Determining Velocities and Mixing Coefficients from Tracers

Abstract

The effort to determine oceanic velocities from tracer distributions relies on a knowledge of the effects of mixing. However, the macroscopic diffusion coefficient, K, is generally not known and must be calculated along with the velocity. The inverse problem to obtain v and K from known tracer distributions is formulated here for steady channel flow which is uniform and/or contains eddies. It is first shown that the problem is well posed; with enough (perfect) tracer data the exact values of v and K can be recovered. It is found that a complete inversion of imperfect data leads to substantial errors, especially if the system is not strongly overdetermined. A crude polynomial approximation for K reduces the required amount of input data and can actually yield a better solution than a full inversion does, even when noise and substantial velocity structure are present. Appending a similar approximation for the streamfunction gives mixed results; smooth flows are recovered with very little error but poor results are obtained when flows have substantial structure.