Finite-mode spectral model of homogeneous and isotropic Navier-Stokes turbulence:: A rapidly depleted energy cascade

An eddy-viscous term is added to Navier-Stokes dynamics at wave numbers k greater than the inflection point k, of the energy flux F(log(k)). The eddy viscosity is fixed so that the energy spectrum satisfies E(k) = E(k(c))(k/k(c))(-3) for k > k(c). This resulting forcing induces a rapid depletion of the energy cascade at k > k(c.) It is observed numerically that the model reproduces turbulence energetics at k less than or equal to k(c) and statistics of two-point velocity correlations at scales r < lambda (Taylor microscale). Compared to a direct numerical simulation of R-lambda = 130 an equivalent run with the present model results in a gain of a factor 20 in CPU time.