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

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 \(h_{\ell }\), 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, \(\eta _{\ell }\), 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, \({\mathcal{A}}_{*} = \eta _{0}/h_{\ell }\), where \(\eta _{0}\) was the initial displacement of the air–water interface, and by the strength of the background rotation controlled by the Burger number, \({\mathcal{S}}\). We set the experiments to explore a transitional regime from moderate- to weak-rotational environments, \(0.65\le {\mathcal{S}} \le 2\), for a wide range of initial perturbations, \(0.05\le {\mathcal{A}}_{*}\le 1.0\). The evolution of \(\eta _{\ell }\) 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 \(T_{d}/T_{g}\approx 11\), a maximum value of \(T_{d}/T_{g}\approx 10^{3}\) and a minimum value of \(T_{d}/T_{g}\approx 5\). 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.