Abstract
In a rotating gratified fluid, with small Ekman number E and Rossby number Ro, vertical diffusion of momentum is balanced by local deceleration for large values of the Burger number S, and hence leads to an increase in S. For small values of S a feature spreads laterally and S decreases; in this case a transformation to density coordinates leads to a horizontal-diffusion equation, which can be generalized to allow for arbitrary values of S and Ro. If Ro ≪ S, as well as Ro ≪ 1, the potential-vorticity equation can be linearized and the relative effect of vertical and horizontal diffusion of either momentum or mass can be examined.
