Viscous spreading of an inertial wave beam in a rotating fluid

TL;DR

This paper experimentally investigates how inertial waves generated by an oscillating cylinder in a rotating fluid spread viscously, confirming the theoretical similarity solution for wave decay and spreading.

Contribution

It provides experimental validation of the viscous spreading and decay of inertial wave beams, aligning with a linear viscous theory under a quasi-parallel assumption.

Findings

Viscous spreading characterized by decay of velocity and vorticity envelopes.

Good agreement with the similarity solution of linear viscous theory.

Wave behavior consistent with classical analysis of internal waves.

Abstract

We report experimental measurements of inertial waves generated by an oscillating cylinder in a rotating fluid. The two-dimensional wave takes place in a stationary cross-shaped wavepacket. Velocity and vorticity fields in a vertical plane normal to the wavemaker are measured by a corotating Particule Image Velocimetry system. The viscous spreading of the wave beam and the associated decay of the velocity and vorticity envelopes are characterized. They are found in good agreement with the similarity solution of a linear viscous theory, derived under a quasi-parallel assumption similar to the classical analysis of Thomas and Stevenson [J. Fluid Mech. 54 (3), 495-506 (1972)] for internal waves.