Near isotropic behavior of turbulent thermal convection

Abstract

We investigate the anisotropy in turbulent convection in a 3D box using direct numerical simulation. We compute the anisotropic parameter A = u 2 ⊥ /(2u 2 ), where u ⊥ and u are the components of velocity perpendicular and parallel to the buoyancy direction, the shell and ring spectra, and shell-to-shell energy transfers. We observe that the flow is nearly isotropic for the Prandtl number Pr ≈ 1, but the anisotropy increases with the Prandtl number. For Pr = ∞, A ≈ 0.3, thus anisotropy is not very significant even in extreme cases. We also observe that u feeds energy to u ⊥ via pressure. The computation of shell-to-shell energy transfers reveals that the energy transfer in turbulent convection is local and forward, similar to hydrodynamic turbulence. These results are consistent with the Kolmogorov's spectrum observed by Kumar et al. [Phys. Rev. E 90, 023016 (2014)] for turbulent convection.

Phenomenology of buoyancy-driven turbulence: recent results

“…For such experiments, the Taylor's hypothesis [56,94,105] is invoked to relate the frequency power spectrum E( f ) of the time series to the one-dimensional wavenumber spectrum E k ; ( ) this connection is under debate due to the absence of any constant mean velocity field [56,63]. Researchers [57,104,122,123] employ 2D particle image velocimetry for high-resolution visualization and computation of an approximate energy spectrum under the assumption of homogeneity and isotropy, which is not strictly valid in convection [75]. In summary, on the experimental front, there is no convergence on which of the two scaling, BO of KO, is valid.…”

“…Convective flows are expected to be anisotropic due to buoyancy; hence it is important to quantify anisotropy using the quantities that are dependent on the polar angle, the angle between zˆand k. For the same, we divide a wavenumber shell into rings [75]. The energy contents of the rings are called ring spectrum b E k, ( ), where β represents the sector index for the polar angles (for details see Nath et al [75]). The ring spectrum b E k, ( ), depicted in figure 9(b), shows that the flow is nearly isotropic, again similar to hydrodynamic turbulence.…”

“…Strong gravity makes the flow anisotropic. Surprisingly the turbulent flow in Rayleigh-Bénard convection (RBC) is nearly isotropic [75], while the SST is nearly isotropic when Richardson number is less than unity [53]. The stably-stratified flows become quasi two-dimensional for larger Richardson numbers.…”

Similarities between the structure functions of thermal convection and hydrodynamic turbulence

“…Velocity structure functions of turbulent convection Sun, Zhou, and Xia 25 and Zhou, Sun, and Xia 53 performed experiments of turbulent thermal convection and observed isotropy in regions away from walls. Using detailed numerical simulations, Nath et al 52 computed the modal energy of the inertial-range Fourier modes of turbulent convection as a function of polar angle Θ (angle between buoyancy direction and the wavenumber), and found it to be approximately independent of Θ. Thus, they showed that turbulent convection is nearly isotropic.…”

Scaling of a Fast Fourier Transform and a pseudo-spectral fluid solver up to 196608 cores

“…Another major feature of Tarang is its rich library for computing the energy transfers in turbulence, e.g., energy flux, shell-to-shell and ring-to-ring energy transfers, etc. [18,35,21]. Tarang also enables us to probe any point in the Fourier space or in the real space [28].…”