Resonant Generation of Internal Waves on a Model Continental Slope

Zhang, Hepeng; King, Benjamin T.; Swinney, Harry L.

doi:10.1103/physrevlett.100.244504

Cited by 53 publications

(54 citation statements)

References 21 publications

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“…[30][31][32]34,38 Indeed, recent numerical simulations have found that turbulence generated near critical topography can reduce the radiated internal wave power. Fig.…”

Section: Discussionmentioning

confidence: 99%

“…Particle image velocimetry 35 has been used in laboratory studies of internal waves to characterize the velocity fields, 27,28,[36][37][38][39][40][41] and synthetic schlieren has been used in a few studies to measure density perturbations averaged along the line of sight; [42][43][44] however, measurements of the accompanying pressure fields have not been made owing to technical challenges in doing so. To circumvent the difficulty in measuring the pressure field to obtain the energy flux of two-dimensional internal waves, Echeverri et al 39 decomposed their experimental velocity fields into the three lowest vertical modes, 45 which could be used to estimate the internal wave energy flux using Eq.…”

Section: Introductionmentioning

confidence: 99%

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Experimental determination of radiated internal wave power without pressure field data

et al. 2014

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We present a method to determine, using only velocity field data, the time-averaged energy flux J and total radiated power P for two-dimensional internal gravity waves. Both J and P are determined from expressions involving only a scalar function, the stream function ψ. We test the method using data from a direct numerical simulation for tidal flow of a stratified fluid past a knife edge. The results for the radiated internal wave power given by the stream function method agree to within 0.5% with results obtained using pressure and velocity data from the numerical simulation. The results for the radiated power computed from the stream function agree well with power computed from the velocity and pressure if the starting point for the stream function computation is on a solid boundary, but if a boundary point is not available, care must be taken to choose an appropriate starting point. We also test the stream function method by applying it to laboratory data for tidal flow past a knife edge, and the results are found to agree with the direct numerical simulation.Supplementary Material includes a Matlab code with a graphical user interface (GUI) that can be used to compute the energy flux and power from any two-dimensional velocity field data.

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“…[30][31][32]34,38 Indeed, recent numerical simulations have found that turbulence generated near critical topography can reduce the radiated internal wave power. Fig.…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Experimental determination of radiated internal wave power without pressure field data

et al. 2014

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“…In the case of a sloping boundary, this property gives a purely geometric reason for a strong variation of the width of internal wave beams (focusing or defocusing) upon reflection. Internal wave focusing provides a necessary condition for large shear and overturning, as well as shear and bottom layer instabilities at slopes [7][8][9][10].…”

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confidence: 99%

Energy cascade in internal-wave attractors

Brouzet¹,

Ermanyuk²,

Joubaud³

et al. 2016

EPL

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-One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose internal wave attractors in the large amplitude regime as a unique self-consistent experimental and numerical setup that models a cascade of triadic interactions transferring energy from large-scale monochromatic input to multi-scale internal wave motion. We also provide signatures of a discrete wave turbulence framework for internal waves. Finally, we show how beyond this regime, we have a clear transition to a regime of small-scale high-vorticity events which induce mixing.Introduction. -The continuous energy input to the ocean interior comes from the interaction of global tides with the bottom topography [1]. The subsequent mechanical energy cascade to small-scale internal-wave motion and mixing is a subject of active debate [2] in view of the important role played by abyssal mixing in existing models of ocean dynamics [3][4][5]. A question remains: how does energy injected through internal waves at large vertical scales [6] induce the mixing of the fluid [2]?In a stratified fluid with an initially constant buoyancy frequency N = [(−g/ρ)(dρ/dz)] 1/2 , where ρ(z) is the density distribution (ρ a reference value) over vertical coordinate z, and g the gravity acceleration, the dispersion relation of internal waves is θ = ± arcsin(Ω). The angle θ is the slope of the wave beam to the horizontal, and Ω the frequency of oscillations non-dimensionalized by N . The dispersion relation requires preservation of the slope of the internal wave beam upon reflection at a rigid boundary. In the case of a sloping boundary, this property gives a purely geometric reason for a strong variation of the width of internal wave beams (focusing or defocusing) upon reflection. Internal wave focusing provides a necessary condition for large shear and overturning, as well as shear and bottom layer instabilities at slopes [7][8][9][10].In a confined fluid domain, focusing usually prevails, leading to a concentration of wave energy on a closed loop, the internal wave attractor [11]. Attractors eventually

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“…One of the main reasons for studying internal waves remains the fact that they are suspected to play an important role in the dynamics of the ocean, especially in affecting the large-scale general circulation model (see e.g., [36], [49]). Furthermore, mutual interactions between internal waves produce mixing in the interior of the ocean providing an important link in the presumed energy cascade from large to small scales (e.g., [40], [47]).…”

Section: Internal Gravity Wave Beams In the Deep Oceanmentioning

confidence: 99%

“…Furthermore, mutual interactions between internal waves produce mixing in the interior of the ocean providing an important link in the presumed energy cascade from large to small scales (e.g., [40], [47]). One of the practical needs to better understand mixing processes in the ocean resides in the fact that mixing plays an important role in maintaining a gradual transition between the sun-warmed surface layer of the ocean and the upwelling cold, dense water formed at high latitudes (e.g., [49], [43], [29], [8]). The subject of mixing processes due to breaking of internal waves in the ocean and atmosphere has received much attention in recent years (see e.g.…”

Section: Internal Gravity Wave Beams In the Deep Oceanmentioning

confidence: 99%

Applications of Lie Group Analysis to Mathematical Modelling in Natural Sciences

Ibragimov

Ibragimov²

2012

Math. Model. Nat. Phenom.

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Abstract. Today engineering and science researchers routinely confront problems in mathematical modeling involving solutions techniques for differential equations. Sometimes these solutions can be obtained analytically by numerous traditional ad hoc methods appropriate for integrating particular types of equations. More often, however, the solutions cannot be obtained by these methods, in spite of the fact that, e.g. over 400 types of integrable second-order ordinary differential equations were summarized in voluminous catalogues. On the other hand, many mathematical models formulated in terms of nonlinear differential equations can successfully be treated and solved by Lie group methods. Lie group analysis is especially valuable in investigating nonlinear differential equations, for its algorithms act here as reliably as for linear cases. The aim of this article is, from the one hand, to provide the wide audience of researchers with the comprehensive introduction to Lie's group analysis and, from the other hand, is to illustrate the advantages of application of Lie group analysis to group theoretical modeling of internal gravity waves in stratified fluids.

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Resonant Generation of Internal Waves on a Model Continental Slope

Cited by 53 publications

References 21 publications

Experimental determination of radiated internal wave power without pressure field data

Experimental determination of radiated internal wave power without pressure field data

Energy cascade in internal-wave attractors

Applications of Lie Group Analysis to Mathematical Modelling in Natural Sciences

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