Numerical simulation of supercritical trapped internal waves over topography

Soontiens, Nancy; Subich, Christopher; Stastna, Marek

doi:10.1063/1.3521532

Cited by 13 publications

(36 citation statements)

References 22 publications

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“…Soontiens et al 25 also noted that in ISWs with trapped cores the density field was typically more stable than the velocity field. They presented a model for trapped core waves in the presence of a background shear flow.…”

Section: B Unsteady Behaviormentioning

confidence: 95%

“…Without exception, all steady state models of ISWs with trapped cores in the literature, that are evolved through time-dependent simulations result in weakly unstable or unstable waves. 18,19,[23][24][25] In the laboratory, both Grue et al 13 and Carr et al 14 have observed unstable ISWs with trapped cores. Grue et al 13 observed trapped cores in which small vortices took place in the leading part of the wave.…”

Section: Introductionmentioning

confidence: 99%

“…As well as in the ocean, 8,9 waves of this type have been observed in the atmosphere, 10-12 the laboratory, 13,14 and in theoretical studies. [15][16][17][18][19][20][21][22][23][24][25] Despite this a physically consistent theory for waves with trapped cores remains elusive and there is debate in the literature as to how ISWs with trapped cores should be modelled.…”

Section: Introductionmentioning

confidence: 99%

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Instability in internal solitary waves with trapped cores

2012

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A numerical method that employs a combination of contour advection and pseudospectral techniques is used to investigate instability in internal solitary waves with trapped cores. A three-layer configuration for the background stratification in which the top two layers are linearly stratified and the lower layer is homogeneous is considered throughout. The strength of the stratification in the very top layer is chosen to be sufficient so that waves of depression with trapped cores can be generated. The flow is assumed to satisfy the Dubriel-Jacotin-Long equation both inside and outside of the core region. The Brunt-Väisälä frequency is modelled such that it varies from a constant value outside of the core to zero inside the core over a sharp but continuous transition length. This results in a stagnant core in which the vorticity is zero and the density is homogeneous and approximately equal to that at the core boundary. The time dependent simulations show that instability occurs on the boundary of the core.The instability takes the form of Kelvin-Helmholtz billows. If the instability in the vorticity field is energetic enough disturbance in the buoyancy field is also seen and fluid 1 exchange takes place across the core boundary. Occurrence of the Kelvin-Helmholtz billows is attributed to the sharp change in the vorticity field at the boundary between the core and the pycnocline. The numerical scheme is not limited by small Richardson number unlike the other alternatives currently available in the literature which appear to be.

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Section: B Unsteady Behaviormentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Instability in internal solitary waves with trapped cores

2012

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“…Soontiens et al . studied trapped internal waves over isolated topography in the presence of a background shear.…”

Section: Introductionmentioning

confidence: 99%

Rotational waves generated by current‐topography interaction

2019

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We study nonlinear free‐surface rotational waves generated through the interaction of a vertically sheared current with a topography. Equivalently, the waves may be generated by a pressure distribution along the free surface. A forced Korteweg–de Vries equation (fKdV) is deduced incorporating these features. The weakly nonlinear, weakly dispersive reduced model is valid for small amplitude topographies. To study the effect of gradually increasing the topography amplitude, the free surface Euler equations are formulated in the presence of a variable depth and a sheared current of constant vorticity. Under constant vorticity, the harmonic velocity component is formulated in a simplified canonical domain, through the use of a conformal mapping which flattens both the free surface as well as the bottom topography. Critical, supercritical, and subcritical Froude number regimes are considered, while the bottom amplitude is gradually increased in both the irrotational and rotational wave regimes. Solutions to the fKdV model are compared to those from the Euler equations. We show that for rotational waves the critical Froude number is shifted away from 1. New stationary solutions are found and their stability tested numerically.

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“…This condition is satisfied when U 0 > c j , where c j is the conjugate flow speed. 27,28 One subcritical case for which upstream propagating modes are permitted is also considered. In this case, the background flow satisfies c l w < U 0 < c j , where c l w is the linear long wave speed.…”

Section: Methodsmentioning

confidence: 99%

Topographically generated internal waves and boundary layer instabilities

2015

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Flow over topography has been shown to generate finite amplitude internal waves upstream, over the topography and downstream. Such waves can interact with the viscous bottom boundary layer to produce vigorous instabilities. However, the strength and size of such instabilities depends on whether viscosity significantly modifies the wave generation process, which is usually treated using inviscid theory in the literature. In this work, we contrast cases in which boundary layer separation profoundly alters the wave generation process and cases for which the generated internal waves largely match inviscid theory. All results are generated using a numerical model that simulates stratified flow over topography. Several issues with using a wave-based Reynolds number to describe boundary layer properties are discussed by comparing simulations with modifications to the domain depth, background velocity, and viscosity. For hill-like topography, three-dimensional aspects of the instabilities are also discussed. Decreasing the Reynolds number by a factor of four (by increasing the viscosity), while leaving the primary two-dimensional instabilities largely unchanged, drastically affects their three-dimensionalization. Several cases at the laboratory scale with a depth of 1 m are examined in both two and three dimensions and a subset of the cases is scaled up to a field scale 10-m deep fluid while maintaining similar values for the background current and viscosity. At this scale, increasing the viscosity by an order of magnitude does not significantly change the wave properties but does alter the wave’s interaction with the bottom boundary layer through the bottom shear stress. Finally, two subcritical cases for which disturbances are able to propagate upstream showcase a set of instabilities forming on the upstream slope of the elevated topography. The time scale over which these instabilities develop is related to but distinct from the advective time scale of the waves. At a non-dimensional time when instabilities have formed in the field scale case, no instabilities have yet formed in the lab scale case.

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Numerical simulation of supercritical trapped internal waves over topography

Cited by 13 publications

References 22 publications

Instability in internal solitary waves with trapped cores

Instability in internal solitary waves with trapped cores

Rotational waves generated by current‐topography interaction

Topographically generated internal waves and boundary layer instabilities

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