VARIATIONAL METHOD IN TURBULENCE THEORY

The weighted mean square of the Navier-Stokes equation is mimimized with a complete set of realizability inequalities as constraints. Expansion of moments in complete orthogonal functions leads to successive approximations without ever involving moments of order higher than 4. Alternatively, the expansions may be in Wiener-Hermite kernels, thereby automatically satisfying the realizability constraints. The approach extends to other classical and quantized systems with polynomial nonlinearity. © 1979 The American Physical Society.