On the spatial evolution of centrifugal instabilities within curved incompressible mixing layers

Abstract

It is known that certain configurations which possess curvature are prone to a class of instabilities which their ‘flat’ counterparts will not support. The main thrust of the study of these centrifugal instabilities has concentrated on curved solid boundaries and their effect on the fluid motion. In this article attention is shifted towards a fluid-fluid interface observed within a curved incompressible mixing layer. Experimental evidence is available to support the conjecture that this situation may be subject to centrifugal instabilities. The evolution of modes with wavelengths comparable with the layer's thickness is considered within moderately curved mixing layers. The high Taylor/Görtler number régime is also discussed which characterizes the ultimate fate of the modes.

Mixing layer in open-channel junction flows

“…As explained by Liou (1994) or Otto et al (1996) in the case of curved mixing layers (as within curved conduits), the curvature of the flow leads to an additional, centrifugal, so-called Görtler instability. Following their terminology, if the fastest flow is located in the inner part of the curve, the mixing layer is "unstable" and both instabilities exist: the Kelvin-Helmholtz mode becomes more unstable, the Görtler mode becomes important and even other modes appear.…”

Centrifugal instabilities in curved compressible wakes

“…It is well known that the maximum scaled growth rate is given by consideration of the large-wavenumber limit of the inviscid Görtler problem ͑see the works of Denier et al 22 for boundary layers and Otto et al 6 for mixing layers͒. The vortex activity becomes localized in a narrow layer away from the wall.…”

“…5 OSO demonstrated that in a compressible mixing layer the centrifugal instabilities can also be observed for certain parameter regimes within the system for which the faster stream curves into a cooler slower stream. Such modes have no counterpart in the corresponding incompressible curved mixing-layer investigation by Otto et al, 6 and they were labeled as the "thermal modes." The work of OSO also indicated that different basic flow models would offer different predictions of the behavior of the Görtler modes within the same system.…”

Nonlinear centrifugal instabilities in curved free shear layers

“…Hu et al 11 and Liou, 14 concerned with the effect of the curvature on the inflectional Rayleigh modes, found that it appears to be small, although the curvature excites an unstable three-dimensional disturbance with the amplitude increasing as the streamwise wavenumber decreases. Otto et al, 18 through a combined analytical and numerical study, showed that the unstable modes are largely dependent on surface curvature. Otto et al 18 also employed numerical simulations to solve for a set of parabolic equations, where the wavenumber and the Görtler number were taken to be of oder one.…”

“…Otto et al, 18 through a combined analytical and numerical study, showed that the unstable modes are largely dependent on surface curvature. Otto et al 18 also employed numerical simulations to solve for a set of parabolic equations, where the wavenumber and the Görtler number were taken to be of oder one. They found that as the difference between the free-stream speeds increased, the layer became more susceptible to centrifugal instabilities.…”