E5 Ocean Waves - Internal and Planetary

Topic

Internal gravity waves are oscillations that propagate within the stratified ocean itself, unlike surface waves, which oscillate solely at the air-water interface. The restoring force is buoyancy, and their frequency is bounded by two limits: the Coriolis parameter at the lower end and the Brunt-Väisälä frequency at the upper end; thus, an internal gravity wave can only exist at a frequency falling between these two values. Internal tidal waves—generated when the barotropic tide interacts with seafloor topography—are the primary energy source for the previously described diapycnal mixing in the ocean interior; this means that tides not only rise and fall along the coast but also stir the ocean's deeper, calmer interior.

Coastal Kelvin waves are gravity waves trapped against the coast by the Coriolis force itself; they propagate along the coastline with the coast to their right in the Northern Hemisphere and, by symmetry, to their left in the Southern Hemisphere. Their speed depends on water depth and—in the case of baroclinic Kelvin waves—on a reduced gravity determined by the density difference between layers, rather than the full gravity governing barotropic Kelvin waves. Barotropic waves are always faster than their baroclinic counterparts, meaning a coastal signal propagates much more rapidly when it involves the entire water column than when it is confined to a single layer. These coastal Kelvin waves are critical both for transmitting signals along a coastline and for the ocean's response to climate forcings, such as the El Niño-Southern Oscillation. Baroclinic Rossby waves, in contrast, are much longer-period disturbances—ranging from months to years—that propagate westward at speeds of between one-hundredth and one-tenth of a meter per second at mid-latitudes, though they move much faster at the equator, reaching speeds of two to three meters per second. It is this westward propagation that makes baroclinic Rossby waves the primary mechanism by which the deep ocean adjusts—with a lag of months or years—to changes in the atmospheric forcing acting upon it.

The expected behavior of all these internal gravity waves includes propagation speeds much slower than those of surface waves—ranging from one-tenth to one meter per second—along with vertical dispersion, wherein the wave reflects off both the pycnocline and the ocean floor itself. When this vertical dispersion specifically involves internal tidal waves, it generates what are known as internal tides: oscillations observed with amplitudes of ten to one hundred meters within the pycnocline and speeds of one-tenth to five-tenths of a meter per second; consequently, these internal tides silently move—far below the surface—quantities of water comparable to those displaced by the astronomical tide along the coast.

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