Unifying constitutive law of vibroconvective turbulence in microgravity

Abstract

The emergence of unified constitutive law is a hallmark of convective turbulence, i.e., $Nu \sim Ra^\beta$ with $\beta \approx 0.3$ in the classical and $\beta=1/2$ in the ultimate regime, where the Nusselt number $Nu$ measures the global heat transport and the Rayleigh number $Ra$ quantifies the strength of thermal forcing. In recent years, vibroconvective flows have been attractive due to its ability to drive flow instability and generate ``artificial gravity'', which have potential to effective heat and mass transport in microgravity. However, the existence of constitutive laws in vibroconvective turbulence remains unclear. To address this issue, we carry out direct numerical simulations in a wide range of frequencies and amplitudes, and report that the heat transport exhibits a universal scaling law $Nu \sim a^{-1} Re_\mathrm{os}^\beta$ where $a$ is the vibration amplitude, $Re_\mathrm{os}$ is the oscillational Reynolds number, and $\beta$ is the universal exponent. We find that the dynamics of boundary layers plays an essential role in vibroconvective heat transport, and the $Nu$-scaling exponent $\beta$ is determined by the competition between the thermal boundary layer (TBL) and vibration-induced oscillating boundary layer (OBL). Then a physical model is proposed to explain the change of scaling exponent from $\beta=2$ in the OBL-dominant regime to $\beta = 4/3$ in the TBL-dominant regime. We conclude that vibroconvective turbulence in microgravity defines a distinct universality class of convective turbulence. This work elucidates the emergence of universal constitutive laws in vibroconvective turbulence, and opens up a new avenue for generating a controllable effective heat transport under microgravity or even microfluidic environment in which gravity is nearly absent.