Abstract
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 2562 and tens of thousands at the resolution 10242 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.
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Gama, S., Frisch, U. & Scholl, H. The two-dimensional Navier-Stokes equations with a large-scale instability of the Kuramoto-Sivashinsky type: Numerical exploration on the Connection Machine. J Sci Comput 6, 425–452 (1991). https://doi.org/10.1007/BF01060033
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DOI: https://doi.org/10.1007/BF01060033