Instability in internal solitary waves with trapped cores

Carr, Magda; King, Stuart; Dritschel, David G.

doi:10.1063/1.3673612

Cited by 15 publications

(11 citation statements)

References 40 publications

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“…Mode-1 waves have a considerably larger extent and their cores can range from nearly quiescent to highly turbulent (Carr et al, 2012;Helfrich and White, 2010;Lamb and Wilkie, 2004;Michallet and Ivey, 1999). Our simulations have the closest analogy with those of Carr et al (2012), who considered cores with weak instabilities, though it is interesting that we found significant, if not dominant, three-dimensionalization, while all past simulations, to our best knowledge, have been two dimensional.…”

Section: Discussionsupporting

confidence: 51%

Analysis of asymmetries in propagating mode-2 waves

Olsthoorn

Baglaenko

Stastna

2013

Nonlin. Processes Geophys.

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Abstract.Using numerical simulations performed with a pseudo-spectral incompressible Navier-Stokes solver, we describe the asymmetries that arise in the recirculating core of mode-2 internal, solitary-like waves. The waves are generated in a manner consistent with many laboratory studies, namely via the collapse of a region of mixed fluid. Analysis of the simulations reveals that asymmetries across both the wave crest and the pycnocline centre develop in the spatial distribution of density, kinetic energy and a passive tracer transported by the mode-2 waves. The simulations are extended to three-dimensions to allow for the formation of spanwise instabilities. We find that three-dimensionalization modifies the structure and energetics of the core, but that the majority of the results obtained from two dimensional simulations remain valid. Taken together, our simulations demonstrate that the cores of solitary-like mode-2 waves are different then their counterparts for mode-1 waves and that their accurate characterization on both lab and field scales should account for the core asymmetry across the pycnocline centre.

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Section: Discussionsupporting

confidence: 51%

Analysis of asymmetries in propagating mode-2 waves

Olsthoorn

Baglaenko

Stastna

2013

Nonlin. Processes Geophys.

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“…While the majority of past work has examined waves of depression (e.g. Lamb, 2002Lamb, , 2003Aghsaee et al, 2012;Carr et al, 2012) as they are commonly observed in oceans and deep lakes, waves of elevation, which occur when the pycnocline is below the mid-depth, are more typical of shallow waters such as near-coastal regions (e.g. Klymak and Moum, 2003;Scotti and Pineda, 2004).…”

Section: Chapter 3 Model Setup and Two-dimensional Simulationsmentioning

confidence: 99%

“…Two-dimensional numerical simulations suggest that shear instability (Helfrich and White, 2010;Carr et al, 2012) and boundary layer instability (Diamessis and Redekopp, 2005;Stastna and Lamb, 2008) can occur in both waves of elevation and depression. The shear instability occurs along the edge of the cores and takes the form of Kelvin-Helmholtz billows, leading to fluid exchange between the cores and the ambient flow.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulations of shoaling internal solitary waves of elevation

Subich

Stastna

2016

Physics of Fluids

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We present high-resolution, two-and three-dimensional direct numerical simulations of laboratory-scale, fully nonlinear internal solitary waves of elevation shoaling onto and over a small-amplitude shelf. The three-dimensional, mapped coordinate, spectral collocation method used for the simulations allows for accurate modelling of both the shoaling waves and the bottom boundary layer. We focus on wave-induced instabilities during the shoaling and de-shoaling processes. The shoaling of the waves is characterized by the formation of a quasi-trapped core which undergoes a spatially growing stratified shear instability at its edge and a lobe-cleft instability in its nose. Both of these instabilities develop and three-dimensionalize concurrently, leading to strong bottom shear stress. During the deshoaling process, the core breaks up and ejects fluid that forms a vortex-rich region near the down-sloping portion of the shelf. The flow in this region is highly turbulent and the bottom shear stress is extremely strong. Experiments with a corrugated bottom boundary are also performed. Boundary layer separation is found inside each of the corrugations during the wave's shoaling process. Our analyses suggest that all of these wave-induced instabilities can lead to enhanced turbulence in the water column and increased shear stress on the bottom boundary. Through the generation and evolution of these instabilities, the shoaling and de-shoaling cycles of internal solitary waves of elevation are likely to provide systematic mechanisms for material mixing and sediment resuspension. These mechanisms have significant environmental implications on the near-coastal regions of the world's oceans.iii

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“…Convectively unstable solutions develop trapped cores (Stastna & Lamb 2002;Helfrich & White 2010;Carr et al 2012;Luzzatto-Fegiz & Helfrich 2014). The trapped core solutions are distinguished by regions of closed streamlines with gravitationally unstable density distributions.…”

Section: Solitary Waves Solutionsmentioning

confidence: 99%

Internal hydraulic jumps in two-layer flows with upstream shear

Ogden¹,

Helfrich

2016

J. Fluid Mech.

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Internal hydraulic jumps in flows with upstream shear are investigated using two-layer shock-joining theories and numerical solutions of the Navier-Stokes equations. The role of upstream shear has not previously been thoroughly investigated, although it is important in many oceanographic situations, including exchange flows. The full solution spaces of several two-layer theories, distinguished by how dissipation is distributed between the layers, with upstream shear are found, and the physically allowable solution space is identified. These two-layer theories are then evaluated using more realistic numerical simulations that have continuous density and velocity profiles and permit turbulence and mixing. Two-dimensional numerical simulations show that none of the two-layer theories reliably predicts the relation between jump height and speed over the full range of allowable solutions. The numerical simulations also show that different qualitative types of jumps can occur, including undular bores, energy-conserving conjugate state transitions, smooth front jumps with trailing turbulence, and overturning turbulent jumps. Simulation results are used to investigate mixing, which increases with jump height and upstream shear. A few three-dimensional simulations results were undertaken and are in quantitative agreement with the two-dimensional simulations.

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Instability in internal solitary waves with trapped cores

Cited by 15 publications

References 40 publications

Analysis of asymmetries in propagating mode-2 waves

Analysis of asymmetries in propagating mode-2 waves

Numerical simulations of shoaling internal solitary waves of elevation

Internal hydraulic jumps in two-layer flows with upstream shear

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