Applicability of Taylor's hypothesis in thermally driven turbulence

TL;DR

This study demonstrates that Taylor's hypothesis is valid in thermally driven turbulence with large-scale circulation, enabling the use of real space probes to accurately measure the energy spectrum in turbulent convection.

Contribution

The paper shows that Taylor's hypothesis can be applied in thermal convection with large-scale circulation, validated through numerical simulations and real space probe measurements.

Findings

Velocity field follows Kolmogorov's spectrum ($k^{-5/3}$).

Frequency spectrum from probes exhibits Kolmogorov's spectrum ($f^{-5/3}$).

Taylor's hypothesis is validated in the presence of large-scale circulation.

Abstract

In this paper, we show that in the presence of large-scale circulation (LSC), Taylor's hypothesis can be invoked to deduce the energy spectrum in thermal convection using real space probes, a popular experimental tool. We perform numerical simulation of turbulent convection in a cube and observe that the velocity field follows Kolmogorov's spectrum ($k^{-5/3}$). We also record the velocity time series using real space probes near the lateral walls. The corresponding frequency spectrum exhibits Kolmogorov's spectrum ($f^{-5/3}$), thus validating Taylor's hypothesis with the steady LSC playing the role of a mean velocity field. The aforementioned findings based on real space probes provide valuable inputs for experimental measurements used for studying the spectrum of convective turbulence.