The motion generated by a body moving through a stratified fluid at large Richardson numbers

Abstract

Experiments are described in which a body was towed at large Richardson numbers through a uniformly stratified fluid, with particular attention being given to the parameter range in which diffusive effects are likely to play an important role. When the Richardson number is only moderately large (i.e. less than about 106) it appears that a linear viscous diffusive theory fails to model the experimental observations, but at larger Richardson numbers it seems that such a theory is a strong candidate for modelling the physical situation. At Richardson numbers of about 103 a non-diffusive viscous model (see the theories of Graebel 1969; Janowitz 1971) appears to give a fairly good description of the experimental results, except for some discrepancies between the theories and the observed flows in the wake downstream from the body. However, the conditions under which the experiments were carried out were not completely favourable for the application of these theories.A brief survey and new interpretations of some of the work on the rotatingfluid counterparts of the present experiments are also given. In view of the theoretical similarities between the two situations we have tried to assess and compare (where possible) the results of experimental investigations in each field and we feel that the observations in the rotating-fluid experiments are in good qualitative agreement with the present results. No measurements of the drag acting on the body were made in the present experiments but this has been done carefully in the rotating-fluid experiments, and the results of those measurements are in poor agreement with the theoretical predictions. Because of the close similarities between the axisymmetric model for viscous rotating fluids (cf. Moore & Saffman 1969) and the two-dimensional model for diffusive stratified fluids (Freund & Meyer 1972), an explanation for the discrepancy should be sought before the linear viscous diffusive model can be applied with any confidence to the flow of stratified fluids at very large Richardson numbers.