On the Geostrophic Adjustment of an Isolated Lens: Dependence on Burger Number and Initial Geometry

Geostrophic adjustment of an isolated axisymmetric lens was examined to better understand the dependence of radial displacements and the adjusted velocity on the Burger number and the geometry of initial conditions. The behavior of the adjustment was examined using laboratory experiments and numerical simulations, which were in turn compared to published analytical solutions. Three defining length scales of the initial conditions were used to distinguish between various asymptotic behaviors for large and small Burger numbers: the Rossby radius of deformation, the horizontal length scale of the initial density defect, and the horizontal length scale of the initial pressure gradient. Numerical simulations for the fully nonlinear time-dependent adjustment agreed both qualitatively and quantitatively with analogous analytical solutions. For large Burger numbers, similar agreement was found in laboratory experiments. Results show that a broad range of final states can result from different initial geometries, depending on the values of the relevant length scales and the Burger number computed from initial conditions. For Burger numbers much larger or smaller than unity, differences between different initial geometries can readily exceed an order of magnitude for both displacement and velocity.