The dynamics of breaking internal solitary waves on slopes

Arthur, Robert S.; Fringer, Oliver B.

doi:10.1017/jfm.2014.641

Cited by 84 publications

(78 citation statements)

References 46 publications

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“…This code employs the method of Zang, Street & Koseff (1994), which has been used extensively in the past to study geophysical flows at the laboratory scale (see Venayagamoorthy & Fringer 2007;Chou & Fringer 2010;Arthur & Fringer 2014). The computational set-up used here is based on that of Arthur & Fringer (2014) and is summarized in figure 1(a,b) The wave cases considered in this study in terms of the dimensionality of the simulation, the domain length L, the domain height H, the upper-layer depth h 1 , the lower-layer depth h 2 , the amplitude of the initial half-Gaussian a 0 , the length scale of the initial half-Gaussian L 0 , the bottom slope s, the kinematic viscosity ν, the internal Iribarren number ξ and the breaker type (S = surging, C = collapsing, P = plunging, F = fission).…”

Section: Computational Set-upmentioning

confidence: 99%

“…Grey shading represents a particle plume just offshore of the intersection of the initial pycnocline and the slope, as shown in figure 4. on slopes. Section 2 summarizes the computational set-up, which is based on that of Arthur & Fringer (2014). Using the results of a three-dimensional direct numerical simulation (DNS), § 3 describes cross-shore transport, while § 4 explores the effects of three-dimensional dynamics on transport.…”

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confidence: 99%

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Transport by breaking internal gravity waves on slopes

Arthur

Fringer

2016

J. Fluid Mech.

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We use the results of a direct numerical simulation (DNS) with a particle-tracking model to investigate three-dimensional transport by breaking internal gravity waves on slopes. Onshore transport occurs within an upslope surge of dense fluid after breaking. Offshore transport occurs due to an intrusion of mixed fluid that propagates offshore and resembles an intermediate nepheloid layer (INL). Entrainment of particles into the INL is related to irreversible mixing of the density field during wave breaking. Maximum onshore and offshore transport are calculated as a function of initial particle position, and can be of the order of the initial wave length scale for particles initialized within the breaking region. An effective cross-shore dispersion coefficient is also calculated, and is roughly three orders of magnitude larger than the molecular diffusivity within the breaking region. Particles are transported laterally due to turbulence that develops during wave breaking, and this lateral spreading is quantified with a lateral turbulent diffusivity. Lateral turbulent diffusivity values calculated using particles are elevated by more than one order of magnitude above the molecular diffusivity, and are shown to agree well with turbulent diffusivities estimated using a generic length scale turbulence closure model. Based on a favourable comparison of DNS results with those of a similar two-dimensional case, we use two-dimensional simulations to extend our cross-shore transport results to additional wave amplitude and bathymetric slope conditions.

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Section: Computational Set-upmentioning

confidence: 99%

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confidence: 99%

Transport by breaking internal gravity waves on slopes

Arthur

Fringer

2016

J. Fluid Mech.

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“…The results obtained can be applied to the interaction dynamics of a subsurface trapped core formed within a shoaling largeamplitude internal wave (Lien et al, 2012). Note, however, that the destruction of the KH billows is essentially a 3-D process; therefore, 3-D high-resolution simulation is necessary to predict turbulence development (Arthur and Fringer, 2014;Deepwell and Stastna, 2016). This is the subject of a separate study, whereas the interaction of the colliding waves as a whole can be described in a 2-D setting.…”

Section: Discussionmentioning

confidence: 99%

Head-on collision of internal waves with trapped cores

Maderich

Jung

Terletska

et al. 2017

Nonlin. Processes Geophys.

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Abstract. The dynamics and energetics of a head-on collision of internal solitary waves (ISWs) with trapped cores propagating in a thin pycnocline were studied numerically within the framework of the Navier-Stokes equations for a stratified fluid. The peculiarity of this collision is that it involves trapped masses of a fluid. The interaction of ISWs differs for three classes of ISWs: (i) weakly non-linear waves without trapped cores, (ii) stable strongly non-linear waves with trapped cores, and (iii) shear unstable strongly nonlinear waves. The wave phase shift of the colliding waves with equal amplitude grows as the amplitudes increase for colliding waves of classes (i) and (ii) and remains almost constant for those of class (iii). The excess of the maximum run-up amplitude, normalized by the amplitude of the waves, over the sum of the amplitudes of the equal colliding waves increases almost linearly with increasing amplitude of the interacting waves belonging to classes (i) and (ii); however, it decreases somewhat for those of class (iii). The colliding waves of class (ii) lose fluid trapped by the wave cores when amplitudes normalized by the thickness of the pycnocline are in the range of approximately between 1 and 1.75. The interacting stable waves of higher amplitude capture cores and carry trapped fluid in opposite directions with little mass loss. The collision of locally shear unstable waves of class (iii) is accompanied by the development of instability. The dependence of loss of energy on the wave amplitude is not monotonic. Initially, the energy loss due to the interaction increases as the wave amplitude increases. Then, the energy losses reach a maximum due to the loss of potential energy of the cores upon collision and then start to decrease. With further amplitude growth, collision is accompanied by the development of instability and an increase in the loss of energy. The collision process is modified for waves of different amplitudes because of the exchange of trapped fluid between colliding waves due to the conservation of momentum.

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“…23 Simulations of shoaling internal waves found major differences in the amount of dissipation and mixing when comparing between two and three dimensions. 25 As such, simulations examining sediment resuspension due to vortex shedding should carefully parametrize the effects of viscosity, as the three-dimensional nature of these instabilities has been shown to be sensitive to this parameter.…”

Section: Discussionmentioning

confidence: 99%

“…Further, recent numerical studies of shoaling internal waves suggest differences in the amount of dissipation and mixing in two versus three dimensions. 25 It is therefore important to examine the three-dimensional nature of boundary layer instabilities in more detail.…”

Section: Introductionmentioning

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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The dynamics of breaking internal solitary waves on slopes

Cited by 84 publications

References 46 publications

Transport by breaking internal gravity waves on slopes

Transport by breaking internal gravity waves on slopes

Head-on collision of internal waves with trapped cores

Topographically generated internal waves and boundary layer instabilities

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