Combining deterministic and statistical approaches to compute two-dimensional turbulent flows with walls
Marie Farge, Nicholas Kevlahan, Claude Bardos, Kai Schneider · Birkhäuser Basel eBooks · 1999
We are searching for the best approximation to compute fully-developed two-dimensional turbulent flows. Fluid mechanics is governed by the Navier-Stokes equations, which are entirely deterministic. Fully-developed turbulence corresponds to very large Reynolds number flows (for which the micro-scale Reynolds number Re is larger than 10 4 ) and is the regime where the nonlinear advective term of Navier-Stokes equations strongly dominates the linear dissipative term. In this limit, the solutions to the Navier-Stokes equations are highly chaotic and we are unable to integrate them. Therefore, in order to compute fully-developed turbulent flows we need to combine a deterministic numerical integration with a statistical model. In this paper we propose a possible solution to this problem, based on the wavelet representation. ‘Although this may seem a paradox, all exact science is dominated by the idea of approximation’ (Bertrand Russell). These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.