Physics and observational signatures of free, forced, and frictional stratified seamount‐trapped waves

Abstract

To interpret measurements at Cobb Seamount, the observational signatures in stratified seamount‐trapped waves, with emphasis on forcing and frictional influences, are demonstrated for bathymetry and stratification representing a typical midlatitude seamount. Inviscid waves propagate azimuthally with standing wave radial and vertical structure. This includes current ellipses parallel or perpendicular to isobaths with uncorrelated radial and azimuthal velocities, nearly horizontal depth regions within which currents rotate in time clockwise or counterclockwise, and velocity turning with depth alternately clockwise and counterclockwise in successive quarter periods. Waves are explained conceptually in terms of “stratified slope‐Kelvin waves” (plane, propagating, ƒ plane topographic Rossby waves in stratification over a planar sloping bottom). An inviscid stratified seamount‐trapped wave is a cross‐isobath (radial and vertical) mode, of equal amplitude stratified slope‐Kelvin waves propagating upslope and downslope, that resonates in the azimuthally reentrant waveguide of the sloping seamount sides. Cross‐isobath structure is controlled by (1) ray refraction by slope angle variations, (2) Airy function behavior near turning points where bottom slope decreases to the ratio between wave and buoyancy frequencies, and (3) geometric compression by cylindrical geometry. In a stationary forced damped wave maintained by ambient tidal currents against dissipation concentrated near the summit where currents are strongest, cross‐isobath standing wave structure is broken with rays carrying energy upslope dominating; currents propagate phase downward and outward in addition to azimuthally, have ellipses oriented across isobaths with positively correlated radial and azimuthal velocities, and are dominated by clockwise rotation in time and counterclockwise turning with depth.