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