A criterion to detect line plumes from velocity fields in turbulent convection

TL;DR

This paper introduces a new velocity-based criterion using horizontal divergence to detect line plumes in turbulent convection, avoiding temperature data and accurately predicting plume length across various Rayleigh and Prandtl numbers.

Contribution

A novel, physically motivated criterion based on horizontal divergence of velocity fields for detecting line plumes in turbulent convection.

Findings

The criterion accurately predicts total plume length across a wide range of Rayleigh numbers.

It estimates plume thickness comparable to temperature fluctuation thresholds.

Existing shear turbulence criteria are inadequate for turbulent convection detection.

Abstract

We present a simple, new criterion to extract line plumes from the velocity fields, without using the temperature field, in a horizontal plane close to the plate in turbulent convection. The existing coherent structure detection criteria from velocity fields, proposed for shear driven wall turbulence, are first shown to be inadequate for turbulent convection. Based on physical arguments, we then propose that the negative values of $\overline{\nabla_H}\cdot\overline{u}$, the horizontal divergence of the horizontal velocity field extracts the plume regions from the velocity field. The $\overline{\nabla_H}\cdot\overline{u}$ criterion is then shown to predict the total length of plumes correctly over a Rayleigh number range of $7.7\times 10^5\le Ra_w\le 1.43\times 10^9$ and a Prandtl number range of $3.96\le Pr\le 5.3$. The thickness of the plume region predicted by the present criterion is approximately same as that obtained by a threshold of RMS temperature fluctuations, $\sqrt{T'^2}=0.2 \Delta T$, where $\Delta T$ is the temperature drop across the fluid layer.