Session Z07: Flow Instability: Kelvin-Helmholtz (12:15pm - 1:00pm CST)

Further experiments and analysis on flow instability in eccentric annular channels

Gap instability (GI), an inviscid, Kelvin-Helmholtz type, was investigated experimentally and numerically in an eccentric annular channel with an inner-to-outer diameter ratio $d/D=0.5$ and a length of 320 hydraulic diameters, under conditions not sufficiently documented in the literature, namely, low and moderate eccentricities ($02000$. A stability map was constructed and an improved physical model of the gap vortex street was proposed.   

Anisotropy of symmetric Holmboe waves

Anisotropic fluctuation fields of symmetric Holmboe waves are investigated using single wavelength direct numerical simulations and multiple wavelength direct numerical simulations. The rightward and leftward propagating instabilities are separated with the Fourier transform enabling a direct comparison of the fluctuation fields between the simulations and linear stability analysis. Both the simulations and linear stability analysis show that horizontal and vertical velocity fluctuation pairs tilt towards the 2nd and 4th quadrants, indicating an anisotropic fluctuation field. This anisotropy is explained by tilted elliptical trajectories of particle orbits in Holmboe waves. As a result, a negative correlation between the horizontal and vertical velocity fluctuations is produced, i.e. negative Reynolds stresses on average. The vertical structure of the Reynolds stresses in the simulations and the laboratory experiments agree with the linear stability theory.   

The effects of Prandtl number on the nonlinear dynamics of Kelvin-Helmholtz instability in two dimensions

It is known that the pitchfork bifurcation of Kelvin-Helmholtz instability occurring at minimum gradient Richardson number $Ri_m \simeq 1/4$ in viscous stratified shear flows can be subcritical or supercritical depending on the value of the Prandtl number, $Pr$. Here we study stratified shear flow restricted to two dimensions at finite Reynolds number, continuously forced to have a constant background density gradient and a hyperbolic tangent shear profile, corresponding to the `Drazin model' base flow. Bifurcation diagrams are produced for fluids with $Pr=0.7$ (typical for air), 3 and $7$ (typical for water). For $Pr=3$ and $7$, steady billow-like solutions are found to exist for strongly stable stratification of $Ri_m$ up to $1/2$ and beyond. Interestingly, these solutions are not a direct product of a Kelvin-Helmholtz instability having too short a wavelength but can give rise to Kelvin-Helmholtz states of twice the wavelength through subharmonic bifurcations. These short-wavelength states can be tracked down to at least $Pr \approx 2.3$ and act as instigators of complex dynamics even in strongly stratified flows when the flow is unforced.