Spatio-temporal stability analysis of linear arrays of 2D density stratified wakes and jets

Abstract

This paper investigates the spatio-temporal stability characteristics of multiple shear flow elements (wakes or jets) with density stratification. While the stability of single jets or wakes has been considered extensively, many applications exist where these canonical flow fields are aligned in multi-element configurations. A fundamental question is the relationship between the stability characteristics of a single element and the larger system. More fundamentally, this question involves the interaction of multiple regions of vorticity concentration and how they modify a system’s absolute stability as well as the manner in which density gradients influence the way these different regions of concentrated vorticity interact. This study presents a generalization of Yu and Monkewitz’s analysis [“The effect of nonuniform density on the absolute instability of two-dimensional inertial jets and wakes,” Phys. Fluids A 2, 1175 (1990)] for multiple jets and wakes, explicitly considering n = 2, 3, 4, and infinity elements. The velocity and density base profiles are parameterized by the density ratio, S, velocity shear ratio, λ, and the wake spatial separation parameter, L/D. The results show that the maximum absolute growth rate (ω0,i) exhibits a non-monotonic dependence on L/D. In addition, the most absolutely unstable mode switches between system-sinuous and system-varicose as the spatial separation parameter is varied, in agreement with prior experiments [I. Peschard and P. Le Gal, “Coupled wakes of cylinders,” Phys. Rev. Lett. 77, 3122 (1996)]. This transition in symmetry, as well as the specific L/D value at which a given mode dominates, can be approximately predicted using the resonant wave interaction model from Juniper et al. [“The effect of confinement on the stability of two-dimensional shear flows,” J. Fluid Mech. 565, 171 (2006)]. Furthermore, there are two distinct L/D regimes: a “near-wake regime” (L/D < ∼3) and a “far-wake regime.” In the near-wake regime, the system stability is a function of the number of elements, n, while in the far-wake regime, it is only the element spacing, not the number of elements that influences ω0,i.