Wake of inertial waves of a horizontal cylinder in horizontal translation

TL;DR

This study investigates the wake behind a horizontally translated cylinder in a rotating fluid, revealing stabilization effects, inertial wave patterns, and the applicability of existing models at low Rossby numbers.

Contribution

The paper provides a combined theoretical and experimental analysis of inertial wave wakes behind a translating cylinder in rotating fluids, highlighting stabilization mechanisms and model validation.

Findings

Rotation stabilizes the wake at high Reynolds numbers.

The wake forms a stationary inertial wave pattern at low Rossby numbers.

Quantitative agreement with Johnson's model at Ro < 0.3.

Abstract

We analyze theoretically and experimentally the wake behind a horizontal cylinder of diameter $d$ horizontally translated at constant velocity $U$ in a fluid rotating about the vertical axis at a rate $\Omega$. Using particle image velocimetry measurements in the rotating frame, we show that the wake is stabilized by rotation for Reynolds number ${\rm Re}=Ud/\nu$ much larger than in a non-rotating fluid. Over the explored range of parameters, the limit of stability is ${\rm Re} \simeq (275 \pm 25) / {\rm Ro}$, with ${\rm Ro}=U/2\Omega d$ the Rossby number, indicating that the stabilizing process is governed by the Ekman pumping in the boundary layer. At low Rossby number, the wake takes the form of a stationary pattern of inertial waves, similar to the wake of surface gravity waves behind a ship. We compare this steady wake pattern to a model, originally developed by [Johnson, J. Fluid Mech. 120, 359 (1982)], assuming a free-slip boundary condition and a weak streamwise perturbation. Our measurements show a quantitative agreement with this model for ${\rm Ro}\lesssim 0.3$. At larger Rossby number, the phase pattern of the wake is close to the prediction for an infinitely small line object. However, the wake amplitude and phase origin are not correctly described by the weak-streamwise-perturbation model, calling for an alternative model for the boundary condition at moderate rotation rate.