Dynamics of a reactive spherical particle falling in a linearly stratified fluid

TL;DR

This study investigates how reactive (melting) spheres fall in stratified fluids, revealing significant drag enhancement due to melting and characterizing the internal wave field generated, with implications for geophysical phenomena.

Contribution

It demonstrates the increased drag caused by melting in stratified fluids and analyzes the internal wave field generated by falling reactive spheres at high Reynolds and Froude numbers.

Findings

Melting causes greater drag enhancement than stratification alone.

Internal gravity waves are generated with a spectrum centered at the Br"unt-V"ais"al"a frequency.

Approximately 1% of potential energy converts into internal wave kinetic energy.

Abstract

Motivated by numerous geophysical applications, we have carried out laboratory experiments of a reactive (i.e. melting) solid sphere freely falling by gravity in a stratified environment, in the regime of large Reynolds ($Re$) and Froude numbers. We compare our results to non-reactive spheres in the same regime. First, we confirm for larger values of $Re$, the stratification drag enhancement previously observed for low and moderate Re (Magnaudet and Mercier, 2020). We also show an even more significant drag enhancement due to melting, much larger than the stratification-induced one. We argue that the mechanism for both enhancements is similar, due to the specific structure of the vorticity field sets by buoyancy effects and associated baroclinic torques, as deciphered for stratification by Zhang et al. (2019). Using particle image velocimetry, we then characterize the long-term evolution (at time $t \gg 1/N$ with $N$ the Br\"unt-V\"ais\"al\"a frequency) of the internal wave field generated by the wake of the spheres. Measured wave field is similar for both reactive and inert spheres: indeed, each sphere fall might be considered as a quasi impulsive source of energy in time and the horizontal direction, as the falling time (resp. the sphere radius) is much smaller than $N$ (resp. than the tank width). Internal gravity waves are generated by wake turbulence over a broad spectrum, with the least damped component being at the Br\"unt-V\"ais\"al\"a frequency and the largest admissible horizontal wavelength. About 1% of the initial potential energy of each sphere is converted in to kinetic energy in the internal waves, with no significant dependence on the Froude number over the explored range.