Estimating bolus velocities from data - how large must they be?

This paper examines the representation of eddy fluxes by bolus velocities. In particular, it asks: Can an arbitrary eddy flux divergence of density be represented accurately by a non-divergent bolus flux which satisfies the condition of no normal flow at boundaries? If not, how close can such a representation come? If such a representation can exist in some circumstances, what is the size of the smallest bolus velocity which fits the data? We find, in agreement with earlier authors, that the answer to the first question is no, although under certain conditions which include a modification to the eddy flux divergence, a bolus representation becomes possible. One such condition is when the eddy flux divergence is required to balance the time mean flux divergence. The smallest bolus flow is easily found by solving a thickness-weighted Poisson equation on each density level. This problem is solved for the north Pacific using time-mean data from an eddy-permitting model. The minimum bolus flow is found to be very small at depth, but larger than is usually assumed near the surface. The magnitude of this minimum flow is of order one-tenth of the mean flow. Similar but larger results are found for a coarse resolution model.