Three-dimensional instabilities and optimal perturbations of a counter-rotating vortex pair in stratified flows

Unbalanced instabilities of rapidly rotating stratified shear flows

The linear stability of a rotating, stratified, inviscid horizontal plane Couette flow in a channel is studied in the limit of strong rotation and stratification. Two dimensionless parameters characterize the flow: the Rossby number ǫ, defined as the ratio of the shear to the Coriolis frequency and assumed small, and the ratio s of the Coriolis frequency to the buoyancy frequency, assumed to sa...

Two-dimensional model problem to explain counter-rotating vortex pair formation in a transverse jet

A two-dimensional model problem is used to study the evolution of the cross section of a transverse jet and the counter-rotating vortex pair CVP . The solution to the model problem shows deformation of the jet similar to that observed in a transverse jet, and also yields a CVP. These phenomena are explained in terms of the acceleration the jet experiences in the direction of the cross-flow, and...

Thin-tube vortex simulations for sinusoidal instability in a counter-rotating vortex pair

A thin-tube vortex method is developed to investigate the intrinsic instability within a counter-rotating vortex pair system and the e ects from the core size and the wavenumbers (or wavelengths). The numerical accuracy and the advantages of the scheme are theoretically estimated. A nearest-neighbour-image method is employed in this three-dimensional vortex simulation. Agreement with Crow’s ins...

Three-dimensional instabilities of a stratified cylinder wake

On the role of vortex stretching in energy optimal growth of three-dimensional perturbations on plane parallel shear flows

The three-dimensional linearized optimal energy growth mechanism, in plane parallel shear flows, is re-examined in terms of the role of vortex stretching and the interplay between the spanwise vorticity and the planar divergent components. For high Reynolds numbers the structure of the optimal perturbations in Couette, Poiseuille and mixing-layer shear profiles is robust and resembles localized...