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Linear and Weakly Nonlinear Instability of Slightly Curved Shallow Mixing Layers

By Irina Eglīte and Andrejs Koliškins


The paper is devoted to linear and weakly nonlinear stability analysis of shallow mixing layers. The radius of curvature is assumed to be large. Linear stability problem is solved numerically using collocation method based on Chebyshev polynomials. It is shown that for stably curved mixing layers curvature has a stabilizing effect on the flow. Weakly nonlinear theory is used to derive an amplitude evolution equation for the most unstable mode. It is shown that the evolution equation in this case is the Ginzburg-Landau equation with complex coefficients. Explicit formulas for the calculation of the coefficients of the Ginzburg-Landau equation are derived. Numerical algorithm for the computation of the coefficients is described in detail

Topics: Linear stability, weakly nonlinear theory, method of multiple scales, Ginzburg-Landau equation, collocation method
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