Numerical simulations of the shear instability and subsequent degeneration of basin scale internal standing waves

Abstract Three-dimensional dynamics of thermohaline staircases are investigated using a series of basin-scale staircase-resolving numerical simulations. The computational domain and forcing fields are chosen to reflect the size and structure of the North Atlantic subtropical thermocline. Salt-finger transport is parameterized using the flux-gradient formulation based on a suite of recent direct numerical simulations. Analysis of the spontaneous generation of thermohaline staircases suggests that thermohaline layering is a product of the gamma instability, associated with the variation of the flux ratio with the density ratio . After their formation, numerical staircases undergo a series of merging events, which systematically increase the size of layers. Ultimately, the system evolves into a steady equilibrium state with pronounced layers 20–50 m thick. The size of the region occupied by thermohaline staircases is controlled by the competition between turbulent mixing and double diffusion. Assuming, in accordance with observations, that staircases form when the density ratio is less than the critical value of , the authors arrive at an indirect estimate of the characteristic turbulent diffusivity in the subtropical thermocline.

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Numerical Analysis of Modified Bed-profiles due to the Presence of a Rubble Mound Breakwater using Physics-Based Morphology Model[SeoulFoam]

Korea Society of Coastal Disaster Prevention ◽

10.20481/kscdp.2021.8.3.151 ◽

2021 ◽

Vol 8 (3) ◽

pp. 151-163

Author(s):

Yong Jun Cho

Keyword(s):

Numerical Simulations ◽

Wave Length ◽

Standing Waves ◽

Sea Waves ◽

Incoming Wave ◽

Sand Waves ◽

Morphology Model ◽

Scouring Depth ◽

Rubble Mound ◽

The Many

Among the many scouring-protection works near a rubble mound breakwater, stacking armoring rocks in multiple or single layers are most popular. The rationale of these scouring-protection works is based on the Equilibrium regime or the maximum scouring depth. However, considering natural beaches, which constantly change their shape according to sea waves conditions, the equilibrium regime or the maximum scouring depth mentioned above seems to foot on the fragile physical background. In this study, in order to test the above hypothesis, numerical simulations were carried out on the partial reflection from the slopes of rubble mound breakwater, and its ensuing standing waves formed in the front seas of a breakwater, the change in the bed profiles due to the formation of standing waves, and scouring depth at the base of a rubble mound breakwater. In doing so, numerical simulations were implemented using OlaFoam, an OpenFoam-based toolbox, and SeoulFoam (Cho, 2020), a physics-based morphology model. Numerical results show that the wave length of sand waves is closely linked with the incoming wave period, while amplitudes of sand waves are determined by incoming wave height. Moreover, the seabed profiles underwent significant changes due to the presence of a rubble mound breakwater. It was shown that the size of sand waves increased when compared before the installation, and the shape of sand waves is getting skewed toward the shore direction. It was also shown that as exposure time to standing waves increased, the amplitude of sand waves also increased, and the scouring depth near the base of a breakwater increased. These results are contrary to the Equilibrium regime, and the scouring prevention works based on the stacking of armoring rocks should be re-evaluated.

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Thermal Buffering by Basement Rocks in Numerical Simulations of Basin-Scale Heat Flow: ABSTRACT

AAPG Bulletin ◽

10.1306/522b374f-1727-11d7-8645000102c1865d ◽

1996 ◽

Vol 80 ◽

Author(s):

Jeffrey A. Nunn, Guichang Lin, Davi

Keyword(s):

Heat Flow ◽

Numerical Simulations ◽

Basement Rocks ◽

Basin Scale ◽

Thermal Buffering

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Laboratory experiments and simulations for solitary internal waves with trapped cores

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.501 ◽

2014 ◽

Vol 757 ◽

pp. 354-380 ◽

Cited By ~ 13

Author(s):

Paolo Luzzatto-Fegiz ◽

Karl R. Helfrich

Keyword(s):

Free Surface ◽

Numerical Simulations ◽

Internal Waves ◽

Number Fields ◽

Rate Of Change ◽

Shear Instability ◽

Homogeneous Layer ◽

Uniform Density ◽

The Core ◽

Solitary Internal Waves

AbstractWe perform simultaneous coplanar measurements of velocity and density in solitary internal waves with trapped cores, as well as viscous numerical simulations. Our set-up comprises a thin stratified layer (approximately 15 % of the overall fluid depth) overlaying a deep homogeneous layer. We consider waves propagating near a free surface, as well as near a rigid no-slip lid. In the free-surface case, all trapped-core waves exhibit a strong shear instability. We propose that Marangoni effects are responsible for this instability, and use our velocity measurements to perform quantitative calculations supporting this hypothesis. These surface-tension effects appear to be difficult to avoid at the experimental scale. By contrast, our experiments with a no-slip lid yield robust waves with large cores. In order to consider larger-amplitude waves, we complement our experiments with viscous numerical simulations, employing a longer virtual tank. Where overlap exists, our experiments and simulations are in good agreement. In order to provide a robust definition of the trapped core, we propose bounding it as a Lagrangian coherent structure (instead of using a closed streamline, as has been done traditionally). This construction is less sensitive to small errors in the velocity field, and to small three-dimensional effects. In order to retain only flows near equilibrium, we introduce a steadiness criterion, based on the rate of change of the density in the core. We use this criterion to successfully select within our experiments and simulations a family of quasi-steady robust flows that exhibit good collapse in their properties. The core circulation is small (at most, around 10 % of the baroclinic wave circulation). The core density is essentially uniform; the standard deviation of the density, in the core region, is less than 4 % of the full density range. We also calculate the circulation, kinetic energy and available potential energy of these waves. We find that these results are consistent with predictions from Dubreil-Jacotin–Long theory for waves with a uniform-density irrotational core, except for an offset, which we suggest is associated with viscous effects. Finally, by computing Richardson-number fields, and performing a temporal stability analysis based on the Taylor–Goldstein equation, we show that our results are consistent with empirical stability criteria in the literature.

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Dynamical phenomena induced by bottleneck

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2010.0118 ◽

2010 ◽

Vol 368 (1928) ◽

pp. 4543-4562 ◽

Cited By ~ 4

Author(s):

I. Gasser ◽

B. Werner

Keyword(s):

Numerical Simulations ◽

Nonlinear Equations ◽

Bifurcation Analysis ◽

Complex Dynamics ◽

Standing Waves ◽

Continuation Methods ◽

Traffic Dynamics ◽

Poincaré Maps ◽

Different Types ◽

The Way

We study a microscopic follow-the-leader model on a circle of length L with a bottleneck. Allowing large bottleneck strengths we encounter very interesting traffic dynamics. Different types of waves—travelling and standing waves and combinations of both wave types—are observed. The way to find these phenomena requires a good understanding of the complex dynamics of the underlying (nonlinear) equations. Some of the phenomena, like the ponies-on-a-merry-go-round solutions, are mathematically well known from completely different applications. Mathematically speaking we use Poincaré maps, bifurcation analysis and continuation methods beside numerical simulations.

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Spectral analysis of the transition to turbulence from a dipole in stratified fluid

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.437 ◽

2012 ◽

Vol 713 ◽

pp. 86-108 ◽

Cited By ~ 26

Author(s):

Pierre Augier ◽

Jean-Marc Chomaz ◽

Paul Billant

Keyword(s):

Reynolds Number ◽

Spectral Analysis ◽

Kinetic Energy ◽

Numerical Simulations ◽

Scaling Laws ◽

Stratified Fluid ◽

Shear Instability ◽

Transition To Turbulence ◽

Small Scale ◽

Wide Range

AbstractWe investigate the spectral properties of the turbulence generated during the nonlinear evolution of a Lamb–Chaplygin dipole in a stratified fluid for a high Reynolds number $Re= 28\hspace{0.167em} 000$ and a wide range of horizontal Froude number ${F}_{h} \in [0. 0225~0. 135] $ and buoyancy Reynolds number $\mathscr{R}= Re{{F}_{h} }^{2} \in [14~510] $. The numerical simulations use a weak hyperviscosity and are therefore almost direct numerical simulations (DNS). After the nonlinear development of the zigzag instability, both shear and gravitational instabilities develop and lead to a transition to small scales. A spectral analysis shows that this transition is dominated by two kinds of transfer: first, the shear instability induces a direct non-local transfer toward horizontal wavelengths of the order of the buoyancy scale ${L}_{b} = U/ N$, where $U$ is the characteristic horizontal velocity of the dipole and $N$ the Brunt–Väisälä frequency; second, the destabilization of the Kelvin–Helmholtz billows and the gravitational instability lead to small-scale weakly stratified turbulence. The horizontal spectrum of kinetic energy exhibits a ${{\varepsilon }_{K} }^{2/ 3} { k}_{h}^{\ensuremath{-} 5/ 3} $ power law (where ${k}_{h} $ is the horizontal wavenumber and ${\varepsilon }_{K} $ is the dissipation rate of kinetic energy) from ${k}_{b} = 2\lrm{\pi} / {L}_{b} $ to the dissipative scales, with an energy deficit between the integral scale and ${k}_{b} $ and an excess around ${k}_{b} $. The vertical spectrum of kinetic energy can be expressed as $E({k}_{z} )= {C}_{N} {N}^{2} { k}_{z}^{\ensuremath{-} 3} + C{{\varepsilon }_{K} }^{2/ 3} { k}_{z}^{\ensuremath{-} 5/ 3} $ where ${C}_{N} $ and $C$ are two constants of order unity and ${k}_{z} $ is the vertical wavenumber. It is therefore very steep near the buoyancy scale with an ${N}^{2} { k}_{z}^{\ensuremath{-} 3} $ shape and approaches the ${{\varepsilon }_{K} }^{2/ 3} { k}_{z}^{\ensuremath{-} 5/ 3} $ spectrum for ${k}_{z} \gt {k}_{o} $, ${k}_{o} $ being the Ozmidov wavenumber, which is the cross-over between the two scaling laws. A decomposition of the vertical spectra depending on the horizontal wavenumber value shows that the ${N}^{2} { k}_{z}^{\ensuremath{-} 3} $ spectrum is associated with large horizontal scales $\vert {\mathbi{k}}_{h} \vert \lt {k}_{b} $ and the ${{\varepsilon }_{K} }^{2/ 3} { k}_{z}^{\ensuremath{-} 5/ 3} $ spectrum with the scales $\vert {\mathbi{k}}_{h} \vert \gt {k}_{b} $.

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On the Dynamics of the Slope Current System along the West European Margin. Part II: Analytical Calculations and Numerical Simulations with Seasonal Forcing

Journal of Physical Oceanography ◽

10.1175/2008jpo3745.1 ◽

2008 ◽

Vol 38 (12) ◽

pp. 2619-2638 ◽

Cited By ~ 6

Author(s):

Yann Friocourt ◽

Bruno Blanke ◽

Sybren Drijfhout ◽

Sabrina Speich

Keyword(s):

Numerical Simulations ◽

Wind Stress ◽

Seasonal Changes ◽

Large Scale ◽

Current System ◽

Joint Analysis ◽

Density Structure ◽

Northern Iberian Peninsula ◽

Basin Scale ◽

Slope Currents

Abstract The seasonality of the baroclinic slope current system along the western European margin in the Bay of Biscay and along the northern Iberian Peninsula is investigated in a joint analysis of an analytical model and numerical simulations with various forcings. A distinction is made between local winds and basin-scale winds, in which the effect of the latter is indirectly apparent through the basin-scale density gradients. The slope currents are mainly forced by the large-scale structure of the density field. The analysis indicates significant differences in the behavior of the uppermost slope current and of the deeper currents. At all depths, seasonal variations in the large-scale density structure of the ocean alter the strength of the slope currents but are not able to cause robust, long-lasting reversals. Reversals of the uppermost slope current appear to be caused by changes in the alongshore component of the local wind stress, provided that the opposing forcing from the density structure is weak enough. However, the deeper slope currents are not very much affected by the wind stress, so that flow reversals can be explained neither by the wind nor by seasonal changes in the density structure. A numerical simulation suggests that the reversals of the deeper slope currents are at least partly forced by seasonal changes in the flow upstream of the slope current system. The authors demonstrate that the larger part of these seasonal changes is associated with annual baroclinic Rossby waves caused by the seasonal cycle of the large-scale wind stress over the whole basin.

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Role of overturns in optimal mixing in stratified mixing layers

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.374 ◽

2017 ◽

Vol 826 ◽

pp. 522-552 ◽

Cited By ~ 15

Author(s):

A. Mashayek ◽

C. P. Caulfield ◽

W. R. Peltier

Keyword(s):

Numerical Simulations ◽

Ocean Circulation ◽

Turbulent Mixing ◽

Isotropic Turbulence ◽

Life Cycles ◽

Shear Instability ◽

Mixing Efficiency ◽

Small Scale ◽

Mean Flow

Turbulent mixing plays a major role in enabling the large-scale ocean circulation. The accuracy of mixing rates estimated from observations depends on our understanding of basic fluid mechanical processes underlying the nature of turbulence in a stratified fluid. Several of the key assumptions made in conventional mixing parameterizations have been increasingly scrutinized in recent years, primarily on the basis of adequately high resolution numerical simulations. We add to this evidence by compiling results from a suite of numerical simulations of the turbulence generated through stratified shear instability processes. We study the inherently intermittent and time-dependent nature of wave-induced turbulent life cycles and more specifically the tight coupling between inherently anisotropic scales upon which small-scale isotropic turbulence grows. The anisotropic scales stir and stretch fluid filaments enhancing irreversible diffusive mixing at smaller scales. We show that the characteristics of turbulent mixing depend on the relative time evolution of the Ozmidov length scale $L_{O}$ compared to the so-called Thorpe overturning scale $L_{T}$ which represents the scale containing available potential energy upon which turbulence feeds and grows. We find that when $L_{T}\sim L_{O}$, the mixing is most active and efficient since stirring by the largest overturns becomes ‘optimal’ in the sense that it is not suppressed by ambient stratification. We argue that the high mixing efficiency associated with this phase, along with observations of $L_{O}/L_{T}\sim 1$ in oceanic turbulent patches, together point to the potential for systematically underestimating mixing in the ocean if the role of overturns is neglected. This neglect, arising through the assumption of a clear separation of scales between the background mean flow and small-scale quasi-isotropic turbulence, leads to the exclusion of an highly efficient mixing phase from conventional parameterizations of the vertical transport of density. Such an exclusion may well be significant if the mechanism of shear-induced turbulence is assumed to be representative of at least some turbulent events in the ocean. While our results are based upon simulations of shear instability, we show that they are potentially more generic by making direct comparisons with $L_{T}-L_{O}$ data from ocean and lake observations which represent a much wider range of turbulence-inducing physical processes.

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