The Use of an Exact Solution of the Navier–Stokes Equations in a Validation Test of a Three-Dimensional Nonhydrostatic Numerical Model

Abstract

An exact analytic solution of the Navier–Stokes equations is used to validate a three-dimensional nonhydrostatic numerical flow model, the Advanced Regional Prediction System developed at the Center for Analysis and Prediction of Storms. The exact solution is a viscously decaying extension of a Beltrami flow used in previous studies of thunderstorm rotation, and consists of a periodic array of counterrotating updrafts and downdrafts. This flow is noteworthy in that it is three-dimensional, free of singularities, and satisfies the Navier–Stokes equations with nontrivial (i.e., nonvanishing) inertial terms. The simple form of the analytic solution and its provision for arbitrarily large spatial gradients suggest its potential utility in validating numerical flow models and in testing the relative merits of various numerical solution algorithms.