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Register a new userTurbulence and heat transfer on a rotating, heated half soap bubble
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We use Direct Numerical Simulations to study the two-dimensional flow of a rotating, half soap bubble that is heated at its equator. The heating produces buoyancy and rotation generates a Coriolis forces in the fluid. However, due to the curved surface of the bubble, the buoyancy and Coriolis forces vary with latitude on the bubble, giving rise to rich flow behavior. We first explore the single-point properties of the flow, including the Reynolds and Nusselt numbers, mean fields, and Reynolds stresses, all as a function of latitude. For a given Rayleigh number, we observe a non-monotonic dependence on the Rossby number Ro, and large scale mean circulations that are strongly influenced by rotation. We then consider quantities that reveal the multiscale nature of the flow, including spectrums and spectral fluxes of kinetic and thermal energy, and enstrophy, and structure functions of velocity and temperature. The fluxes show that just a for nonbuoyant two-dimensional turbulence on a flat surface, there is an upscale flux of kinetic energy at larger scales (fed by buoyancy injection of turbulent kinetic energy at smaller scales), and a downscale flux of enstrophy at smaller scales. The kinetic energy spectrum and velocity structure functions are well described by Bolgiano-Obukhov (BO) scaling at scales where the effects of rotation are weak. The temperature structure functions do not, however, satisfy BO scaling in general, due to strong intermittency in the temperature field.
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3D-Particle Tracking (3D-PTV) and Phase Sensitive Constant Temperature Anemometry in pseudo-turbulence--i.e., flow solely driven by rising bubbles-- were performed to investigate bubble clustering and to obtain the mean bubble rise velocity, distributions of bubble velocities, and energy spectra at dilute gas concentrations ($alpha leq2.2$%). To characterize the clustering the pair correlation function $G(r,theta)$ was calculated. The deformable bubbles with equivalent bubble diameter $d_b=4-5$ mm were found to cluster within a radial distance of a few bubble radii with a preferred vertical orientation. This vertical alignment was present at both small and large scales. For small distances also some horizontal clustering was found. The large number of data-points and the non intrusiveness of PTV allowed to obtain well-converged Probability Density Functions (PDFs) of the bubble velocity. The PDFs had a non-Gaussian form for all velocity components and intermittency effects could be observed. The energy spectrum of the liquid velocity fluctuations decayed with a power law of -3.2, different from the $approx -5/3$ found for homogeneous isotropic turbulence, but close to the prediction -3 by cite{lance} for pseudo-turbulence.
We report heat transfer and temperature profile measurements in laboratory experiments of rapidly rotating convection in water under intense thermal forcing (Rayleigh number $Ra$ as high as $sim 10^{13}$) and unprecedentedly strong rotational influence (Ekman numbers $E$ as low as $10^{-8}$). Measurements of the mid-height vertical temperature gradient connect quantitatively to predictions from numerical models of asymptotically rapidly rotating convection, separating various flow phenomenologies. Past the limit of validity of the asymptotically-reduced models, we find novel behaviors in a regime we refer to as rotationally-influenced turbulence, where rotation is important but not as dominant as in the known geostrophic turbulence regime. The temperature gradients collapse to a Rayleigh-number scaling as $Ra^{-0.2}$ in this new regime. It is bounded from above by a critical convective Rossby number $Ro^*=0.06$ independent of domain aspect ratio $Gamma$, clearly distinguishing it from well-studied rotation-affected convection.
We use an extended laser Doppler technique to track optically the velocity of individual particles in a high Reynolds number turbulent flow. The particle sizes are of the order of the Kolmogorov scale and the time resolution, 30 microseconds, resolves the fastest scales of the fluid motion. Particles are tracked for mean durations of the order of 10 Kolmogorov time scales. The fastest scales of the particle motion are resolved and the particle acceleration is measured. For neutrally buoyant particles, our measurement matches the performance of the silicon strip detector technique introduced at Cornell University cite{Voth,MordantCornell}. This reference dynamics is then compared to that of slightly heavier solid particles (density 1.4) and to air bubbles. We observe that the acceleration variance strongly depends on the particle density: bubbles experience higher accelerations than fluid particles, while heavier particles have lower accelerations. We find that the probability distribution functions of accelerations normalized to the variance are very close although the air bubbles have a much faster dynamics.
We present an effective thermal open boundary condition for convective heat transfer problems on domains involving outflow/open boundaries. This boundary condition is energy-stable, and it ensures that the contribution of the open boundary will not cause an ``energy-like temperature functional to increase over time, irrespective of the state of flow on the open boundary. It is effective in coping with thermal open boundaries even in flow regimes where strong vortices or backflows are prevalent on such boundaries, and it is straightforward to implement. Extensive numerical simulations are presented to demonstrate the stability and effectiveness of our method for heat transfer problems with strong vortices and backflows occurring on the open boundaries. Simulation results are compared with previous works to demonstrate the accuracy of the presented method.
Energy flux plays a key role in the analyses of energy-cascading turbulence. In isotropic turbulence, the flux is given by a scalar as a function of the magnitude of the wavenumber. On the other hand, the flux in anisotropic turbulence should be a geometric vector that has a direction as well as the magnitude, and depends not only on the magnitude of the wavenumber but also on its direction. The energy-flux vector in the anisotropic turbulence cannot be uniquely determined in a way used for the isotropic flux. In this work, introducing two ansatzes, net locality and efficiency of the nonlinear energy transfer, we propose a way to determine the energy-flux vector in anisotropic turbulence by using the Moore--Penrose inverse. The energy-flux vector in strongly rotating turbulence is demonstrated based on the energy transfer rate obtained by direct numerical simulations. It is found that the direction of the energy-flux vector is consistent with the prediction of the weak turbulence theory in the wavenumber range dominated by the inertial waves. However, the energy flux along the critical wavenumbers predicted by the critical balance in the buffer range between in the weak turbulence range and the isotropic Kolmogorov turbulence range is not observed in the present simulations. This discrepancy between the critical balance and the present numerical results is discussed and the dissipation is found to play an important role in the energy flux in the buffer range.
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