Laboratory modeling of topographic Rossby normal modes

The physical modeling of topographic Rossby normal modes carried out at the “Coriolis” Rotating Platform (Grenoble), is presented. The basic feature of the bottom topography is a linear slope of 4.3 m×2 m delimited by two lateral walls. Since the studied motions are essentially barotropic, homogeneous water was used. Unsheared currents were generated by a simple movement of a wavemaker located in front of the topographic barrier. The conservation of potential vorticity for the currents flowing onto the channel slope produced Rossby waves: reflections at the lateral boundaries then led to the formation of propagating barotropic Rossby normal modes, whose frequencies and spatial structures were selected by the physical system. The currents were measured through the correlation imaging velocimetry (CIV) method, which allowed an extremely detailed synoptic map of the horizontal velocities in an area (13 m²) including the slope to be obtained every 30 s.A variety of experiments were performed in order to provide a complete process study in which the effect of different channel lengths and rotation periods could be tested. Two different lengths of the linear slope, 4.3 and 3.3 m, and rotation periods ranging from 30 to 50 s were considered. The qualitative analysis of the 2D current patterns, and the good agreement found between the measured eigenperiods and the periods obtained by means of a simple analytical model, show that in all cases the first Rossby normal mode was generated. Moreover, numerical simulations based on the shallow-water equations, for a geometry and paddle movements that match closely the experimental setup, allow to calibrate the analytical model and provide useful information on a discrepancy found between experimental and analytical eigenperiods due to an oscillation of the normal mode trajectory.