Years ago, Armi [1978] made the case for the importance of boundary mixing in mixing the abyssal ocean below 1 km. Caldwell et al. [1978] observed increasing thermal microstructure as they approached a lake slope, and suggested that internal waves were the cause. Now there is new evidence indicating enhanced mixing near steeply-sloping boundaries, at least near seamounts. Toole et al. [1994] observed enhanced internal wave energy and enhanced deep mixing near the flank of Fieberling Guyot as did Mudge and Lueck [1994] near Cobb Seamount (in relatively shallow water). The source of the mixing is presumably internal wave reflection from the sloping bottom [ Eriksen, 1982; Gilbert and Garrett, 1989]. Physically, conservation of wave frequency requires internal waves to be reflected at the same (incident) angle relative to the vertical, rather than to the normal to the sloping surface [ Phillips, 1977]. Consequently, waves originating in deep water and incident upon the boundary cause increased wave energy density upon reflection as well as increased wave shear due to increased vertical wavenumber. As a result, the local Richardson number (a measure of the tendency for the occurrence of turbulence in a stratified fluid, defined as the square of the buoyancy frequency divided by the square of the shear) may be sufficiently reduced that mixing ensues. Gilbert and Garrett [1989] suggest that mixing is more intense over convex boundaries than over concave boundaries.
There has been some concern that the overall contribution of boundary regions to mixing the abyss may be inconsequential for two reasons:
First, enhanced turbulence must act on the stratified part of the ocean, not merely on an already well-mixed bottom boundary layer. Either mixing processes must extend far enough from the slope to encounter stratified fluid or fluid mixed near the slope must subsequently be replenished by stratified fluid. Eriksen [1982] and Garrett and Gilbert [1988] suggest that enhanced shear from internal wave reflection may extend far enough from the slope to be effective in mixing. Numerical investigations by Slinn and Riley [1994] of internal wave breakdown over sloping terrain show continual replacement of mixed fluid at the slope by stratified fluid away from the slope.
Second, the mixed fluid must get to the interior of the abyssal ocean. Phillips et al. [1986] investigated the effect of boundary mixing on an interior pycnocline. They argued that mixing at a sloping boundary could spread isopycnals up and down the slope and that resulting buoyancy forces could drive a flow which converges at the pycnocline causing an outflow toward the ocean interior. In this manner, isopycnals may spread just as if the mixing had occurred in the interior [ Garrett et al., 1993]. Although flow velocities may be too small to be measured directly, tracers may mark the flow at the slope so that we can detect it.
So, there is evidence for enhanced deep mixing near seamounts, there is a mechanism proposed to cause the mixing and there are arguments suggesting that boundary mixing is efficient and communicated to the interior. Can these mechanisms be tested experimentally? Ultimately the question is: Can boundary mixing be sufficiently effective to explain basin-averaged vertical diffusion?
Leaving this question for future investigations, we proceed to issues concerning the nature of turbulence in the ocean.