Obtaining velocities from tracer distributions.

Abstract

A simple advective/diffusive system with uniform horizontal flow in a channel and fixed boundary concentration of two tracers is analysed for the tracer concentrations in the interior. The deduced concentrations are treated as given information to invert the analysis to obtain the velocity field. Examines the methodology by a study of the direct and inverse problems, and mathematical precision and significance. Analyses underdetermined and overdetermined systems. When the diffusion coefficients are known, two independent tracers permit good approximation to the actual velocity field even where there is truncation error. Noisy data can lead to problems. Suggest use of an empirical criterion based on the condition number of the matrix and the rms residual of an overdetermined system. (C.J.U.)