Linear Stability Analysis of a Hypersonic Boundary Layer in Equilibrium and Non-Equilibrium

A non-parallel linear stability analysis which utilizes the assumptions made in the parabolized stability equations is applied to the buoyancy-driven flow in a differentially heated cavity. Numerical integration of the complete Navier–Stokes and energy equations is used to validate the non-parallel theory by introducing an oscillatory heat input at the upstream end of the boundary layer. In this way the stability properties are obtained by analysing the evolution of the resulting disturbances. The solutions show that the spatial growth rate and wavenumber are highly dependent on the transverse location and the disturbance flow quantity under consideration. The local solution to the parabolized stability equations accurately predicts the wave properties observed in the direct simulation whereas conventional parallel stability analysis overpredicts the spatial amplification and the wavenumber.

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Deep-water sediment wave formation: linear stability analysis of coupled flow/bed interaction

Journal of Fluid Mechanics ◽

10.1017/jfm.2011.171 ◽

2011 ◽

Vol 680 ◽

pp. 435-458 ◽

Cited By ~ 8

Author(s):

L. LESSHAFFT ◽

B. HALL ◽

E. MEIBURG ◽

B. KNELLER

Keyword(s):

Boundary Layer ◽

Stability Analysis ◽

Internal Wave ◽

Linear Stability ◽

Linear Stability Analysis ◽

Stokes Equations ◽

Wave Mode ◽

Bottom Current ◽

Field Observations ◽

Sediment Bed

A linear stability analysis is carried out for the interaction of an erodible sediment bed with a sediment-laden, stratified flow above the bed, such as a turbidity or bottom current. The fluid motion is described by the full, two-dimensional Navier–Stokes equations in the Boussinesq approximation, while erosion is modelled as a diffusive flux of particles from the bed into the fluid. The stability analysis shows the existence of both Tollmien–Schlichting and internal wave modes in the stratified boundary layer. For the internal wave mode, the stratified boundary layer acts as a wave duct, whose height can be determined analytically from the Brunt–Väisälä frequency criterion. Consistent with this criterion, distinct unstable perturbation wavenumber regimes exist for the internal wave mode, which are associated with different numbers of pressure extrema in the wall-normal direction. For representative turbidity current parameters, the analysis predicts unstable wavelengths that are consistent with field observations. As a key condition for instability to occur, the base flow velocity boundary layer needs to be thinner than the corresponding concentration boundary layer. For most of the unstable wavenumber ranges, the phase relations between the sediment bed deformation and the associated wall shear stress and concentration perturbations are such that the sediment waves migrate in the upstream direction, which again is consistent with field observations.

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Linear Stability Analysis for Manipulated Boundary-Layer Flows using Plasma Actuators

Seventh IUTAM Symposium on Laminar-Turbulent Transition - IUTAM Bookseries ◽

10.1007/978-90-481-3723-7_23 ◽

2009 ◽

pp. 153-158 ◽

Cited By ~ 15

Author(s):

A. Duchmann ◽

A. Reeh ◽

R. Quadros ◽

J. Kriegseis ◽

C. Tropea

Keyword(s):

Boundary Layer ◽

Stability Analysis ◽

Linear Stability ◽

Linear Stability Analysis ◽

Plasma Actuators ◽

Boundary Layer Flows

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