component vortices. The dynamics display a sequence of bifurcations as one moves through the heton-induced velocity field in height. These bifurcations create and destroy unstable fixed points whose associated invariant manifolds bound the trapped volume. Heton configurations fall into three categories. Vertically aligned hetons, which are parallel to the vertical axis and have zero horizontal separation, do not move and do not transport fluid. Horizontally aligned hetons, which lie on the horizontal plane and have zero vertical separation, have a single parameter, the horizontal vortex half-separation Y, and simple scaling shows the dimensional trapped volume scales as Y3. Tilted hetons are described by two parameters, Y and the vertical vortex half-separation Z, rendering the scaling analysis more complex. A scaling theory is developed for the trapped volume of tilted hetons, showing that it scales as Z4/Y for large Z. Numerical calculations illustrate the structure of the trapped volume and verify the scaling theory. Full article
(This article belongs to the Special Issue Instabilities and Nonlinear Dynamics in Oceanic Flows)
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17 pages, 1075 KiB  
Article
Linear Non-Modal Growth of Planar Perturbations in a Layered Couette Flow
by Emmanouil G. Iliakis and Nikolaos A. Bakas
Fluids 2021, 6(12), 442; https://doi.org/10.3390/fluids6120442 - 8 Dec 2021
Cited by 1 | Viewed by 2795
Abstract
Layered flows that are commonly observed in stratified turbulence are susceptible to the Taylor–Caulfield Instability. While the modal stability properties of layered shear flows have been examined, the non-modal growth of perturbations has not been investigated. In this work, the tools of Generalized [...] Read more.
Layered flows that are commonly observed in stratified turbulence are susceptible to the Taylor–Caulfield Instability. While the modal stability properties of layered shear flows have been examined, the non-modal growth of perturbations has not been investigated. In this work, the tools of Generalized Stability Theory are utilized to study linear transient growth within a finite time interval of two-dimensional perturbations in an inviscid, three-layer constant shear flow under the Boussinesq approximation. It is found that, for low optimization times, small-scale perturbations utilize the Orr mechanism and achieve growth equal to that in the case of an unstratified flow. For larger optimization times, transient growth is much larger compared to growth for an unstratified flow as the Kelvin–Orr waves comprising the continuous spectrum of the dynamical operator and the gravity edge-waves comprising the discrete spectrum interact synergistically. Maximum growth is obtained for perturbations with scales within the region of instability, but significant growth is maintained for modally stable perturbations as well. For perturbations with scales within the unstable region, the unstable normal modes are excited at high amplitude by their bi-orthogonals. For perturbations with modally stable scales, the Orr mechanism is utilized to excite at high amplitude neutral propagating waves resembling the neutral Taylor–Caulfield modes. Full article
(This article belongs to the Special Issue Instabilities and Nonlinear Dynamics in Oceanic Flows)
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25 pages, 2079 KiB  
Article
Instability of Lenticular Vortices: Results from Laboratory Experiments, Linear Stability Analysis and Numerical Simulations
by Noé Lahaye, Alexandre Paci and Stefan G. Llewellyn Smith
Fluids 2021, 6(11), 380; https://doi.org/10.3390/fluids6110380 - 23 Oct 2021
Viewed by 1560
Abstract
The instability of surface lenticular vortices is investigated using a comprehensive suite of laboratory experiments combined with numerical linear stability analysis as well as nonlinear numerical simulations in a two-layer Rotating Shallow Water model. The development of instabilities is discussed and compared between [...] Read more.
The instability of surface lenticular vortices is investigated using a comprehensive suite of laboratory experiments combined with numerical linear stability analysis as well as nonlinear numerical simulations in a two-layer Rotating Shallow Water model. The development of instabilities is discussed and compared between the different methods. The linear stability analysis allows for a clear description of the origin of the instability observed in both the laboratory experiments and numerical simulations. While global qualitative agreement is found, some discrepancies are observed and discussed. Our study highlights that the sensitivity of the instability outcome is related to the initial condition and the lower-layer flow. The inhibition or even suppression of some unstable modes may be explained in terms of the lower-layer potential vorticity profile. Full article
(This article belongs to the Special Issue Instabilities and Nonlinear Dynamics in Oceanic Flows)
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13 pages, 3998 KiB  
Article
The Finite Size Lyapunov Exponent and the Finite Amplitude Growth Rate
by Thomas Meunier and J. H. LaCasce
Fluids 2021, 6(10), 348; https://doi.org/10.3390/fluids6100348 - 2 Oct 2021
Cited by 3 | Viewed by 3268
Abstract
The finite size Lyapunov exponent (FSLE) has been used extensively since the late 1990s to diagnose turbulent regimes from Lagrangian experiments and to detect Lagrangian coherent structures in geophysical flows and two-dimensional turbulence. Historically, the FSLE was defined in terms of its computational [...] Read more.
The finite size Lyapunov exponent (FSLE) has been used extensively since the late 1990s to diagnose turbulent regimes from Lagrangian experiments and to detect Lagrangian coherent structures in geophysical flows and two-dimensional turbulence. Historically, the FSLE was defined in terms of its computational method rather than via a mathematical formulation, and the behavior of the FSLE in the turbulent inertial ranges is based primarily on scaling arguments. Here, we propose an exact definition of the FSLE based on conditional averaging of the finite amplitude growth rate (FAGR) of the particle pair separation. With this new definition, we show that the FSLE is a close proxy for the inverse structural time, a concept introduced a decade before the FSLE. The (in)dependence of the FSLE on initial conditions is also discussed, as well as the links between the FAGR and other relevant Lagrangian metrics, such as the finite time Lyapunov exponent and the second-order velocity structure function. Full article
(This article belongs to the Special Issue Instabilities and Nonlinear Dynamics in Oceanic Flows)
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