Upstream motions in stratified flow

Abstract

In this paper experimental measurements of the time-dependent velocity and density perturbations upstream of obstacles towed through linearly stratified fluid are presented. Attention is concentrated on two-dimensional obstacles which generate turbulent separated wakes at Froude numbers, based on velocity and body height, of less than 0.5. The form of the upstream columnar modes is shown to be largely that of first-order unattenuating disturbances, which have little resemblance to the perturbations described by small-obstacle-height theories. For two-dimensional obstacles the disturbances are similar to those found by Wei, Kao & Pao (1975) and it is shown that provided a suitable obstacle drag coefficient is specified, the lowest-order modes (at least) are quantitatively consistent with the results of the Oseen inviscid model.Discussion of some results of similar measurements upstream of three-dimensional obstacles, the importance of towing tank endwalls and the relevance of the Foster & Saffman (1970) theory for the limit of zero Froude number is also included.