When Does Eddy Viscosity Damp Subfilter Scales Sufficiently?

Large eddy simulation (LES) seeks to predict the dynamics of spatially filtered turbulent flows. The very essence is that the LES-solution contains only scales of size ≥Δ, where Δ denotes some user-chosen length scale. This property enables us to perform a LES when it is not feasible to compute the full, turbulent solution of the Navier-Stokes equations. Therefore, in case the large eddy simulation is based on an eddy viscosity model we determine the eddy viscosity such that any scales of size <Δ are dynamically insignificant. In this paper, we address the following two questions: how much eddy diffusion is needed to (a) balance the production of scales of size smaller than Δ; and (b) damp any disturbances having a scale of size smaller than Δ initially. From this we deduce that the eddy viscosity νe has to depend on the invariants q = ½tr(S^2) and r =−⅓tr(S^3) of the (filtered) strain rate tensor S. The simplest model is then given by νe = 3/2(Δ/π)^2|r|/q. This model is successfully tested for a turbulent channel flow (Reτ = 590).

Elementary Vortex Processes in Thermal Superfluid Turbulence

By solving pertinent mathematical models with numerical and computational methods, we analyze the formation of superfluid vorticity structures in a turbulent normal fluid with an inertial range exhibiting Kolmogorov scaling. We demonstrate that mutual friction forcing causes quantum vortex instabilities whose signature is spiral vortical configurations. The spirals expand until they accidentally meet metastable, intense normal fluid vorticity tubes of similar curvature and vorticity orientation that trap them by driving them towards low mutual friction sites where superfluid bundles are formed. The bundle formation sites are located within the tube cores, but, due to tube curvature and many-tube interaction effects, are displaced by variable distances from the tube centerlines as they follow the contours of the latter. We analyze possible implications of these processes in fully developed thermal superfluid turbulence dynamics

Application of Fast Parallel and Sequential Tree Codes to Computing Three-Dimensional Flows with the Vortex Element and Boundary Element Methods

A fast parallel oct-tree code originally developed for three-dimensional N-body gravitational simulations was modified into (1) a fast N-vortex code for viscous and inviscid vortex flow computations using the regularized vortex particle method (VEM), and (2) a fast N-panel code for solving boundary integral equations in potential flow aerodynamics using the boundary element method (BEM). The core of the fast tree code remains essentially unchanged between the different application codes: gravitation, VEM, BEM, etc. Only the modules that actually encode the physical model are changed. Particular attention is given to controlling the error introduced by the use of multipole expansions to represent the field produced by groups of elements, i.e., the tree code error. In particular, the acceptable error bound for use of any multipole expansion approximation is a run-time parameter. Program outputs include statistics on the errors for the field evaluation at all element locations. Problems in VEM..