Session H07: Flow Instability: Elastic and Complex Fluids and Geophysical (5:45pm - 6:30pm CST)

Fingers or fractures in viscoplastic gravity currents? Part II

Experiments in which viscoplastic fluid such as an aqueous suspension of Carbopol is extruded from a vent into a shallow ambient layer of water suffer a dramatic pattern-forming instability: if the Carbopol is extruded onto a dry surface, and the spreading dynamics is dominated by shear, the gravity current expands axisymmetrically. However, when the Carbopol is extruded onto a surface coated by an ambient layer of water, the outer radial edge becomes non-axisymmetrical and the current develops into a regular petal-like pattern. In view of a complementary theoretical analysis, one explanation for this phenomenon is an extensional flow instability of shear-thinning or yield-stress fluids, promoted by effective slip caused by water trapped underneath the Carbopol. However, the relatively early onset of the fractures and their elimination with an immiscible ambient fluid layer casts doubt on this explanation, suggesting instead that a different mechanism might be at play: the fracture under tension of the material, exacerbated by the presence of water.   

Fingers or fractures in viscoplastic gravity currents? Part I

Experiments in which viscoplastic fluid such as an aqueous suspension of Carbopol is extruded from a vent into a shallow ambient layer of water suffer a dramatic pattern-forming instability: if the Carbopol is extruded onto a dry surface, and the spreading dynamics is dominated by shear, the gravity current expands axisymmetrically. However, when the Carbopol is extruded onto a surface coated by an ambient layer of water, the outer radial edge becomes non-axisymmetrical and the current develops into a regular petal-like pattern. In this talk, a theoretical analysis is presented of freely sliding viscoplastic gravity currents to examine whether they suffer an extensional flow instability that may rationalize the experiments. The theoretical analysis confirms the existence of instability and suggests that it is particularly strong at late times, if the fluid has a yield stress or is sufficiently shear-thinning.   

Viscous Fingering in Viscoelastic Fluids: Numerical Simulations and Experiments

Polymer additives are widely used to alter the viscous fingering instability attributed mainly to the shear-rate dependent viscosity and elasticity. Present study aims to examine the role of these two rheological properties on the instability, simultaneously. The flow systems considered are: viscoelastic displacing Newtonian fluid (VN) and Newtonian displacing viscoelastic fluid (NV). Numerical simulations are performed using spectral method and Adams-Bashforth technique. To incorporate shear-thinning viscosity and elasticity, the White-Metzner model is adopted. Evaluation of concentration, mixing length and contact area shows that shear-thinning feature has a destabilizing effect while elasticity always stabilize the flow, irrespective of the flow system. In the experiments, polyethylene oxide (PEO) of different concentrations and molecular weights are used to incorporate non-Newtonian features. The VN system shows wider and less fingers as concentration of PEO increases while ramified fingers are observed in the NV system. The instability is further intensified for high molecular weight PEO, for similar viscosity contrast. The strong shear-thinning and elastic features contribute to the formation of ramified patterns and create locally stable/unstable regions in the flow field.   

A Model Experiment of the Quasi-Biennial Oscillation

The quasi-biennial oscillation is the periodic reversal of the wind in the lower equatorial stratosphere. The period of the oscillation is 28 months on average, and is not linked to the year duration. This wind is known to be generated by atmospheric waves, in particular internal gravity waves. We have set up an experiment which reproduces this phenomenon in the laboratory. This experiment is inspired by the one of Plumb and McEwan (1978). Linearly stratified salty water is located between two plexiglas cylinders. Internal gravity waves are generated in the fluid using 16 membranes located at the top of the fluid. Each membrane oscillates sinusoidally in the vertical direction, in opposition of phase with its two neighbors. When the amplitude of the forcing is large enough, a mean flow is generated, and oscillates with a period which is much larger than the wave period. This oscillation of the mean flow is similar to the one observed in the atmosphere. We report the first quantitative measurements of the saturated velocity of the mean flow. We show experimentally and theoretically that the QBO is generated by a bifurcation that is either supercritical or subcritical depending on the dominant dissipative process (Semin et al., Phys. Rev. Lett., 2018).   

Gravity Wave Instability Dynamics at High Reynolds Numbers

Internal gravity waves play a central role in the fluid dynamics of the earth's atmosphere. Comprehensive knowledge of the dynamics of gravity waves is crucial in numerical weather prediction, large-scale interactions, and climate and general circulation models. Direct numerical simulations of the Boussinesq form of the Navier-Stokes in conjunction with a Fourier spectral method are used to investigate the instability dynamics of monochromatic gravity waves. We focus on gravity wave instability dynamics for higher Reynolds numbers (up to 30k) and a broader range of intrinsic frequencies than considered previously. The morphology of the instability structures is studied through visualizations of the vorticity magnitude and $\lambda_2$ fields. These studies highlight structural differences associated with both changes to intrinsic frequency and Reynolds number.   

Effects of Schmidt number on small-scale instabilities in stratified vortices

Small-scale instabilities represent mechanisms that lead to complex and often three-dimensional flow features in vortical flows. We use the local stability approach, based on geometrical optics, to explore the effects of Schmidt number (Sc) on the small-scale instabilities in planar vortices with a stable stratification along their vortical axis. Assuming small diffusive coefficients, we investigate the effects of Schmidt number on three different instabilities: centrifugal, elliptic and hyperbolic. A centrifugally stable axisymmetric vortex remains stable in the presence of any out-of-plane stable stratification and arbitrary Sc, whereas, in a centrifugally unstable axisymmetric vortex, the region of instability is shown to increase as Sc is taken away from unity. In an elliptical vortex with a stable stratification, Sc away from unity is shown to non-trivially influence the subharmonic, fundamental and superharmonic inviscid instabilities, apart from introducing a new branch of oscillatory instability that is not present at Sc = 1.