A ‘poor man’s Navier-Stokes equation’: Derivation and numerical experiments – the 2-D case. (English) Zbl 1081.76033

Summary: We present a systematic derivation of a discrete dynamical system directly from the two-dimensional incompressible Navier-Stokes equations via a Galerkin procedure and provide a detailed numerical investigation (covering more than \(10^7\) cases) of the characteristic behaviours exhibited by the discrete mapping for specified combinations of the four bifurcation parameters. We show that this simple 2-D algebraic map, which consists of a bilinearly coupled pair of logistic maps, can produce essentially any (temporal) behaviour observed either experimentally or computationally in incompressible Navier-Stokes flows as the bifurcation parameters are varied in pairs over their ranges of stable behaviours. We conclude from this that such discrete dynamical systems deserve consideration as sources of temporal fluctuations in synthetic-velocity forms of subgrid-scale models for large eddy simulation.


76F20 Dynamical systems approach to turbulence
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76F65 Direct numerical and large eddy simulation of turbulence
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