Oceanic Isopycnal Slope Spectra. Part I: Internal Waves

Abstract

Horizontal tow measurements of internal waves are rare and have been largely supplanted in recent decades by vertical profile measurements. Here, estimates of isotherm displacements and turbulence dissipation rate from a towed vehicle deployed near Hawaii are presented. The displacement data are interpreted in terms of horizontal wavenumber spectra of isopycnal slope. The spectra span scales from 5 km to 0.1 m, encompassing both internal waves and turbulence. The turbulence subrange is identified using a standard turbulence fit, and the rest of the motions are deemed to be internal waves. The remaining subrange has a slightly red slope ( ϳ k Ϫ1/2 x ) and vertical coherences compatible with internal waves, in agreement with previous towed measurements. However, spectral amplitudes in the internal wave subrange exhibit surprisingly little variation despite a four-order-of-magnitude change in turbulence dissipation rate observed at the site. The shape and amplitude of the horizontal spectra are shown to be consistent with observations and models of vertical internal wave spectra that consist of two subranges: a "linear" subrange ( ϳ k 0 z ) and a red "saturated" subrange ( ϳ k Ϫ1 z ). These two subranges are blurred in the transformation to horizontal spectra, yielding slopes close to those observed. The saturated subrange does not admit amplitude variations in the spectra yet is an important component of the measured horizontal spectra, explaining the poor correspondence with the dissipation rate.

Submesoscale turbulence in the upper ocean

“…The GM spectra predict the spectral densities of the kinetic and potential energies as functions of frequency and vertical wavenumber; they can be converted to horizontal-wavenumber space using the dispersion relation of internal waves and summing over all vertical wavenumbers (e.g. Klymak and Moum, 2007). These wavenumber spectra scale like…”

Estimating Oceanic Turbulence Dissipation from Seismic Images

“…In the region of interest, turbulence dissipation is then estimated by fitting the mean reflector slope spectra to the KM07 model for the turbulence subrange [Eq. (12) of Klymak and Moum 2007b], using a nonlinear least squares inversion. Eddy diffusivity is then estimated as K r 5 0.2«N…”

“…Subsequent work has corroborated the sensitivity of the seismic method to internal waves (Krahmann et al 2008), although wavenumber spectra may be distorted in the presence of strong currents (Vsemirnova et al 2009). At the highest wavenumbers accessible to seismic imaging, turbulence may also be detectable: Holbrook and Fer (2005) pointed out an apparent k x 25/3 subrange in their spectra and speculated that this might indicate turbulence dissipation; this was supported using slope spectra by Klymak and Moum (2007b). Sheen et al (2009) applied Klymak and Moum's slope spectra method to seismic images and interpreted spatial variations in turbulence dissipation on a seismic section in the Southern Ocean.…”

“…The right-hand side of (2) contains two terms that describe turbulence: an inertial-convective subrange, which is dependent only on dissipation and wavenumber, and an inertial-diffusive subrange, which also depends on the viscosity of seawater. At the wavenumbers relevant to seismic imaging, the inertialconvective subrange dominates, producing slope spectra that are proportional to k x 1/3 (Klymak and Moum 2007b), according to the second term in Eq. (2), as will be seen below.…”

First images and orientation of fine structure from a 3-D seismic oceanography data set

“…Features that affect thermohaline fine structure, such as internal waves, tidal beams, solitons, eddies, fronts, warm core rings, and turbulent patches, are expected to vary in both space and time. To study these kinds of features, oceanographers typically use a combination of surface measurements (e.g., satellite sea surface elevation and surface temperature; Egbert et al, 1994;Ikeda and Emery, 1984), vertical profiles (by expendable instruments, non-expendable lowered instruments, or moored instrument arrays; e.g., Cooper et al, 1990;Rudnick et al, 2003), and towed instruments that can take measurements either along one horizontal line or in a "tow-yo" sawtooth pattern (e.g., Rudnick and Ferrari, 1999;Klymak and Moum, 2007). These methods can capture large-scale patterns over a wide area or fine-scale patterns at a discrete location or depth.…”