EXACT PARTICLE TRAJECTORIES FOR NONVISCOUS FLOW IN A PLANE WITH A CONSTANT CORIOLIS PARAMETER

Abstract

The pressure and density fields are assumed known exactly for all time, and the wind is to be forecast by obtaining the trajectory of each air particle from the equations of nonviscous motion in a plane. The importance of initial conditions is stressed. For sufficiently simple pressure and density fields the particle trajectories and hodographs may be obtained explicitly without approximation. The appropriate mathematical methods are reviewed. When the pressure force depends only on time, the solutions are compared with the Brunt–Douglas “isallobaric-wind” formula. For one case of stationary circular isobars the exact solution is shown to consist of a superposition of so-called “normal” and “abnormal” solutions of the gradient wind equation. Explicit trajectories believed to be new are found for an air parcel in a certain high-pressure center whose horizontal pressure gradient is equal to or greater than that of the so-called maximum anticyclone. The general nonlinear case of circular isobars is discussed. Several numerical examples are included.