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Register a new userLaboratory Investigation of Entrainment and Mixing in Oceanic Overflows
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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.
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We present a new physically-motivated parameterization, based on the ratio of Thorpe and Ozmidov scales, for the irreversible turbulent flux coefficient $Gamma_{mathcal M}= {mathcal M}/epsilon$, i.e. the ratio of the irreversible rate ${mathcal M}$ at which the background potential energy increases in a stratified flow due to macroscopic motions to the dissipation rate of turbulent kinetic energy. Our parameterization covers all three key phases (crucially, in time) of a shear-induced stratified turbulence life cycle: the initial, `hot growing phase, the intermediate energetically forced phase, and the final `cold fossilization decaying phase. Covering all three phases allows us to highlight the importance of the intermediate one, to which we refer as the `Goldilocks phase due to its apparently optimal (and so neither too hot nor too cold, but just right) balance, in which energy transfer from background shear to the turbulent mixing is most efficient. $Gamma_{mathcal M}$ is close to 1/3 during this phase, which we demonstrate appears to be related to an adjustment towards a critical or marginal Richardson number for sustained turbulence $sim 0.2-0.25$.
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.
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.
We provide a first-principles explanation of the renown phenomenological formula for the turbulent dissipation rate in the ocean which is known as the Finescale Parameterization. The prediction is based on the wave turbulence theory of internal gravity waves and on a new methodology devised for the computation of the associated energy fluxes. In the standard spectral representation of the wave energy density, in the two-dimensional vertical wavenumber - frequency domain, the energy fluxes associated with the steady state are found to be directed downscale in both coordinates, closely matching the Finescale-Parameterization formula in functional form and in magnitude. These energy transfers are composed of a `local and a `scale-separated contributions; while the former is quantified numerically, the latter is dominated by the Induced Diffusion process and is amenable to analytical treatment. Contrary to previous results indicating an inverse energy cascade from high frequency to low, at odds with observations, our analysis of all non-zero coefficients of the diffusion tensor predicts a direct energy cascade. Moreover, by the same analysis fundamental spectra that had been deemed `no-flux solutions are reinstated to the status of `constant-downscale-flux solutions. This is consequential for an understanding of energy fluxes, sources and sinks that fits in the observational paradigm of the Finescale Parameterization, solving at once two long-standing paradoxes that had earned the name of `Oceanic Ultraviolet Catastrophe.
We analyze analytically and numerically the scale invariant stationary solution to the internal wave kinetic equation. Our analysis of the resonant energy transfers shows that the leading order contributions are given (i) by triads with extreme scale separation and (ii) by triads of waves that are quasi-colinear in the horizontal plane. The contributions from other types of triads is found to be subleading. We use the modified scale invariant limit of the Garrett and Munk spectrum of internal waves to calculate the magnitude of the energy flux towards high wave numbers in both the vertical and the horizontal directions. Our results compare favorably with the finescale parametrization of ocean mixing that was proposed in [Polzin et al. (1995)].
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