A new integral method for directly partitioning flow fields in limited domains over complex underlying surfaces

Abstract

A new integral method is developed for directly partitioning a horizontal velocity field into its rotational and divergent components in a limited domain without actually computing stream-function and velocity potential. In this method, the previous integral method is reformulated to skip the intermediate steps that solve for stream-function and velocity potential first and then compute the rotational and divergent velocities via finite-differencing from stream-function and velocity potential, respectively. This reformulation takes the advantage that the previous integral formulations for computing stream-function and velocity potential are spatially differentiable and thus can be used to derive new integral formulations for directly computing rotational and divergent velocities. By skipping the intermediate steps, the new method eliminates the finite-difference discretization errors that cause the previous integral method fail to retain adequate accuracies when applied to complicate flow fields induced by severe weather and complex underlying surfaces over limited domains. The superior performances and improved accuracies of the new integral method over the previous integral method as well as another widely used previous method are demonstrated by numerical experiments with both idealized complex flow and real severe weather events in limited domains over complicated terrains. Thus, unless stream-function and velocity potential must be computed and actually used for some applications, the new integral method is recommended.