Computations of the geographical distribution of the energy flux to mixing processes via internal tides and the associated vertical circulation in the ocean

Abstract

The global flux of tidal energy to mixing processes via topographically generated internal waves is estimated utilizing gridded databases for bathymetry, vertical density stratification and barotropic tides together with a simple, local model for the generation of progressive internal tides at vertical steps in the ocean floor. Both the horizontal distribution of the energy flux to internal tides and its ocean mean are discussed. The computed oceanic mean value is 44 × 10−4W m−2, a factor of about 2–3 greater than previous estimates (Munk, 1966, Deep-Sea Research, 13, 707–730; Bell, 1975, Journal of Geophysical Research, 80, 320–327).The global distribution of vertical diffusivity in the abyss is computed by assuming that topographically generated baroclinic motions dissipate locally and that the dissipation is distributed vertically according to an empirical law. Our results are linearly dependent on the flux Richardson number Rf. From the computed vertical diffusivities and the known vertical stratification we finally compute the global distribution of vertical velocities. Choosing a value of Rf≈0.05 we obtain an upward vertical transport in the interior of the ocean, at the 1000 m level, of about 15 × 106m3s−1, which agrees with Warren's (1981, in: Evolution of physical oceanography, B. A. Warren and C. Wunsch, editors, 6–41) estimated rate of sinking from surface waters at high latitudes. Below the 1000 m level the upward vertical transport increases and a maximum value of about 25 × 106m3s−1 is found at the 2000 m level, after which the transport decreases to about 8 × 106m3s−1 at the 4000 m level. This may be explained by the action of bottom currents. These currents entrain ambient water whereby the upward interior vertical transports tend to increase with depth. However, because of the entrainment of lighter ambient fluid the dense currents become less dense and only the most dense flows penetrate to the greatest depths.