Instability and cross-boundary-layer transport by shoaling internal waves over realistic slopes

Xu, Chengzhu; Stastna, Marek

doi:10.1017/jfm.2020.389

Cited by 16 publications

(23 citation statements)

References 18 publications

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“…This dynamics is in good agreement with fission described in past studies (e.g. Aghsaee et al 2010;Xu & Stastna 2020).…”

Section: Fissionsupporting

confidence: 92%

“…Although these same geophysically realistic slopes are typically difficult to replicate in the laboratory, or in numerical models, laboratory experiments in an 18 m wave tank identified the formation of boluses propagating up-slope from the evolution of periodic waves propagating over gentle slopes (Wallace & Wilkinson 1988). Additionally, Xu & Stastna (2020) recently identified the role of boundary layer instability in fissioning waves propagating over realistic slopes in a high resolution model. When shoaling, energy transported by the ISWs has been observed to dissipate at rates at least 100 times background levels (Lien et al 2005), and is used to enhance turbulent mixing (Moum et al 2003).…”

Section: Introductionmentioning

confidence: 99%

“…Michallet & Ivey 1999;Boegman, Ivey & Imberger 2005;Sutherland, Barrett & Ivey 2013), and numerical models (e.g. Aghsaee, Boegman & Lamb 2010;Arthur & Fringer 2014;Nakayama et al 2019;Xu & Stastna 2020). These studies have created a coherent classification scheme for the key breaking processes, namely plunging, collapsing, surging and fission, as the waves shoal (Boegman et al 2005;Aghsaee et al 2010;Sutherland et al 2013;Lamb 2014;Nakayama et al 2019).…”

Section: Introductionmentioning

confidence: 99%

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Stratification effects on shoaling internal solitary waves

et al. 2021

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This combined numerical/laboratory study investigates the effect of stratification form on the shoaling characteristics of internal solitary waves propagating over a smooth, linear topographic slope. 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). It is found that the form of stratification affects the breaking type associated with the shoaling wave. In the thin tanh stratification, good agreement is seen with past studies. Waves over the shallowest slopes undergo fission. Over steeper slopes, the breaking type changes from surging, through collapsing to plunging with increasing wave steepness $A_w/L_w$ for a given topographic slope, where $A_w$ and $L_w$ are incident wave amplitude and wavelength, respectively. In the surface stratification regime, the breaking classification differs from the thin tanh stratification. Plunging dynamics is inhibited by the density gradient throughout the upper layer, instead collapsing-type breakers form for the equivalent location in parameter space in the thin tanh stratification. In the broad tanh profile regime, plunging dynamics is likewise inhibited and the near-bottom density gradient prevents the collapsing dynamics. Instead, all waves either fission or form surging breakers. As wave steepness in the broad tanh stratification increases, the bolus formed by surging exhibits evidence of Kelvin–Helmholtz instabilities on its upper boundary. In both two- and three-dimensional simulations, billow size grows with increasing wave steepness, dynamics not previously observed in the literature.

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“…This dynamics is in good agreement with fission described in past studies (e.g. Aghsaee et al 2010;Xu & Stastna 2020).…”

Section: Fissionsupporting

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stratification effects on shoaling internal solitary waves

et al. 2021

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“…The boundary conditions are free slip for velocity and no flux for temperature and the model achieves spectral accuracy. Previous studies have used SPINS to simulate the formation and propagation of gravity currents in numerous circumstances; Xu, Subich & Stastna (2016) and Xu & Stastna (2020) being two recent examples. The length of the domain is m and the height is m. The number of grid points in the horizontal and vertical directions are and respectively, and are uniformly spaced.…”

Section: Methodsmentioning

confidence: 99%

Asymmetries in gravity currents attributed to the nonlinear equation of state

et al. 2021

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“…For example, Zhang et al (2012) established a variable water depth internal wave numerical model in a continuously stratified fluid system based on the Euler equation. Xu and Stastna (2020) used the viscid incompressible Boussinesq model to study cross-boundary-layer transport (Boegman and Stastna, 2019) by the fissioning process of shoaling ISWs. Lamb (1994) established a non-hydrostatic model, using a second-order projection method developed by Bell and Marcus (1992), which is used for internal wave research including boundary layer instability (Aghsaee et al, 2012), reflection (Lamb, 2009), and the interaction of the tides with the topography (Lamb, 2007;Aghsaee et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

ISWFoam: A numerical model for internal solitary wave simulation in continuously stratified fluids

Zhang

Chen

2021

Preprint

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Abstract. A numerical model, ISWFoam, for simulating internal solitary waves (ISWs) in continuously stratified, incompressible, viscous fluids is developed based on a fully three-dimensional (3D) Navier-Stokes equation using the open source code OpenFOAM. This model combines the density transport equation with the Reynolds-averaged Navier-Stokes equation with the Coriolis force, and the model discrete equation adopts the finite volume method. The k-ω SST turbulence model has also been modified accordingly to the variable density field. ISWFoam provides two initial wave generation methods to generate an ISW in continuously stratified fluids, including solving the weakly nonlinear models of the extended Korteweg–de Vries (eKdV) equation and the fully nonlinear models of the Dubreil-Jacotin-Long (DJL) equation. Grid independence tests for ISWFoam are performed, considering the accuracy and computing efficiency, the appropriate grid size of the ISW simulation is recommended to be one-one hundred and fiftieth of the characteristic length and one-twenty fifth of the ISW amplitude. Model verifications are conducted through comparisons between the simulated and experimental data for ISW propagation examples over a flat bottom section, including laboratory scale and actual ocean scale, a submerged triangular ridge, a Gaussian ridge and slope. The laboratory test results, including the ISW profile, wave breaking location, ISW arrival time, and the spatial and temporal changes in the mixture region, are well reproduced by ISWFoam. The ISWFoam model with unstructured grids and local mesh refinement can accurately simulate the generation and evolution of ISWs, the ISW breaking phenomenon and the interaction between ISWs and complex structures and topography.

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Instability and cross-boundary-layer transport by shoaling internal waves over realistic slopes

Cited by 16 publications

References 18 publications

Stratification effects on shoaling internal solitary waves

Stratification effects on shoaling internal solitary waves

Asymmetries in gravity currents attributed to the nonlinear equation of state

ISWFoam: A numerical model for internal solitary wave simulation in continuously stratified fluids

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