Evolution and decay of gravity wavefields in weak-rotating environments: a laboratory study

Abstract

Gravity waves are prominent physical features that play a fundamental role in transport processes of stratified aquatic ecosystems. In a two-layer stratified basin, the equations of motion for the first vertical mode are equivalent to the linearised shallow water equations for a homogeneous fluid. We adopted this framework to examine the spatiotemporal structure of gravity wavefields weakly affected by the background rotation of a single-layer system of equivalent thickness h , via laboratory experiments performed in a cylindrical basin mounted on a turntable. The wavefield was generated by the release of a diametral linear tilt of the air-water interface, , inducing a basin-scale perturbation that evolved in response to the horizontal pressure gradient and the rotation-induced acceleration. The basin-scale wave response was controlled by an initial perturbation parameter,  * = 0 ∕h , where 0 was the initial displacement of the air-water interface, and by the strength of the background rotation controlled by the Burger number, . We set the experiments to explore a transitional regime from moderate-to weak-rotational environments, 0.65 ≤  ≤ 2 , for a wide range of initial perturbations, 0.05 ≤  * ≤ 1.0. The evolution of was registered over a diametral plane by recording a laser-induced optical fluorescence sheet and using a capacitive sensor located near the lateral boundary. The evolution of the gravity wavefields showed substantial variability as a function of the rotational regimes and the radial position. The results demonstrate that the strength of rotation and nonlinearities control the bulk decay rate of the basin-scale gravity waves. The ratio between the experimentally estimated damping timescale, T d , and the seiche period of the basin, T g , has a median value of T d ∕T g ≈ 11 , a maximum value of T d ∕T g ≈ 10 3 and a minimum value of T d ∕T g ≈ 5. The results of this study are significant for the understanding the dynamics of gravity waves in waterbodies weakly affected by Coriolis acceleration, such as mid-to small-size lakes.

Dynamics of Internal Envelope Solitons in a Rotating Fluid of a Variable Depth

“…[24,11,14,12,20,18,25,31] and references therein). As is well-know, wave propagation in big lakes can be also affected by the Earth's rotation [5,7,28,32,29]. In particular, the dynamics of solitary waves has been investigated within the framework of the Ostrovsky equation and it has been established that they cannot propagate steadily due to the permanent radiation of small-amplitude long waves [23,9] (they can steadily propagate, however, being supported by a long background wave [10,27]).…”