Nonhydrostatic effects in gravity currents

We extend hydraulic theory to include nonhydrostatic effects that may be present in compositionally-driven, fixed-volume gravity current releases in rectangular geometry. Unlike past attempts to include these effects that arise in flow problems when, say, interface deflections are not small we will work in the time-dependent domain, avoid layer averaging, and make no assumptions on the amplitudes of disturbances. An asymptotic development of the Euler equations in terms of the small parameter δ², where δ is the aspect ratio of the flow, is carried out and model equations obtained at leading and first orders. The leading order model enforces hydrostatic balance whereas the first order model accounts for nonhydrostatic effects in the flow. Similarity solutions are obtained at both orders and used as checks on our numerical results as well as to delineate the time-dependent region 0 ≤ x < x _f(t) in which our numerical, code is applicable. Here x = x _f gives the location of the front shock. An initial value problem is solved and numerical results presented graphically.