Laboratory Realizations of Stratified Seamount-trapped Waves

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Abstract
The response of a uniformly rotating, uniformly stratified fluid surrounding an axisymmetric Gaussian seamount to barotropic, rectilinear tidal forcing at a range of subinertial frequencies is examined in a rotating table laboratory experiment. Flow is compared to numerical solutions for linear, stratified, seamount-trapped waves. As is appropriate to model the oceanic system at Fieberling Guyot, laboratory forcing is weak and motions have small Rossby number and small wave steepness, the ratio between particle orbit length and seamount circumference. The numerical solutions are used to explore properties of the gravest first azimuthal seamount-trapped wave mode, which is most likely to be observed in the ocean. Particles execute nearly circular orbits in a bottom-trapped region above the seamount summit. On the sloping flanks below, particles follow narrow elliptical paths oriented along seamount contours, and the azimuthal velocity is reversed relative to that above the summit. Force balances are described. Nonlinearities for a geophysically relevant wave steepness are strong only in a relatively thin bottom layer on the summit. Stokes drift is cyclonic near the summit, where it is strongest. Many dimensionless numbers of the laboratory flow are near their values at Fieberling Guyot, including the fractional seamount height, Burger number, off-seamount tidal excursion relative to seamount scale, amplification of the tide, normalized wave frequency, Rossby number, wave steepness, and ratio between mean drift and oscillation amplitude. The experimental aspect ratio is higher than in the ocean, yet has no effect on the frequency or structure of a linear wave for a given fractional height and Burger number. The laboratory Ekman number is orders of magnitude higher than oceanic estimates and damping is correspondingly strong, though the Ekman layer remains a small fraction of the total depth. Experimental data are consistent with the frequency, amplification structure, and velocity reversal with depth of the numerical solution for a linear stratified seamount-trapped wave using laboratory parameters. There is a more gradual reduction of amplification away from the summit than in the numerical prediction. This is likely associated with the exaggeration of viscous effects on laboratory scales, as is the broad resonance peak suggested by the frequency response. Significant anticyclonic particle drift indicates that an anticyclonic wave-rectified Eulerian mean overcomes the cyclonic Stokes drift.

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