Browsing by Subject "Flow instability"

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Open Access
Linear and nonlinear stability of a quasigeostrophic mixing layer subject to a uniform background shear
(American Physical Society, 2019) Biancofiore, Luca; Umurhan, O. M.
The aim of this work is to shed light by revisiting, from the kernel-wave (KW) perspective, the breakdown of a quasigeostrophic (QG) mixing layer (or vortex strip or filament) in atmosphere under the influence of a background shear. The QG mixing layer is modeled with a family of quasi-Rayleigh velocity profiles in which the potential vorticity (PV) is constant in patches. From the KW perspective, a counterpropagating Rossby wave (CRW) is created at each PV edge, i.e., the edge where a PV jump is located. The important parameters of our study are (i) the vorticity of the uniform shear m and (ii) the Rossby deformation radius Ld, which indicates how far the pressure perturbations can vertically propagate. While an adverse shear (m<0) stabilizes the system, a favorable shear (m>0) strengthens the instability. This is due to how the background shear affects the two uncoupled CRWs by shifting the optimal phase difference towards large (small) wave number when m<0 (m>0). As a finite Ld is introduced, a general weakening of the instability is noticed, particularly for m>0. This is mainly due to the reduced interaction between the two CRWs when Ld is finite. Furthermore, nonlinear pseudospectral simulations in the nominally infinite-Reynolds-number limit were conducted using as the initial base flow the same quasi-Rayleigh profiles analyzed in the linear analysis. The growth of the mixing layer is obstructed by introducing a background shear, especially if adverse, since the vortex pairing, which is the main growth mechanism in mixing layers, is strongly hindered. Interestingly, the most energetic configuration is for m=0, which differs from the linear analyses for which the largest growth rates were found for a positive m. In the absence of a background shear additional modes are subharmonically triggered by the initial disturbance enhancing the turbulent character of the flow. We also confirm energy spectrum trends for broken-down mixing layers reported in the literature. We interpret the character of mixing-layer breakdown as being a phenomenological hybrid of Kraichnan's [R. H. Kraichnan, Phys. Fluids 10, 1417 (1967)] direct enstrophy cascade picture and the picture of self-similar vortex production.
Open Access
Spatiotemporal evolution of evaporating liquid films sheared by a gas
(American Physical Society, 2021-11-04) Mohamed, Omair A. A.; Dallaston, M. C.; Biancofiore, Luca
We study the spatiotemporal evolution of an evaporating liquid film sheared by a gas considering both inertial and thermal instabilities, the latter arising from a combination of evaporation and Marangoni effects. The shearing gas is modeled by imposing a constant shear stress applied along the liquid's interface. Following in the footsteps of Joo et al. [S. W. Joo et al., J. Fluid Mech. 230, 117 (1991)], long-wave theory is used to derive a Benney-like equation governing the temporal volution of the liquid interface under the effects of inertia, hydrostatic pressure, surface tension, thermocapillarity, evaporation, and gas shear. Linear stability theory is used to investigate the temporal and spatiotemporal characteristics of the flow, where it is found that the evaporation of the film promotes absolute instabilities and can cause convective-absolute transitions of the perturbations. It is also found that a strong enough counterflowing shearing gas can suppress the inertial instability, commonly known as the H mode, affirming similar conclusions found by previous studies for a strongly confined isothermal film. Additionally, our temporal stability analysis indicates that the thinning of the film reduces the phase speed of thermal perturbations, due to the increasing dominance of viscosity. However, our spatiotemporal analysis shows that the thinning of the film actually results in the growth of additional modes with higher group velocities resulting in faster contamination of the flow field. Moreover, the interface evolution equation is solved numerically to (i) simulate the film's interface evolution subject to finite perturbations and (ii) compare to the results of the linear stability analysis. We find qualitative agreement between the temporal dynamics of the linear and nonlinear instabilities. Our subsequent numerical nonlinear spatiotemporal stability analysis demonstrates that for weaker thermal instabilities, the wave-front dynamics are imposed by the nonlinearly saturated wave packet, while for stronger thermal instabilities, the wave-front dynamics are dictated by the linear dispersion relationship. We also study the effects of the dimensionless parameters on the rupture location and the time it takes for the fluid film to rupture. Finally, the shear stress's effect on the rupture mechanics of the film is studied using self-similarity analysis, where we identify the fate of the evolution equation's solutions.