Classification of internal solitary wave breaking over a slope

Nakayama, Keisuke; Satô, Takahiro; Shimizu, Kenji; Boegman, Leon

doi:10.1103/physrevfluids.4.014801

Cited by 45 publications

(33 citation statements)

References 77 publications

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“…Higher temporal resolution velocity observations would allow more detailed analysis. The wave form was similar to the result of a collapsing wave of depression as modeled by Nakayama et al (2019) and Arthur and Fringer (2014). The largest overturns were found at the trailing‐face of this wave.…”

Section: Characterizing the Instabilities Of Nliw Of Elevationsupporting

confidence: 79%

Mixing Driven by Breaking Nonlinear Internal Waves

Jones

Ivey

Rayson

et al. 2020

Geophysical Research Letters

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Non-linear internal waves (NLIW) are important to processes such as heat transfer, nutrient replenishment and sediment transport on continental shelves. Our unique field observations of shoaling NLIW of elevation revealed a variety of different wave shapes, varying from relatively symmetric waves, to waves with either steepened leading-or trailing-faces; many had evidence of trapped cores. The wave shape was related to the position of maximum density overturns and diapycnal mixing. We observed both shear (where sheared currents overcome the stabilizing effects of stratification) and convective (where the local velocity exceeds the wave propagation speed) instabilities. The elevated diapycnal mixing (>10 −3 m 2 s −1) and heat flux (>500 Wm −2) were predominantly local to the NLIW of elevation packets, and were transported onshore 10s kilometers with the wave packets. We demonstrate that wave steepness may be a useful bulk property for the parameterization of wave-averaged diapycnal heat flux. Plain Language Summary Predicting the distribution of constituents such as nutrients, heat, sediment and pollutants on the continental shelf is key to processes such as: the safe operation of offshore infrastructure; understanding the variation in primary productivity; the prediction of marine heat waves; and environmental impact assessments of new activities. Non-linear internal waves, waves that travel within the stratified water column, are likely to have a significant impact on constituent transport; however, they are poorly understood. Here we present unique observations that quantify the properties of a class of these nonlinear internal waves, known as waves of elevation. These waves can break in a similar way to surface waves at the beach, leading to dramatic increases in turbulent mixing over horizontal length scales of 10s kilometers. We have used our observations to define the amount of vertical heat transport induced by the breaking waves as a function of wave steepness. The vertical heat transport can be used as a proxy to estimate the vertical nutrient transport. This study has made a step change in quantifying the impact of NLIW of elevation on vertical transport.

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Section: Characterizing the Instabilities Of Nliw Of Elevationsupporting

confidence: 79%

Mixing Driven by Breaking Nonlinear Internal Waves

Jones

Ivey

Rayson

et al. 2020

Geophysical Research Letters

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“…Many of the above flow features are also observed with shoaling mode-1 waves, where several extensive laboratory and numerical model studies have been undertaken (see, for example, Boegman et al (2005); Aghsaee et al (2010); Sutherland et al (2013); Nakayama et al (2019) and references therein). These studies have been successful in not only delineating the different processes determining the shoaling behaviour of mode-1 ISWs for different combinations of boundary slope s and wave slope s w (= a/L w ) but also characterising and classifying the shoaling regimes in terms of these parameters.…”

Section: Introductionmentioning

confidence: 97%

“…Reflection (with no breaking) is seen for very steep slopes. For intermediate (moderate to steep) slopes, several different types (surging, collapsing, collapsing plunging, plunging) of wave breaking occur, with the breaking regimes being classified conveniently in terms of s, s w and the relative values of the time scales characterising the individual wave breaking processes (Aghsaee et al 2010;Nakayama et al 2019). Sutherland et al (2013) demonstrate that shoaling-induced breaking regimes of mode-1 ISWs can be classified successfully in terms of the bed slope s and an internal Iribarren † number Ir = s/(s w ) 1/2 , subject to careful definition of the length scale L w .…”

Section: Introductionmentioning

confidence: 99%

Shoaling mode-2 internal solitary-like waves

et al. 2019

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The propagation of a train of mode-2 internal solitary-like waves (ISWs) over a uniformly sloping, solid topographic boundary, has been studied by means of a combined laboratory and numerical investigation. The waves are generated by a lock-release method. Features of their shoaling include (i) formation of an oscillatory tail, (ii) degeneration of the wave form, (iii) wave run up, (iv) boundary layer separation, (v) vortex formation and re-suspension at the bed and (vi) a reflected wave signal. Slope steepness, $s$, is defined to be the height of the slope divided by the slope base length. In shallow slope cases ($s\leqslant 0.07$), the wave form is destroyed by the shoaling process; the leading mode-2 ISW degenerates into a train of mode-1 waves of elevation and little boundary layer activity is seen. For steeper slopes ($s\geqslant 0.13$), boundary layer separation, vortex formation and re-suspension at the bed are observed. The boundary layer dynamics is shown (numerically) to be dependent on the Reynolds number of the flow. A reflected mode-2 wave signal and wave run up are seen for slopes of steepness $s\geqslant 0.20$. The wave run up distance is shown to be proportional to the length scale $ac^{2}/g^{\prime }h_{2}\sin \unicode[STIX]{x1D703}$ where $a,c,g^{\prime },h_{2}$ and $\unicode[STIX]{x1D703}$ are wave amplitude, wave speed, reduced gravity, pycnocline thickness and slope angle respectively.

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“…In field observations, Pineda (1994), Inall (2009) and Bourgault et al (2014) show that internal waves induce long-term mass transport due to breaking over a sill or a bottom slope and have an important influence on the environment in stratified fluids. In numerical calculations it has been shown that the breaking of internal solitary waves can be categorized using the wave slope, bottom slope and an internal solitary wave Reynolds number (Aghsaee, Boegman & Lamb 2010;Nakayama et al 2012Nakayama et al , 2019b. Additionally, the occurrence of long-term mass transport by internal waves has been observed in laboratory experiments (Nakayama & Imberger 2010;Nakayama et al 2012;Sutherland, Barrett & Ivey 2013).…”

Section: Introductionmentioning

confidence: 99%