Kinetic energy and scalar spectra in high Rayleigh number axially homogeneous buoyancy driven turbulence

Abstract

Kinetic energy and scalar spectra from the measurements in high Rayleigh number axially homogeneous buoyancy driven turbulent flow are presented. Kinetic energy and concentration (scalar) spectra are obtained from the experiments wherein density difference is created using brine and fresh water and temperature spectra are obtained from the experiments in which heat is used. Scaling of the frequency spectra of lateral and longitudinal velocity near the tube axis is closer to the Kolmogorov-Obukhov scaling, while the scalar spectra show some evidence of dual scaling, Bolgiano-Obukhov scaling followed by Obukhov-Corrsin scaling. These scalings are also observed in the corresponding second order spatial structure functions of velocity and concentration fluctuations.

On the energy spectrum of rapidly rotating forced turbulence

“…For the anisotropic regime, we have also investigated the behaviour of the kinetic energy spectrum as a function of k ⊥ and k , which is convenient to showcase the manifestations of anisotropic behaviour of system. We observed that the kinetic energy spectrum varies as k −2.35±0.30 ⊥ in wavenumber range k ⊥ ∈ [1,6] for grid resolution of 512 3 , and scales as k −2.66±0.30 ⊥ in wavenumber range k ⊥ ∈ [1,11] for grid resolution of 1024 3 . The kinetic energy spectrum as a function of k shows power scalings for fixed k ⊥ , specifically, E(35, k ) ∼ k −0.52±0.12 in wavenumber range k ∈ [1,6] for grid resolution of 512 3 and E(35, k ) ∼ k −0.62±0.11 in wavenumber range k ∈ [1,11] for 1024 3 grid.…”

“…It is well known that, Kolmogorov 2,3 proposed an inertial range energy spectrum for homogeneous and isotropic 3D hydrodynamics turbulence: E(k) ∼ 2/3 k −5/3 , where is the constant energy dissipation rate. The Kolmogorov spectrum is quite universal and observed in plethora of other realistic settings, e.g., shear flows 4 , viscoelastic fluids 5 , buoyancy-driven systems 6,7 , and jet flows 8 . On the other hand, the energy cascade for the two-dimensional (2D) turbulence system shows dual behaviour [9][10][11][12][13] : an inverse cascade at large scales with E(k) ∼ k −5/3 and a forward cascade of enstrophy at relatively small scales with E(k) ∼ k −3 .…”

Ultimate heat transfer in ‘wall-bounded’ convective turbulence

“…In the permeable case with isothermal wall boundaries, different from the thermal convection without horizontal walls (Calzavarini et al. 2005; Pawar & Arakeri 2016), there exists a thermal conduction layer on the wall, where heat transfer by conduction dominates over that by convection. In figure 3( c , d ) are shown the mean temperature profiles as a function of , where is the thickness of a thermal conduction layer defined as All the profiles in the impermeable case collapse onto a single curve in the thermal conduction layer .…”

“…2005), and was experimentally investigated in a vertical tube connecting high- and low-temperature chambers (Gibert et al. 2006; Pawar & Arakeri 2016). The ultimate scaling has also been reported for the thermal convection in a cylindrical container radiatively heated from below, instead of conventional RBC heating (Lepot, Aumaître & Gallet 2018; Bouillaut et al.…”

Phenomenology of buoyancy-driven turbulence: recent results

“…Scientists have studied spectra of the velocity field and the scalar field in other buoyancy-driven systems. Pawar and Arakeri [87] performed experiment on the vertical tube described in section 2.8.3. They observed that the velocity field exhibitsk 5 3 spectrum, while the scalar spectrum is closer tok 7 5 .…”