Scaling turbulent dissipation in the thermocline

TLDR

The functional form agrees with estimates by McComas and Müller and by Henyey, Wright, and Flatté of the rate of energy transfer within the internal wave spectrum, provided the energy density of the internal waves is treated as a variable instead of one of the constant parameters. The study assumes a relationship between observed internal wave energy density (E IW) and the Garrett–Munk energy density (E GM) following Garrett and Munk. Observations from six mid‑latitude thermocline sites show that the average internal‑wave–driven dissipation rate 〈ε IW〉 scales within a factor of two with the shear and buoyancy frequency, is twice that reported by Henyey et al.

Abstract

By comparing observations from six diverse sites in the mid‐latitude thermocline, we find that, to within a factor of 2, , where 〈ε IW 〉 is the average dissipation rate attributable to internal waves; N 0 = 0.0052 s −1 is a reference buoyancy frequency; S 10 is the observed shear having vertical wavelengths greater than 10 m; and S GM is the corresponding shear in the Garrett and Munk spectrum of internal waves. The functional form agrees with estimates by McComas and Müller and by Henyey, Wright, and Flatté of the rate of energy transfer within the internal wave spectrum, provided the energy density of the internal waves is treated as a variable instead of one of the constant parameters. Following Garrett and Munk, we assume that , where E IW is the observed energy density and E GM is the energy density used by Garrett and Munk. The magnitude of ε IW is twice that of Henyey et al. and one third that of McComas and Müller. Thus the observations agree with predictions sufficiently well to suggest that (1) a first‐order understanding of the link between internal waves and turbulence has been achieved, although Henyey et al. made some ad hoc assumptions and Garrett and Munk's model does not match important features in the internal wave spectrum reported by Pinkel, and (2) the simplest way to obtain average dissipation rates over large space and time scales is to measure . Even though the observations were taken at latitudes of 42°−11.5°, the variability in the Coriolis parameter ƒ was too limited for a conclusive test of the ƒ dependence also predicted for 〈ε IW 〉 by the wave‐wave interaction models. An exception to the scaling occurs east of Barbados in the thermohaline staircase that is apparently formed and maintained by salt fingers. Although ε in the staircase is very low compared with rates at mid‐latitude sites, it is 8 times larger than predicted for ε due only to internal waves.