# Similarities between the structure functions of thermal convection and hydrodynamic turbulence

## TL;DR

This study demonstrates that the velocity structure functions in turbulent thermal convection exhibit scaling similar to hydrodynamic turbulence, with non-Gaussian velocity increment distributions and differing energy flux and dissipation rates.

## Contribution

The paper reveals that thermal convection shares similar structure function scaling with hydrodynamic turbulence, supported by high-resolution simulations and analysis of probability distributions.

## Key findings

- Structure functions scale similarly to hydrodynamic turbulence
- Velocity increment distributions are non-Gaussian with wide tails
- Energy flux in convection differs from viscous dissipation rate

## Abstract

In this paper, we analyze the scaling of velocity structure functions of turbulent thermal convection. Using high-resolution numerical simulations, we show that the structure functions scale similar to those of hydrodynamic turbulence, with the scaling exponents in agreement with She and Leveque's predictions [Phys. Rev. Lett. 72, 336-339 (1994)]. The probability distribution functions of velocity increments are non-Gaussian with wide tails in the dissipative scales and become close to Gaussian in the inertial range. The tails of the probability distribution follow a stretched exponential. We also show that in thermal convection, the energy flux in the inertial range is less than the viscous dissipation rate. This is unlike in hydrodynamic turbulence where the energy flux and the dissipation rate are equal.