Influence of the multipole order of the source on the decay of an inertial wave beam in a rotating fluid

TL;DR

This paper investigates how the multipole order of a source influences the decay of inertial wave beams in rotating fluids through theoretical analysis and experiments, revealing the role of conserved quantities in beam structure.

Contribution

It introduces a theoretical framework linking source multipole order to wave beam decay and validates it with experimental measurements using different wavemakers.

Findings

Monopole and dipole sources produce distinct wave beam decay behaviors.

The conserved flowrate along the beam determines the source type and decay characteristics.

Experimental results agree with theoretical predictions for beam structure and decay exponent.

Abstract

We analyze theoretically and experimentally the far-field viscous decay of a two-dimensional inertial wave beam emitted by a harmonic line source in a rotating fluid. By identifying the relevant conserved quantities along the wave beam, we show how the beam structure and decay exponent are governed by the multipole order of the source. Two wavemakers are considered experimentally, a pulsating and an oscillating cylinder, aiming to produce a monopole and a dipole source, respectively. The relevant conserved quantity which discriminates between these two sources is the instantaneous flowrate along the wave beam, which is non-zero for the monopole and zero for the dipole. For each source the beam structure and decay exponent, measured using particle image velocimetry, are in good agreement with the predictions.