A stochastic Lamb-Oseen vortex solution of the 2D Navier-Stokes equations

The exact solution of the Lamb-Oseen vortices is reported for a random viscosity characterized by a Gamma probability density function. This benchmark solution allowed to quantify the analytic error of the polynomial chaos (PC) expansion as a function of the number of stochastic modes considered and compare it with its numerical counterpart. The last was obtained in the framework of the PC expansion method together with a finite difference numerical discretization of the resulting system of Navier-Stokes equations for the expansion modes considered. The obtained solution may be used to test other numerical approaches for the solution of the Navier-Stokes equations with random inputs. Copyright (C) 2009 John Wiley & Sons, Ltd.