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The two-dimensional Navier-Stokes equations with a large-scale instability of the Kuramoto-Sivashinsky type: Numerical exploration on the connection machine. (English) Zbl 0742.76044
Summary: The two-dimensional Navier-Stokes equations with a large-scale instability of the Kuramoto-Sivashinsky type, describing marginally negative eddy-viscosity situations, is simulated on a connection machine \(CM-2\). Up to millions of time steps at the resolution \(256^ 2\) and tens of thousands at the resolution \(1024^ 2\) are performed. Advantage is taken of a novel complex variable form of the two-dimensional Navier- Stokes equations, which requires only two complex FFTs per time step. A linear growth phase, a disorganized inverse cascade phase, and a structured vortical phase are successively observed. In the vortical phase monopolar and multipolar structures are proliferating and display strongly depleted nonlinearities.

MSC:
76F99 Turbulence
76D05 Navier-Stokes equations for incompressible viscous fluids
65Y10 Numerical algorithms for specific classes of architectures
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