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Register a new userEntrainment in dry and moist thermals
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Sivaramakrishnan Ravichandran
Publication date
2021
fields
Physics
and research's language is
English
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We study entrainment in dry thermals in neutrally and unstably stratified ambients, and moist thermals in dry-neutrally stratified ambients using direct numerical simulations (DNS). We find, in agreement with results of Lecoanet and Jeevanjee [1] that turbulence plays a minor role in entrainment in dry thermals in a neutral ambient for Reynolds numbers $Re < 10^4$ . We then show that the net entrainment rate increases when the buoyancy of the thermals increases, either by condensation heating or because of an unstably stratified ambient. This is in contrast with the findings of Morrison et al. [2]. We also show that the role of turbulence is greater in these cases than in dry thermals and, significantly, that the combined action of condensation heating and turbulence creates intense small scale vorticity, destroying the vortex ring that is seen in dry and moist laminar thermals. These findings suggest that fully resolved simulations at Reynolds numbers significantly larger than the mixing transition Reynolds number $Re = 10^4$ are necessary to understand the role of turbulence in the entrainment in growing cumulus clouds, which consist of a series of thermals rising and decaying in succession.
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Spark plasma discharges induce vortex rings and a hot gas kernel. We develop a model to describe the late stage of the spark induced flow and the role of the vortex rings in the entrainment of cold ambient gas and the cooling of the hot gas kernel. The model is tested in a plasma-induced flow, using density and velocity measurements obtained from simultaneous stereoscopic particle image velocimetry (S-PIV) and background oriented schlieren (BOS). We show that the spatial distribution of the hot kernel follows the motion of the vortex rings, whose radial expansion increases with the electrical energy deposited during the spark discharge. The vortex ring cooling model establishes that entrainment in the convective cooling regime is induced by the vortex rings and governs the cooling of the hot gas kernel, and the rate of cooling increases with the electrical energy deposited during the spark discharge.
We present experimental measurements of a wall-bounded gravity current, motivated by characterizing natural gravity currents such as oceanic overflows. We use particle image velocimetry and planar laser-induced fluorescence to simultaneously measure the velocity and density fields as they evolve downstream of the initial injection from a turbulent channel flow onto a plane inclined at 10$^circ$ with respect to horizontal. The turbulence level of the input flow is controlled by injecting velocity fluctuations upstream of the output nozzle. The initial Reynolds number based on Taylor microscale of the flow, R$_lambda$, is varied between 40 and 120, and the effects of the initial turbulence level are assessed. The bulk Richardson number $Ri$ for the flow is about 0.3 whereas the gradient Richardson number $Ri_g$ varies between 0.04 and 0.25, indicating that shear dominates the stabilizing effect of stratification. Kelvin-Helmholtz instability results in vigorous vertical transport of mass and momentum. We present baseline characterization of standard turbulence quantities and calculate, in several different ways, the fluid entrainment coefficient $E$, a quantity of considerable interest in mixing parameterization for ocean circulation models. We also determine properties of mixing as represented by the flux Richardson number $Ri_f$ as a function of $Ri_g$ and diapycnal mixing parameter $K_rho$ versus buoyancy Reynolds number $Re_b$. We find reasonable agreement with results from natural flows.
Gravity currents modify their flow characteristics by entraining ambient fluid, which depends on a variety of governing parameters such as the initial density, $Delta rho$, the total initial height of the fluid, $H$, and the slope of the terrain, $alpha$, from where it is released. Depending on these parameters, the gravity current may be designated as sub-critical, critical, or super-critical. It is imperative to study the entrainment dynamics of a gravity current in order to have a clear understanding of mixing transitions that govern the flow physics, the shear layer thickness, $delta_{u}$, and the mixing layer thickness, $delta_{rho}$. Experiments were conducted in a lock-exchange facility in which the dense fluid was separated from the ambient lighter fluid using a gate. As the gate is released instantaneously, an energy conserving gravity current is formed, for which the only governing parameter is the Reynolds number defined as $Re=frac{Uh}{ u}$, where $U$ is the front velocity of the gravity current, and $h$ is the height of the current. In our study, the bulk Richardson number, $Ri_{b}$=$frac{g^{}H}{U_{b}^{2}}$=1, takes a constant value for all the experiments, with $U_{b}$ being the bulk velocity of the layer defined as $U_{b}$=$sqrt{g^{}H}$. Simultaneous Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF) measurement techniques are employed to get the velocity and density statistics. A flux-based method is used to calculate the entrainment coefficient, E$_{F}$, for a Reynolds number range of $Reapprox$400-13000 used in our experiments. The result shows a mixing transition at $Reapprox$2700 that is attributed to the flow transitioning from weak Holmboe waves to Kelvin-Helmholtz type instabilities.
The entrainment of air by advancing contact lines is studied by plunging a solid plate into a very viscous liquid. Above a threshold velocity, we observe the formation of an extended air film, typically 10 microns thick, which subsequently decays into air bubbles. Exploring a large range of viscous liquids, we find an unexpectedly weak dependence of entrainment speed on liquid viscosity, pointing towards a crucial role of the flow inside the air film. This induces a striking asymmetry between wetting and dewetting: while the breakup of the air film strongly resembles the dewetting of a liquid film, the wetting speeds are larger by orders of magnitude.
Dry lakes covered with a salt crust organised into beautifully patterned networks of narrow ridges are common in arid regions. Here, we consider the initial instability and the ultimate fate of buoyancy-driven convection that could lead to such patterns. Specifically, we look at convection in a deep porous medium with a constant through-flow boundary condition on a horizontal surface, which resembles the situation found below an evaporating salt lake. The system is scaled to have only one free parameter, the Rayleigh number, which characterises the relative driving force for convection. We then solve the resulting linear stability problem for the onset of convection. Further exploring the non-linear regime of this model with pseudo-spectral numerical methods, we demonstrate how the growth of small downwelling plumes is itself unstable to coarsening, as the system develops into a dynamic steady state. In this mature state we show how the typical speeds and length-scales of the convective plumes scale with forcing conditions, and the Rayleigh number. Interestingly, a robust length-scale emerges for the pattern wavelength, which is largely independent of the driving parameters. Finally, we introduce a spatially inhomogeneous boundary condition -- a modulated evaporation rate -- to mimic any feedback between a growing salt crust and the evaporation over the dry salt lake. We show how this boundary condition can introduce phase-locking of the downwelling plumes below sites of low evaporation, such as at the ridges of salt polygons.
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