Spontaneous instability in internal solitary-like waves

Xu, Chengzhu; Stastna, Marek; Deepwell, David

doi:10.1103/physrevfluids.4.014805

Cited by 19 publications

(15 citation statements)

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“…Grid doubling/halving experiments were performed to ensure that the numerical results were robust. The details of the physics of the dual pycnocline and collision cases will be discussed in future publications, while the details of the spontaneous instability case may be found in [29]. As the focus here is on the data analysis method presented, all data sets throughout this manuscript are presented in terms of grid points, time output number, and numeric field values.…”

Section: Resultsmentioning

confidence: 99%

“…The first data set is the spontaneous shear instability of a very large amplitude internal solitary wave, studied in detail in [29], following previous related work [30], [31]. Here the flow is initialized from a solution to the Dubreil–Jacotin–Long (DJL) equation, which is formally equivalent to the stratified Euler equations.…”

Section: Resultsmentioning

confidence: 99%

“…The instability grows and eventually exits the wave. Detailed discussion, including the effects of three-dimensionalization can be found in [29]. See the top four panels of Fig 5 for a visual representation of the density field’s evolution in this case.…”

Section: Resultsmentioning

confidence: 99%

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Feature identification in time-indexed model output

Shaw

Stastna

2019

PLoS ONE

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We present a method for identifying features (time periods of interest) in data sets consisting of time-indexed model output. The method is used as a diagnostic to quickly focus the attention on a subset of the data before further analysis methods are applied. Mathematically, the infinity norm errors of empirical orthogonal function (EOF) reconstructions are calculated for each time output. The result is an EOF reconstruction error map which clearly identifies features as changes in the error structure over time. The ubiquity of EOF-type methods in a wide range of disciplines reduces barriers to comprehension and implementation of the method. We apply the error map method to three different Computational Fluid Dynamics (CFD) data sets as examples: the development of a spontaneous instability in a large amplitude internal solitary wave, an internal wave interacting with a density profile change, and the collision of two waves of different vertical mode. In all cases the EOF error map method identifies relevant features which are worthy of further study.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Feature identification in time-indexed model output

Shaw

Stastna

2019

PLoS ONE

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“…billows in the case of shear instability (Xu et al. 2019), or a separation bubble beneath shoaling internal waves Boegman & Stastna 2019). In contrast to these instabilities, which typically have their vorticity oriented in a plane with constant density, the vorticity here is primarily directed normal to isopycnals.…”

Section: Discussionmentioning

confidence: 99%

“…Because ISWs generate strong currents throughout the water column, interaction with side boundaries may lead to a coherent response from surface to seabed. This can be contrasted with the more commonly studied situation of cross-BBL transport, in which an adjustment occurs only at depth (Boegman & Stastna 2019) or at shear layers (Xu, Stastna & Deepwell 2019). The only possible exception is the case of ‘local hydraulics’ observed by Harnanan, Stastna & Soontiens (2017) for instabilities below an ISW of elevation within a secondary, near-bottom stratified layer.…”

Section: Introductionmentioning

confidence: 99%

Vortex generation due to internal solitary wave propagation past a sidewall constriction

et al. 2021

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Dense pulses formed from fissioning internal waves

2022

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Cold pulses generated by the fission of internal solitary waves over gentle slopes are an important source of nutrients and relief from excess heat to benthic ecosystems. This numerical study investigates the effect of stratification form on pulses produced by fission of internal solitary waves propagating over a smooth, gentle, linear topographic slope in 2D simulations. Three stratification types are investigated, namely (i) thin tanh (homogeneous upper and lower layers separated by a thin pycnocline), (ii) surface stratification (linearly stratified layer overlaying a homogeneous lower layer) and (iii) broad tanh (continuous density gradient throughout the water column). Incident wave amplitude was varied. In the thin tanh stratification, good agreement is seen with past studies, whilst the dynamics observed in the surface stratification are very similar to those in the thin tanh stratification. However, in the broad tanh stratification, due to the different form of incident waves, the fission dynamics differ, but produce pulses similar in form to those produced by fission in the other stratifications. Pulse amplitude, wavelength and propagation velocity are found to strongly depend on incident wave amplitude, and each degenerate linearly as the pulse propagates upslope.

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Spontaneous instability in internal solitary-like waves

Cited by 19 publications

References 32 publications

Feature identification in time-indexed model output

Feature identification in time-indexed model output

Vortex generation due to internal solitary wave propagation past a sidewall constriction

Dense pulses formed from fissioning internal waves

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