On a 1/2-equation model of turbulence
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In 1-equation URANS models of turbulence the eddy viscosity is given by ν_T=0.55l(x,t)√(k(x,t)) . The length scale l must be pre-specified and k(x,t) is determined by solving a nonlinear partial differential equation. We show that in interesting cases the spacial mean of k(x,t) satisfies a simple ordinary differential equation. Using its solution in ν_T results in a 1/2-equation model. This model has attractive analytic properties. Further, in comparative tests in 2d and 3d the velocity statistics produced by the 1/2-equation model are comparable to those of the full 1-equation model.
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