Abstract
The dissipation of the kinetic energy (KE) associated with oceanic flows is believed to occur primarily in the oceanic bottom boundary layer (BBL), where bottom drag converts the KE from mean flows to heat loss through irreversible mixing at molecular scales. Due to the practical difficulties associated with direct observations on small-scale turbulence close to the seafloor, most up-to-date estimates on bottom drag rely on a simple bulk formula (CdU3) proposed by G.I. Taylor that relates the integrated BBL dissipation rate to a drag coefficient (Cd) as well as a flow magnitude outside of the BBL (U). Using output from several turbulence-resolving direct numerical simulations, it is shown that the true BBL-integrated dissipation rate is approximately 90% of that estimated using the classic bulk formula, applied here to the simplest scenario where a mean flow is present over a flat and hydrodynamically smooth bottom. It is further argued that Taylor’s formula only provides an upper bound estimate and should be applied with caution in the future quantification of BBL dissipation; the performance of the bulk formula depends on the distribution of velocity and shear stress near the bottom, which, in the real ocean, could be disrupted by bottom roughness.
Highlights
Estimate of the Energy DissipationLarge-scale ocean currents are primarily powered by atmospheric winds and astronomical tidal forces at rates well quantified through satellite observations [1]
Four direct numerical simulations (DNS) experiments were used to demonstrate that the kinetic energy (KE) dissipation rate in the bottom boundary layer (BBL) over a flat wall is less than predicted by the celebrated formula proposed by Taylor [9]: D ' Cd U 3, where Cd is a constant drag coefficient and U the "far-field" velocity above the BBL
The discrepancy arises due to the assumption that the shear in the BBL is confined to an infinitesimally thin layer within the viscous sublayer in Taylor’s formula
Summary
Large-scale ocean currents are primarily powered by atmospheric winds and astronomical tidal forces at rates well quantified through satellite observations [1]. Bottom drag is experienced by oceanic flows above the seafloor, where a stress develops that brings the flow to zero This occurs in a thin bottom boundary layer (BBL). Where Cd is a drag coefficient and U is the magnitude of the mean flow above the BBL, the so-called “far-field” velocity This formula relates the bottom stress to dynamic pressure (proportional to U 2 ) associated with the mean flow [8]. Sij = ∂ui /∂x j + ∂u j /∂xi is the rate of strain tensor Taylor used this bulk formula to estimate the dissipation experienced by barotropic tides over continental shelves and set. U to be the barotropic tidal velocity [9] This bulk formula was later used to estimate the dissipation of sub-inertial flows in the global ocean and returned values anywhere between.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
