A conundrum in conversion

Focus on Fluids A conundrum in conversion Stefan G. Llewellyn Smith 1 Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, 9500 Gilman Drive, La Jolla CA 92093-0411, USA (Received 22 June 2011) Maintaining the stratification of the ocean requires deep mixing. Part of the energy that provides this mixing is transferred over topography from the surface tides into the internal tides. This conversion mechanism has been the subject of extensive investigation, and theoretical, numerical and experimental studies have aimed at quantifying this energy transfer. Maas (this issue) constructs model topographies with localized response and no energy transfer into the propagating internal tide, a surprising result that raises questions about models of tidal conversion. Keywords. Internal waves; ocean processes; topographic effects. 1. Introduction The Moon is receding from the Earth at a rate of 38 mm/s. This could be called the most accurately known constant in physical oceanography: it is an oceanographic value because the motion of the Moon leads to an energy loss of about 3.7 TW from the Earth-Moon system through tidal dissipation that mostly takes place in the ocean. This is responsible for the maintenance of oceanic stratification, along with energy input from the winds (Munk 1997). Munk & Wunsch (1998) calculated that, to maintain the abyssal stratification, mechanical energy is needed to drive mixing and evaluated the origins of this mixing, bringing to the fore the role of tides. Estimates of the flux are 3.5 TW in the surface tide of which 2.6 TW goes to mixing the shallow bottom boundary layer and 0.9 TW goes into the internal tide. For comparison, the wind is estimated to produce 1.2 TW, combining with the internal tide to produce 2.1 TW of deep-ocean mixing. The dissipation of tides by bottom drag in shallow reasons was well known to Tay- lor (1919) and Jeffreys (1920). A simple estimate of the power input or energy flux is P ∼ 0.0025ρ 0 u 3 (W m −2 ), where ρ 0 and u are representative values for the density of seawater and the tidal velocity respectively. The energy budget was closed by dissipation over continental shelves. The advent of satellite oceanography has transformed our un- derstanding of tides in the ocean. Ray & Mitchum (1997) showed direct evidence of the coherent internal tide radiating away from the Hawaiian Ridge. Assimilating numerical tidal models have shown where energy loss from the global tide occurred: Egbert & Ray (2000) produced maps showing that in fact dissipation was occurring in the deep ocean over topographic features such as mid-ocean ridges. This mechanism had previously been estimated to be small (e.g. Baines 1973). The underlying mechanism is that the usual surface tide moves deep stratified fluid over topography and in so doing generates internal waves, which are called the internal tide. The power dissipation scales like P ∼ ρ 0 u 2 N l (W m −2 ), where N is the buoyancy frequency at the ocean floor and l is a length scale related to the topography. Since Munk & Wunsch (1998) there has been a great deal of interest in the tidal conversion problem: how the internal tide is produced by the interaction of the barotropic