On the spatial structure of global modes in wake flow

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Abstract
Numerical simulations of wake flow behind an equilateral triangular obstacle are presented. The form of global modes and their dependence on the Reynolds number found in this study are in accordance with recent experimental results of Goujon–Durand et al. [Phys. Rev. E 50, 308 (1994)]. A scaling law of the amplitude oscillating with the fundamental frequency corresponding to the maximum of the global mode is found to agree with the Landau model in a range of Reynolds Re numbers larger than in previous studies. The position of the maximum amplitude of the fundamental modes scales as (Re−Re c )−1/2. The amplitude of the second harmonic of the longitudinal component of the velocity as well as the correction to the mean flow have different critical behavior than the velocity components oscillating with fundamental frequency. During linear growth the position of the maximum of the global modes is constant and moves only in the nonlinear regime. The effects of the blockage and the boundary conditions on the side walls on the form of the global modes are discussed.