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Nonlinear interactions in a rotating disk flow: From a Volterra model to the Ginzburg-Landau equation. (English) Zbl 1014.76094
Summary: The physical system under consideration is the flow above a rotating disk and its cross-flow instability, which is a typical route to turbulence in three-dimensional boundary layers. Our aim is to study the nonlinear properties of the wavefield through a Volterra series equation. The kernels of Volterra expansion, which contain relevant physical information about the system, are estimated by fitting two-point measurements via a nonlinear parametric model. We then describe the wavefield with the complex Ginzburg-Landau equation, and derive analytical relations which express the coefficients of Ginzburg-Landau equation in terms of the kernels of Volterra expansion. These relations must hold for a large class of weakly nonlinear systems, in fluid as well as in plasma physics.

MSC:
76U05 General theory of rotating fluids
76E07 Rotation in hydrodynamic stability
76F06 Transition to turbulence
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