Session MD: Taylor-Couette and Richtmyer-Meshkov Instabilities

The strato-rotational instability

The linear stability of a Taylor Couette Flow, linearly stratified in the direction of the cylinders axis with a constant Brunt-V\"ais\"al\"a frequency $N$, is analysed by asymptotical, numerical and experimental methods. The marginal stability curve in the parameter plane $(\eta=R_i/R_o; \mu=\Omega_o/\Omega_i)$, where $R_i$ and $\Omega_i$ (resp. $R_o$ and $\Omega_o$) are the radius and angular velocity of the inner (resp. outer) cylinder, is obtained for various Froude number $F=\Omega_i/N$ and Reynolds number $Re= \Omega_i r_i^2/\nu$. A particular attention is paid to the infinite gap limit ($\eta=0$) for which an inviscid estimate for the critical $\mu$ for instability is derived theoretically. The instability mechanism is discussed using an asymptotical description for large axial perturbation wavenumbers. The numerical and theoretical results are compared to new experimental data obtained for large gaps.   

Convective and absolute instabilities in Taylor-Couette system with axial and radial through-flows

Imposing axial and/or radial flow in a Taylor-Couette system alters its stability. In the framework of linear convective and absolute stability analysis, analytical methods and numerical simulations are used to determine this impact on the destabilization of the laminar state. Although axisymmetric modes are selected for limited axial flows, non-axisymmetric modes are then found to become the most convectively unstable ones as the axial flow increases and the most absolutely unstable ones when axial and outward radial flows are combined. Non-axisymmetric convective and absolute modes exhibit opposite threads. These analytical predictions in terms of critical conditions and patterns are confirmed by numerical simulations using spectral methods and help to clarify previous experimental results.   

Mode transition in bubbly Taylor-Couette flow

The frictional drag acting on cylindrical surfaces in Taylor-Couette flow is significantly reduced by injection of small bubbles. This results in delayed mode transitions from the original scenario in pure fluid. In our study, the relationship between the drag reduction and the change of vortical structure is successfully measured by particle tracking velocimetry. In this system, three major patterns of bubble distribution are observed depending on Re numbers and gas flow rate; i.e., uniform, toroidal, and spiral modes. We found that the power gain of the drag reduction gets largest when the toroidal and the spiral modes coexist. Furthermore, Taylor vortex bifurcates and a pair of vortices coalesces when the flow switches between these two modes in time. Through this experiment, we can grasp how the bubbles affect the vortices to restrict the momentum exchange in the shear layer during the two-way interaction between two phases. This will yield to new universal understanding of drag reduction by means of small amount of bubbles.   

Boundary Slip Effects on the Linear Stability of Circular and Spiral Poiseuille Flow

In this work, we consider the effect of boundary slip on the linear stability of various internal flows having boundary curvature. For the case of annular flow, slip can have a small to moderate affect on the linear stability analysis, with results showing that if the linear stability analysis gives a finite transition for no-slip boundary conditions, then the addition of slip can have either a stabilizing or destabilizing effect on the flow depending on the radius ratio. The results also show that for fixed Knudsen number, there is a value of the radius ratio for which there is no difference between linear stability results with and without slip, and that this value of the radius ratio changes with Reynolds number as does the number of crossings (i.e., one crossing for a Reynolds number of zero and two for a Reynolds number of 100). As for the annular special case (i.e., Taylor-Couette flow with $\mu>\eta^2$), results show that relaxing the no-slip condition on the cylinder walls does not destabilize this flow (i.e., computations still give a critical value of infinity). Similar to these results, for circular Poiseuille flow (i.e., pipe flow) current results show that relaxing the no-slip boundary condition on the cylinder wall does not destabilize the flow.   

Experiments on the Ricthmyer-Meshkov instability with an imposed, random initial perturbation

A vertical shock tube is used to perform experiments on the Richtmyer-Meshkov instability with a three-dimensional random initial perturbation. A membrane-less flat interface is formed by opposed gas flows in which the light and heavy gases enter the shock tube from the top and from the bottom of the driven section. An air/SF$_{6}$ gas combination is used and an $M_{s} = 1.2$ incident shock wave impulsively accelerates the interface. Initial perturbations on the interface were created using an electromagnetic actuator located near the bottom of the shock tube. The actuator produces a vertical oscillation of the gas column within the shock tube and this motion generates small random three-dimensional perturbations on a flat mixing zone. Mie scattering is used to visualize the mixing zone. Light from a laser sheet is scattered by smoke particles seeded in the air. The laser sheet slices the shock tube trough the diagonal of the square test section in the vertical direction at a frequency of 6 kHz. Image sequences are captured by three high-speed CMOS video cameras, which cover the full visualization zone. Measurements of the integral penetration depth are obtained and are compared to existing models.   

Experimental investigation of the late late-time 2D Richtmyer-Meshkov instability

Experiments were performed in the University of Arizona 10 m vertical shock tube. The fluid interface is created by opposed gas flows of SF$_{6 }$entering from the bottom and air entering from the top. Oscillating the 89 mm square test section transversely forms an a single mode initial perturbation with 36 mm wavelength and 3.2 mm post-shock initial amplitude. A normal shock wave with M$_{s}$= 1.2 impulsively accelerates the interface. Mie scattering using smoke particles mixed in the air is used to visualize the flow. Data was recorded using four CMOS video cameras operating at 6 kHz. The four video cameras allow the acquisition of image sequences and thus multiple measurements from the same initial perturbation. This is a significant improvement over earlier experiments that were limited to the acquisition of a single image per experiment. The vortex cores can be tracked due to low smoke concentrations at their centers and are observed to move up and then down relative to the bubble. The average bubble and spike amplitude and growth rates measured from the experiments will be compared with current models.   

Linearized Navier-Stokes Solution of the Richtmyer-Meshkov Instability

Results are presented from a numerical investigation of the two-dimensional Richtmyer-Meshkov instability, using a linearization about a fully-resolved, 1-D numerical solution of the Navier-Stokes equations. An asymptotically-stable, non-dissipative, fourth-order finite-difference scheme is used with local grid refinement to properly resolve the internal structure of all shocks and the contact zone. Detailed results are shown for the case of a single fluid with constant viscosity and heat conductivity, $\rm{Pr} = 3/4$, and incident shock Mach number 1.2, across a range of contact-zone perturbation wavenumbers.   

DNS of Herringbone Streaks in Rotating Turbulence Near Curved Walls

Near-wall streaks are a hallmark of turbulence. In turbulence near curved rotating walls the streaks form intricate herringbone-like patterns. We demonstrate the near-wall herringbone streaks using Taylor-Couette turbulence. We report the first direct numerical simulations of herringbone streaks in normal and counter-rotating Taylor-Couette turbulence, and characterize several of their remarkable aspects.