Effect of the deformation radius on the evolution of vortex properties in geostrophic turbulence

Abstract

Coherent vortices in geostrophic turbulence grow in size and become fewer as they merge. It is shown that the deformation radius L(D) has no effect on the growth of the average vortex radius a as a grows from a L(D) to a>> L(D) . Its growth is algebraic, given by a proportional to t(xi/4) , where xi=0.72 . However, the deformation radius does have an effect on the decay of the number of vortices or vortex density rho, given by rho proportional to t(-xi) for a <<L(D) and rho t(-xi/2) for a>> L(D) . Thus the decay of rho becomes slower once a has grown to a size comparable to that of L(D) . One scaling theory for the entire range from a<< L(D) to a>> L(D) is presented and verified by numerical experiments. A special method for quadruplicating the numerical domain when the vortices become too few is proposed, which keeps the computation inexpensive. This work generalizes and agrees with previous work, in which the two special cases a<<L(D) and a>> L(D) are independently investigated.