Experimental determination of radiated internal wave power without pressure field data

Determination of energy transport is crucial for understanding the energy budget and fluid circulation in density varying fluids such as the ocean and the atmosphere. However, it is rarely possible to determine the energy flux field J = pu, which requires simultaneous measurements of the pressure and velocity perturbation fields, p and u. We present a method for obtaining the instantaneous J (x, z, t) from density perturbations alone: a Green's function-based calculation yields p, and u is obtained by integrating the continuity equation and the incompressibility condition. We validate our method with results from Navier-Stokes simulations: the Green's function method is applied to the density perturbation field from the simulations, and the result for J is found to agree typically to within 1% with J computed directly using p and u from the Navier-Stokes simulation. We also apply the Green's function method to density perturbation data from laboratory schlieren measurements of internal waves in a stratified fluid, and the result for J agrees to within 6% with results from Navier-Stokes simulations. Our method for determining the instantaneous velocity, pressure, and energy flux fields applies to any system described by a linear approximation of the density perturbation field, e.g., to small amplitude lee waves and propagating vertical modes. The method can be applied using our Matlab graphical user interface EnergyFlux.

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“…Because of the transformation (10), the boundary conditions on p, (15) and (17), imply the following boundary conditions on the variable q:…”

Section: A Energy Flux From a Density Perturbation Fieldmentioning

confidence: 99%

“…This finite-volume based solver implements a fractional-step time-marching scheme, with subgrid modeling deactivated. The code has been validated in previous laboratory and computational studies of internal waves [9,15,[25][26][27].…”

Section: A Navier-stokes Numerical Simulationsmentioning

confidence: 99%

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

et al. 2016

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“…The simulations use the CDP-2.4 algorithm, which is a finite volume solver that implements a fractional-step time-marching scheme (Ham & Iaccarino 2004;Mahesh et al 2004). This code has previously been used to simulate internal waves and has been validated with experiments (King et al 2009;Lee et al 2014;Dettner et al 2013;Zhang & Swinney 2014;Paoletti et al 2014;Allshouse et al 2016).…”

Section: Simulation Of the Density Perturbation Fieldmentioning

confidence: 99%

“…One method assumed a constant buoyancy frequency and calculated the energy flux (averaged over a tidal period) given only the stream function, thus eliminating the need to measure the pressure perturbation field (Balmforth et al 2002). The stream function method was subsequently extended to a buoyancy frequency varying exponentially with depth Lee et al (2014). Another method applied the polarization relations to density perturbation data to obtain estimates for the velocity and pressure perturbation amplitudes (Clark & Sutherland 2010).…”

Section: Introductionmentioning

confidence: 99%

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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“…From our PIV velocity field measurements, we calculate the energy flux field for the different frequency components using a recently established method. 17 First, the stream function field ψ(x, z) is obtained from the two-dimensional velocity field data via the relation (u, w) = (−∂ z ψ, ∂ x ψ) and path integration. The stream function field, as well as the background density and wave frequency, are subsequently incorporated into the expression for energy flux,…”

Section: -4 Ghaemsaidi Et Almentioning

confidence: 99%

Nonlinear internal wave penetration via parametric subharmonic instability

et al. 2016

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6 pages, 5 figuresInternational audienceWe present the results of a laboratory experimental study of an internal wave field generated by harmonic, spatially-periodic boundary forcing from above of a density stratification comprising a strongly-stratified, thin upper layer sitting atop a weakly-stratified, deep lower layer. In linear regimes, the energy flux associated with relatively high frequency internal waves excited in the upper layer is prevented from entering the lower layer by virtue of evanescent decay of the wave field. In the experiments, however, we find that the development of parametric subharmonic instability (PSI) in the upper layer transfers energy from the forced primary wave into a pair of subharmonic daughter waves, each capable of penetrating the weakly-stratified lower layer. We find that around $10\%$ of the primary wave energy flux penetrates into the lower layer via this nonlinear wave-wave interaction for the regime we study

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Experimental determination of radiated internal wave power without pressure field data

Cited by 8 publications

References 59 publications

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

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

Internal wave energy flux from density perturbations in nonlinear stratifications

Nonlinear internal wave penetration via parametric subharmonic instability

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