Internal wave pressure, velocity, and energy flux from density perturbations

Allshouse, Michael; Lee, Frank M.; Morrison, Philip; Swinney, Harry L.

doi:10.1103/physrevfluids.1.014301

Cited by 10 publications

(28 citation statements)

References 38 publications

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“…As this work builds off the theoretical foundation presented in Allshouse et al (2016), we present the general equations in §2.1. These equations provide the velocity perturbation field as a function of the density perturbation, and a functional relationship between the density and pressure perturbation fields is established.…”

Section: Theoretical Developmentmentioning

confidence: 99%

“…Our goal of obtaining the energy flux (1.1) from the density perturbation field alone requires calculating the pressure perturbation and components of the velocity perturbation from the density perturbation field. The details of these calculations were given in Allshouse et al (2016) for a uniform N profile, but here we present a condensed version of the pressure perturbation calculation, as needed for the calculations for the tanh N 2 and linear N profiles.…”

Section: Generalitiesmentioning

confidence: 99%

“…Laboratory observations of internal waves have been made by particle image velocimetry (PIV) (Echeverri et al 2009;King et al 2009King et al , 2010Paoletti et al 2014), synthetic schlieren (Sutherland et al 1999;Dalziel et al 2000;Clark & Sutherland 2010;Allshouse et al 2016), and light attenuation (Dossmann et al 2016). In PIV, neutrally buoyant particles scatter incident laser light, and movies of the scattered light field yield the time-varying velocity field.…”

Section: Introductionmentioning

confidence: 99%

“…The method can be applied to ocean density perturbation space-time data when such data becomes available. The methods presented here and in Allshouse et al (2016) provide the instantaneous rather than time-averaged energy flux field. Thus the resultant energy flux and integrated far-field power include all spectral components, while previous methods provided only the global conversion rates or monochromatic results.…”

Section: Introductionmentioning

confidence: 99%

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Internal wave energy flux from density perturbations in nonlinear stratifications

et al. 2018

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Internal gravity wave energy contributes significantly to the energy budget of the oceans, affecting mixing and the thermohaline circulation. Hence it is important to determine the internal wave energy flux J = p v, where p is the pressure perturbation field and v is the velocity perturbation field. However, the pressure perturbation field is not directly accessible in laboratory or field observations. Previously, a Green's function based method was developed to calculate the instantaneous energy flux field from a measured density perturbation field ρ(x, z, t), given a constant buoyancy frequency N . Here we present methods for computing the instantaneous energy flux J (x, z, t) for a spatially varying N (z), as in the oceans where N (z) typically decreases by two orders of magnitude from shallow water to the deep ocean. Analytic methods are presented for computing J (x, z, t) from a density perturbation field for N (z) varying linearly with z and for N 2 (z) varying as tanh(z). To generalize this approach to arbitrary N (z), we present a computational method for obtaining J (x, z, t). The results for J (x, z, t) for the different cases agree well with results from direct numerical simulations of the Navier-Stokes equations. Our computational method can be applied to any density perturbation data using the MATLAB graphical user interface EnergyFlux.

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Section: Theoretical Developmentmentioning

confidence: 99%

Section: Generalitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Internal wave energy flux from density perturbations in nonlinear stratifications

et al. 2018

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“…Density perturbations obtained with the synthetic schlieren technique can lead to the estimation of the energy flux for linear (Clark & Sutherland 2010; Allshouse et al. 2016) or nonlinear stratifications (Lee et al. 2018).…”

Section: Introductionmentioning

confidence: 99%

Energy budget in internal wave attractor experiments

et al. 2019

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The current paper presents an experimental study of the energy budget of a twodimensional internal wave attractor in a trapezoidal domain filled with uniformly stratified fluid. The injected energy flux and the dissipation rate are simultaneously measured from a two-dimensional, two components, experimental velocity field. The pressure perturbation field needed to quantify the injected energy is determined from the linear inviscid theory. The dissipation rate in the bulk of the domain is directly computed from the measurements, while the energy sink occurring in the boundary layers are estimated using the theoretical expression of the velocity field in the boundary layers, derived recently by Beckebanze et al. (J. Fluid Mech. 841, 614 (2018)). In the linear regime, we show that the energy budget is closed, in the steady-state and also in the transient regime, by taking into account the bulk dissipation and, more important, the dissipation in the boundary layers without any adjustable parameters. The dependence of the different sources on the thickness of the experimental set-up is also discussed. In the nonlinear regime, the analysis is extended by estimating the dissipation due to the secondary waves generated by triadic resonant instabilities showing the importance of the energy transfer from large scales to small scales. The method tested here on internal wave attractors can be generalized straightforwardly to any quasi two-dimensional stratified flow.

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Asymmetric internal tide generation in the presence of a steady flow

Dossmann

Shakespeare²,

Stewart

et al. 2020

Preprint

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The generation of topographic internal waves (IWs) by the sum of an oscillatory and a steady flow is investigated experimentally and with a linear model. The two forcing flows represent the combination of a tidal constituent and a weaker quasi-steady flow interacting with an abyssal hill. The combined forcings cause a coupling between internal tides and lee waves that impacts their dynamics of IWs as well as the energy carried away. An asymmetry is observed in the structure of upstream and downstream IW beams due to a quasi-Doppler shift effect. This asymmetry is enhanced for the narrowest ridge on which a superbuoyancy (𝜔 > N) downstream beam and an evanescent upstream beam are measured. Energy fluxes are measured and compared with the linear model, that has been extended to account for the coupling mechanism. The structure and amplitude of energy fluxes match well in most regimes, showing the relevance of the linear prediction for IW wave energy budgets, while the energy flux toward IW beams is limited by the generation of periodic vortices in a particular experiment. The upstream-bias energy flux-and consequently net horizontal momentum-described in Shakespeare (2020, https://doi.org/10.1175/JPO-D-19-0179.1) is measured in the experiments. The coupling mechanism plays an important role in the pathway to IW-induced mixing, that has previously been quantified independently for lee waves and internal tides. Hence, future parameterizations of IW processes ought to include the coupling mechanism to quantify its impact on the global distribution of mixing.Plain Language Summary When tides and currents interact with abyssal topographies, such as ridges and hills, they generate internal waves that propagate in the ocean interior. The energy transported by these waves sustains the largest scale oceanic motions. To improve our understanding of how and where energy is transferred to oceanic currents, an important step is to describe the fate of internal waves, from their generation to their breaking. Previous studies have independently described the dynamics of internal waves generated by tides, or by a steady current. Here we combine the two types of currents-a situation that is met at many oceanic sites-using laboratory experiments and a linear model. The combined currents cause an asymmetry in the internal wave structure. Internal waves are more energetic on the upstream side of the ridge, a phenomenon that is amplified when decreasing the ridge width. The measured energy matches the model prediction in all but one experiment. This gap is likely related to the formation of a vertical swirl close to the ridge that limits energy transfers to internal waves. These results contributes to improve our understanding of the internal wave dynamics and to better represent their effects in oceanic models.

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Internal wave pressure, velocity, and energy flux from density perturbations

Cited by 10 publications

References 38 publications

Internal wave energy flux from density perturbations in nonlinear stratifications

Internal wave energy flux from density perturbations in nonlinear stratifications

Energy budget in internal wave attractor experiments

Asymmetric internal tide generation in the presence of a steady flow

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