A Ginzburg—Landau Model for Linear Global Modes in Open Shear Flows

The Ginzburg—Landau equation(GLE) can phenomenologically model several important features of non-equilibrium systems including those in fluid dynamics.Here we show that the linear GLE can be formulated such that it has the same Wentzel—Kramers—Brillouin(WKB) approximation as for the linear global stability problem in open shear flows.We use the GLE to model the linear global modes of different wakes and find that it can accurately capture the linear growth rate and frequency to first order in the WKB approximation.Furthermore,we find that it can also provide the shapes of the direct and adjoint eigenvectors and the regions of maximal structural sensitivity.The proposed model thus opens up new possibilities for GLE-based control strategies,as well as it makes accurate stability calculations possible even for some computationally intractable open shear flows.