A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer

A scale-dependent dynamic subgrid-scale model for large-eddy simulation of turbulent flows is proposed. Unlike the traditional dynamic model, it does not rely on the assumption that the model coefficient is scale invariant. T he model is based on a second test-filtering operation which allows us to d etermine from the simulation how the coefficient varies with scale. The sca le-dependent model is tested in simulations of a neutral atmospheric bounda ry layer. In this application, near the ground the grid scale is by necessi ty comparable to the local integral scale (of the order of the distance to the wall). With the grid scale and/or the test-filter scale being outside t he inertial range, scale invariance is broken. The results are compared wit h those from (a) the traditional Smagorinsky model that requires specificat ion of the coefficient and of a wall damping function, and (b) the standard dynamic model that assumes scale invariance of the coefficient. In the nea r-surface region the traditional Smagorinsky and standard dynamic models ar e too dissipative and not dissipative enough, respectively. Simulations wit h the scale-dependent dynamic model yield the expected trends of the coeffi cient as a function of scale and give improved predictions of velocity spec tra at different heights from the ground. Consistent with the improved diss ipation characteristics, the scale-dependent model also yields improved mea n velocity profiles.