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This paper reports on a computational study of the model error in theLANS-alpha and NS-alpha deconvolution models of homogeneous isotropicturbulence. The focus is on how well the model error may be characterized by astochastic force. Computations are also performed for a new turbulence modelobtained as a rescaled limit of the deconvolution model. The technique used isto plug a solution obtained from direct numerical simulation of theincompressible Navier--Stokes equations into the competing turbulence modelsand to then compute the time evolution of the resulting residual. Allcomputations have been done in two dimensions rather than three for convenienceand efficiency. When the effective averaging length scale in any of the modelsis $\alpha_0=0.01$ the time evolution of the root-mean-squared residual errorgrows as $\sqrt t$. This growth rate is consistent with the hypothesis that themodel error may be characterized by a stochastic force. When $\alpha_0=0.20$the residual error grows linearly. Linear growth suggests that the model errorpossesses a systematic bias which dominates the stochastic terms. Finally, for$\alpha_0=0.04$ the LANS-alpha model possessed systematic bias; however, forthis value of $\alpha_0$ the higher-order alpha models that were tested didnot.

Stochastic model error in the LANS-alpha and NS-alpha deconvolution models of turbulence