X
Effects of Schmidt number on the short-wavelength instabilities in stratified vortices
Suraj Singh,
Published in Cambridge University Press
2019
Volume: 867

Pages: 765 - 803
Abstract
We present a local stability analysis to investigate the effects of differential diffusion between momentum and density (quantified by the Schmidt number ) on the three-dimensional, short-wavelength instabilities in planar vortices with a uniform stable stratification along the vorticity axis. Assuming small diffusion in both momentum and density, but arbitrary values for , we present a detailed analytical/numerical analysis for three different classes of base flows: (i) an axisymmetric vortex, (ii) an elliptical vortex and (iii) the flow in the neighbourhood of a hyperbolic stagnation point. While a centrifugally stable axisymmetric vortex remains stable for any , it is shown that can have significant effects in a centrifugally unstable axisymmetric vortex: the range of unstable perturbations increases when is taken away from unity, with the extent of increase being larger for than for . Additionally, for 1$]]>, we report the possibility of oscillatory instability. In an elliptical vortex with a stable stratification, is shown to non-trivially influence the three different inviscid instabilities (subharmonic, fundamental and superharmonic) that have been previously reported, and also introduce a new branch of oscillatory instability that is not present at . The unstable parameter space for the subharmonic (instability IA) and fundamental (instability IB) inviscid instabilities are shown to be significantly increased for , respectively. Importantly, for sufficiently small and large and 1$]], respectively, the maximum growth rate for instabilities IA and IB occurs away from the inviscid limit. The new oscillatory instability (instability III) is shown to occur only for sufficiently small
Journal Data powered by TypesetJournal of Fluid Mechanics Data powered by TypesetCambridge University Press 00221120 No
Concepts (19)
• Aerodynamics
• Growth rate
• Stability
• DIFFERENTIAL DIFFUSION
• INVISCID INSTABILITY
• LOCAL STABILITY ANALYSIS
• OSCILLATORY INSTABILITY
• STABLE STRATIFICATION
• Stratified flows
• TRANSVERSE PERTURBATION
• VORTEX INSTABILITY
• Vortex flow
• Computer simulation
• Flow stability
• FLUID MECHANICS
• Instability
• Numerical model
• Stratified flow
• Wavelength