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 $$h_{\ell }$$ , 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.