Estimating Internal Wave Energy Fluxes in the Ocean

Abstract

Energy flux is a fundamental quantity for understanding internal wave generation, propagation, and dissipation. In this paper, the estimation of internal wave energy fluxes ͗uЈpЈ͘ from ocean observations that may be sparse in either time or depth are considered. Sampling must be sufficient in depth to allow for the estimation of the internal wave-induced pressure anomaly pЈ using the hydrostatic balance, and sufficient in time to allow for phase averaging. Data limitations that are considered include profile time series with coarse temporal or vertical sampling, profiles missing near-surface or near-bottom information, moorings with sparse vertical sampling, and horizontal surveys with no coherent resampling in time. Methodologies, interpretation, and errors are described. For the specific case of the semidiurnal energy flux radiating from the Hawaiian ridge, errors of ϳ10% are typical for estimates from six full-depth profiles spanning 15 h.

Tidal forcing, energetics, and mixing near the Yermak Plateau

“…The calculation of the baroclinic energetics follows the common methods, see, e.g., Kunze et al (2002) and Nash et al (2005), and also accounts for isopycnal heaving by movement of the free surface (Kelly et al, 2010). For a sinusoidal wave, the calculation requires perturbation profiles of velocity and pressure isolated at the corresponding frequency band, sampled over the whole water column, for an integer number of wave periods.…”

“…Using the observed velocity and density profiles, baroclinic perturbation fields of velocity, u , and buoyancy, b, are calculated similar to the methods described in Kunze et al (2002) and Nash et al (2005). The calculation of baroclinic pressure requires cumulative full-depth integrals, and is deferred to Sect.…”

“…The analysis of the STORMTIDE model data is free from these errors because modal analysis is not employed, and the inertial and tidal frequencies are delineated by the harmonic analysis of sufficiently long time series. Errors and systematic bias in baroclinic energy flux calculations for a variety of oceanographic sampling schemes are discussed thoroughly in Nash et al (2005). Using Monte Carlo simulations of synthetic data, including a combination of semidiurnal, near-inertial and internal wave continuum signal, they assess magnitude and parameter dependence of flux estimates made from temporally or vertically imperfect data.…”

Transition from partly standing to progressive internal tides in Monterey Submarine Canyon

“…where u is the velocity perturbation, p is the pressure perturbation, and · denotes an average over a tidal cycle (e.g., Kunze et al, 2002;Nash et al, 2005). The perturbations u and p are reconstructed from the harmonic constants.…”

Internal tides and energy fluxes over Great Meteor Seamount

“…Kunze et al (2002) proposed a "baroclinicity condition for pressure" to the effect that its vertical integral is assumed to be zero; this indeed fixes the constant. Although they added a cautionary remark ("this condition may not hold in regions of direct forcing"), they did not restrain its application to regions away from topography, nor did later authors (Nash et al, 2005. So, it has been indiscriminately applied over large canyons and ridges, even though its validity has not been demonstrated.…”