Frontal jump conditions for models of shallow, buoyant surface layer hydrodynamics

Abstract

Moving frontal regions are often observed in coastal and inland waters when a buoyant surface layer is present. Examples of such phenomena are moving fronts behind which the spreading of buoyant surface plumes occur and the passage of thermocline surges in lakes. An approach to modeling the hydrodynamics of shallow, buoyant surface layers is suggested which partitions the flow field into a frontal region where dissipative effects are important and an internal wave region where they are not. This approach treats the frontal region as a horizontal discontinuity described by appropriate jump conditions and the wave region by the nonlinear, long internal wave equations. Frontal jump conditions are derived for use in such a model when applied to small-scale flows where earth rotation has a negligible effect. These conditions account for the transport of mass and momentum across the interface with the underlying fluid. They are also applicable to flows where the depth of the buoyant upper layer vanishes on the upstream side of the front. They thus represent an extension of the classical jump conditions associated with an internal bore or hydraulic jump. To illustrate their use in conjunction with the nonlinear internal wave equations, a problem is solved representing the sudden release of a shallow, buoyant upper layer into an unbounded domain. For zero interfacial transport the results are identical to the classical description of the analogous single layer problem posed by the sudden breaking of a dam. For nonzero transport, however, new features of the flow arise.