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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 © 2009 John Wiley & Sons, Ltd.