Large eddy simulation of stably stratified turbulence

Stable stratification turbulence, as a common phenomenon in atmospheric and oceanic flows, is an important mechanism for numerical prediction of such flows. In this paper the large eddy simulation is utilized for investigating stable stratification turbulence numerically. The paper is expected to provide correct statistical results in agreement with those measured in the atmosphere or ocean. The fully developed turbulence is obtained in the stable stratification fluid by large eddy simulation with different...     

Phenomenology of two-dimensional stably stratified turbulence under large-scale forcing

In this paper, we characterise the scaling of energy spectra, and the interscale transfer of energy and enstrophy, for strongly, moderately and weakly stably stratified two-dimensional (2D) turbulence, restricted in a vertical plane, under large-scale random forcing. In the strongly stratified case, a large-scale vertically sheared horizontal flow (VSHF) coexists with small scale turbulence. The VSHF consists of internal gravity waves and the turbulent flow has a kinetic energy (KE) spectrum that follows an approximate k^?3 scaling with zero KE flux and a robust positive enstrophy flux. The spectrum of the turbulent potential energy (PE) also approximately follows a k^?3 power-law and its flux is directed to small scales. For moderate stratification, there is no VSHF and the KE of the turbulent flow exhibits Bolgiano–Obukhov scaling that transitions from a shallow k^?11/5 form at large scales, to a steeper approximate k^?3 scaling at small scales. The entire range of scales shows a strong forward enstrophy flux, and interestingly, large (small) scales show an inverse (forward) KE flux. The PE flux in this regime is directed to small scales, and the PE spectrum is characterised by an approximate k^?1.64 scaling. Finally, for weak stratification, KE is transferred upscale and its spectrum closely follows a k^?2.5 scaling, while PE exhibits a forward transfer and its spectrum shows an approximate k^?1.6 power-law. For all stratification strengths, the total energy always flows from large to small scales and almost all the spectral indicies are well explained by accounting for the scale-dependent nature of the corresponding flux.     

Preferential concentration of heavy particles in stably stratified turbulence

The effect of preferential concentration of heavy particles in a homogeneous stably stratified turbulent flow is studied by means of direct numerical simulations. Particle distributions show different clustering patterns in horizontal and vertical directions, thereby representing the anisotropy of the flow. Preferential concentration in stably stratified turbulence can be quantified using 2D and 3D radial distribution functions and the correlation dimension D2. With increasing stratification strength, the effect of preferential concentration decreases. Furthermore, it is found that in stably stratified turbulence preferential accumulation is enhanced when gravitational forces act on heavy particles.     

Surface tension driven flow on a thin reaction front

Surface tension driven convection affects the propagation of chemical reaction fronts in liquids. The changes in surface tension across the front generate this type of convection. The resulting fluid motion increases the speed and changes the shape of fronts as observed in the iodate-arsenous acid reaction. We calculate these effects using a thin front approximation, where the reaction front is modeled by an abrupt discontinuity between reacted and unreacted substances. We analyze the propagation of reaction fronts of small curvature. In this case the front propagation equation becomes the deterministic Kardar-Parisi-Zhang (KPZ) equation with the addition of fluid flow. These results are compared to calculations based on a set of reaction-diffusion-convection equations.     

Transitions in convection driven by a horizontal temperature gradient

We report the first detailed experimental study of transitions in the convection of a low Prandtl number fluid driven by a horizontal temperature gradient. The observed states, from time independent to one frequency with noise, to pure noise, to two frequencies with noise, can be related to the two secondary flows predicted for a cavity with large lateral extent, transverse stationary and longitudinal oscillatory rolls. Measured wavelengths and frequencies for the longitudinal rolls are in agreement with theoretical values, while the critical Grashof number is much higher than expected. Our results call for a new theoretical approach which takes both instability mechanisms into account.     

On the numerical modelling of the turbulent layer penetration into a stably stratified fluid

The improved numerical models based on the algebraic representations of the Reynolds stresses and fluxes and the use of the differential equation for the transfer of the dispersion of fluctuations of the vertical velocity component are considered for describing the processes of a vertical turbulent exchange in a stably stratified reservoir. Numerical modelling of the penetration of a turbulent layer of a mixed fluid in a linearly stratified medium under the action of constant shear stress is carried out. Computational results agree well with known experimental data and point to a substantial influence of the anisotropy of the flow on its main characteristics.     

The onset of thermomagnetic convection in stratified ferrofluids

A non-uniform magnetic field causes an inhomogeneous distribution of magnetic grains in colloidal magnetics (so-called ferrofluids). The rate of concentration equilibrium settling is very low owing to the smallness of the particle diffusion coefficient. Therefore, if the equilibrium does not have enough time to settle, a ferrofluid behaves like a pure fluid, so that stationary convection occurs and no other. In the opposite case, that is when some non-uniform concentration profile has been formed, an oscillatory instability arises. The latter can be effectively excited under the action of a low-amplitude time-periodic magnetic field of an appropriate frequency.     

Magnetic effect for electrochemically driven cellular convection

Hydrodynamic instability analogous to Rayleigh-Bénard convection is observed in an electrolytic solution between two parallel copper wire electrodes. The laser interferometric technique can reveal the dissipation structure created by the motion of the fluid, which is controlled electrochemically. It is shown that under the presence of horizontal magnetic field the roll cells move horizontally along the electrodes. The electrochemically driven convection is simply controlled and monitored by setting and measuring the electrochemical parameters and forms many kinds of spatiotemporal patterns, especially under the magnetic field. The phenomenon is modeled by considering a Boussinesq fluid under a concentration gradient. The stability of the resulting equations is studied by linear stability analysis. The time dependent nonlinear system is investigated numerically and the main features of the experimental response are reproduced.     

Water tank studies of plume rise and diffusion in a stably stratified layer under calm conditions

Summary Water tank experiments were conducted to investigate plume rise and diffusion of gases discharged from stacks under calm conditions with field wind velocity less than 0.4 m/s with stable thermal stratification. Similarity rules of scaled model experiments were obtained from nondimensional analysis of the fundamental equation. The densimetric Froude number of a plume and the buoyancy ratio of the plume and the atmosphere were varied during the water tank experiments while plume rise height, plume thickness, etc. were measured. It was found that the experimental results could be expressed in terms of these two dimensionless parameters. Papper presented at the GNFAO/EURASAP Meeting, Turin, September 1989. To speed up publication, proofs were not sent to the authors and were supervised by the Scientific Committee.     

Superdiffusive wave front propagation in a chemical active flow

We present experiments on the propagation of a wave front in a fluid forced by Faraday waves. The vertical periodical modulation of the acceleration induces flows in the system that modifies the Belousov-Zhabotinsky (BZ) chemical reaction dynamics. Phase waves spreading through standing waves with different symmetries results in superdiffusion. The anomalous diffusion is characterized in terms of a non-integer transport exponent which is compared with exponents resulting from tracer particles trajectories undergoing rapid, distant jumps called Lévy flights.     

Dynamics of local density perturbation in stably stratified fluid: Results of numerical experiments

Linear and nonlinear numerical models of dynamics of local density perturbation in a stably stratified medium are constructed. The influence of viscosity on the process of generation and propagation of internal waves generated by the local density perturbation in a pycnocline is evaluated. The problem on the dynamics of local density perturbation in the presence of wave background is considered.     

Evolution of melt convection in a liquid metal driven by a pulsed electric current

Gain refinement in metal alloy can be achieved by applying an electric current pulse (ECP) in solidification process. Forced flow inside the melt has been proved to be a key role in grain refinement. In this paper, the fluid flow inside Ga 20 wt%-In 12 wt%-Sn alloy induced by a damping sinusoidal ECP flowing through two parallel electrodes into the cylindrical melt was investigated by both experimental measurements and numerical simulations. Experimental results showed that a strong descending jet was induced beneath the bottom of electrodes under the application of ECP. Besides, it was found that flow intensity increases with the increase of amplitude, frequency, and pulse width, respectively. In order to unlock the formation mechanism of flow pattern and the relevance of flow intensity varied with electrical parameters, a three-dimensional numerical model under the application of ECP was established. Meanwhile, a comparative study was conducted by numerical simulations to reveal the distributions of electromagnetic fields and forced flow. Numerical results showed that the downward Lorentz force induced by ECP was concentrated beneath the bottom of electrodes. This downward Lorentz force induces a descending jet and provokes a global forced flow. According to numerical simulations, the evolution of flow intensity with electrical parameters under the application of ECP can be understood by the time averaged impulse of Lorentz force.     

Mixed convection boundary layer flow over a vertical surface embedded in a thermally stratified porous medium

The mixed convection boundary layer flow through a stable stratified porous medium bounded by a vertical surface is investigated. The external velocity and the surface temperature are assumed to vary as xm, where x is measured from the leading edge of the vertical surface and m is a constant. Numerical solutions for the governing Darcy and energy equations are obtained. The results indicate that the thermal stratification significantly affects the surface shear stress as well as the surface heat transfer, besides delays the boundary layer separation.     

Interfacial instabilities driven by chemical reactions

We investigate the interaction of thin films with chemical reactions by using as a model system a horizontal film with a reactive mixture of insoluble surfactants on its free surface. The reaction is modeled by a bistable/excitable FitzHugh-Nagumo (FHN) prototype. The chemical reaction can destabilize the film leading to the propagation of solitary pulses on its free surface.     

Pattern of flow around a sphere oscillating an neutrally buoyancy horizon in a continuously stratified fluid

The flow pattern produced by a sphere freely sinking to the neutral buoyancy horizon in a continuously stratified liquid is visualized with different schlieren methods. Dispersion of light in the brine produces colouring of conventional schlieren images when cutting diaphragm is at the edge of blade or thread and is used to form “natural rainbow” colour schlieren image. With sensitive schlieren methods a new structural element is distinguished in the flow pattern. That is a narrow jet covered with a high gradient envelope forming in the neighbourhood of the turning points on the trajectory of the oscillating body. Due to the interaction of the body with the emitted internal waves, and also with the wake and secondary jets, the rate of amplitude damping decreases with time