Stratified flow over finite obstacles with weak stratification

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Abstract
The time-dependent problem of inviscid stratified flow over finite obstacles in fluid of infinite depth is considered in the limit of vanishing stratification (Nu/U→0), as a perturbation about the state of potential flow. The object of this study is to shed light on the “upstream influence” question, namely, under what circumstances does the motion of the obstacle generate steady motions which will eventually be felt at an arbitrarily large distance upstream? In the present study the flow develops on both short and long length and time scales, and a matched asymptotic expansion procedure is required. The results from this expansion are consistent with those from the corresponding “classical” expansion in small obstacle height [McIntyre (1972)). In particular, no permanent effects far upstream are obtained by this procedure, and this implies that “Long's model” is applicable for the case of infinite depth if Nh/U is sufficiently small.