Trapped disturbances and finite amplitude downstream wavetrains on the f-plane

Stastna, Marek; Subich, Christopher; Soontiens, Nancy

doi:10.1063/1.4759499

Cited by 4 publications

(3 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[31][32][33][34] One of these steady states includes a downstream recovery jump when the flow upstream of the topography is subcritical but transitions to supercritical as it passes over the topography (i.e., a finite amplitude topography effect). A form of the downstream recovery jump was also observed by Stastna et al 35 in rotating continuously stratified flows. Similar features are presented in this article for nonrotating continuously stratified subcritical flows.…”

Section: And 5 For An Overview)supporting

confidence: 74%

“…Such flows preclude the upstream propagation of both linear and nonlinear waves. However, there has been some suggestion in the literature 32,33,35 that it is possible for a finite amplitude, steady wave train to form in the lee of topography for flows over a hill for inflows that are subcritical away from the hill, but reach supercritical values somewhere over the hill. This subcritical to supercritical transition can lead to a downstream recovery jump (DRJ) and possibly a steady state that, unlike the supercritical cases discussed above, is horizontally asymmetric across the crest of the topography.…”

Section: Subcritical Flowsmentioning

confidence: 99%

See 1 more Smart Citation

Trapped internal waves over topography: Non-Boussinesq effects, symmetry breaking and downstream recovery jumps

2013

Self Cite

View full text Add to dashboard Cite

It is well-known that in certain parameter regimes, the steady flow of a density stratified fluid over topography can yield large amplitude internal waves. We discuss an embedded boundary method to solve the Dubreil-Jacotin-Long (DJL) equation for steady-state, supercritical flows over topography in an inviscid, stratified fluid. The DJL equation is equivalent to the full set of stratified steady Euler equations and thus the waves we compute are exact nonlinear solutions. The numerical method presented yields far better scaling with increase in grid size than other iterative methods that have been used to solve this equation, and this in turn allows for a more thorough exploration of parameter space. For waves under the Boussinesq approximation, we contrast the properties of trapped waves over hill-like and valley-like topography, finding that the symmetry of freely propagating solitary waves when the stratification is reflected across the middepth is not present for trapped waves. We extend the derivation of the DJL equation to the non-Boussinesq case and discuss the effect of the new, non-Boussinesq terms on the structure of the trapped waves, finding that the sharp transition between large and small amplitude waves observed under the Boussinesq approximation is much more gradual when the Boussinesq approximation is relaxed. Finally, we demonstrate the existence of asymmetric steady states over hill-like topography where the flow is subcritical upstream of the topography but transitions to supercritical somewhere over the hill. Waves in this new class of exact solutions are related to so-called downstream recovery jumps predicted on the basis of hydrostatic (shallow water) theories, but when breaking does not occur the recovery jump does not stop propagating downstream and an asymmetric state across the topography maximum is reached for long times.

show abstract

Section: And 5 For An Overview)supporting

confidence: 74%

Section: Subcritical Flowsmentioning

confidence: 99%

Trapped internal waves over topography: Non-Boussinesq effects, symmetry breaking and downstream recovery jumps

2013

Self Cite

View full text Add to dashboard Cite

show abstract

“…Simultaneously, these waves can have secondary instabilities, either in the wave itself or in the bottom boundary layer , which is itself influenced by the presence of boundary topography . The generation of these waves depends greatly on the topography , with long downstream effects possible for even small‐scale topography . Similarly, complex behavior arises when these waves shoal, where wave energy is partially reflected and partially converted into irreversible mixing .…”

Section: Introductionmentioning

confidence: 99%

Simulation of the Navier–Stokes equations in three dimensions with a spectral collocation method

Subich

Lamb

Stastna

2013

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

SUMMARYThis paper describes a nonlinear, three‐dimensional spectral collocation method for the simulation of the incompressible Navier–Stokes equations under the Boussinesq approximation, motivated by geophysical and environmental flows. These flows are driven by the interaction of stratified fluid with topography, which this model accurately accounts for by using a mapped coordinate system. The spectral collocation method is implemented with both a Fourier trigonometric expansion and the Chebyshev polynomials, as appropriate for the domain boundary conditions. The coordinate mapping prohibits the use of existing, fast solution methods that rely on the separation of variables, so a preconditioner based on the approximate solution of a corresponding finite‐difference problem with geometric multigrid is used. The model is parallelized with the Message Passing Interface library, and it runs effectively on shared and distributed‐memory systems. Copyright © 2013 John Wiley & Sons, Ltd.

show abstract

Concluding Thoughts

Stastna

2022

Internal Waves in the Ocean

View full text Add to dashboard Cite

Trapped disturbances and finite amplitude downstream wavetrains on the f-plane

Cited by 4 publications

References 30 publications

Trapped internal waves over topography: Non-Boussinesq effects, symmetry breaking and downstream recovery jumps

Trapped internal waves over topography: Non-Boussinesq effects, symmetry breaking and downstream recovery jumps

Simulation of the Navier–Stokes equations in three dimensions with a spectral collocation method

Concluding Thoughts

Contact Info

Product

Resources

About