A THEORETICAL AND NUMERICAL STUDY OF DENSITY CURRENTS IN NONCONSTANT SHEAR FLOWS

The previous idealized two-fluid model of a density current in constan t shear is extended to the case where the inflow shear is confined to the low levels. The analytical solution is determined by the conservat ion of mass, momentum, vorticity, and energy. It is found that a low-l evel shear acts in a similar manner to a uniform vertical shear in con trolling the depth of a steady-state density current. When the shear e nhances the low-level Row against the density current propagation, the current is deeper than half of the domain depth. Time-dependent numer ical experiments are conducted for a variety of parameter settings, in cluding various depths and strengths of the shear layer. The numerical results agree closely with the theoretical analyses. Numerical experi ments are also performed for a case where the initial depth of the den sity current is sri to be comparable to the low-level shear, which is much shallower than that given by the steady-state solution. The circu lation at the density current head remains shallow and is nonsteady in this case. whereas the time-averaged flow still exhibits a deep jump updraft pattern that is close to the theoretical solution, suggesting the applicability of the theoretical results to even more transient fl ows. The simulated flow features are discussed in terms of balanced an d unbalanced dynamics, and in the context of forcing and uplifting at the frontal zone in long-lived convective systems. Here the term balan ce refers to a flow configuration that satisfies the steady-state solu tion of the idealized theoretical model.