Internal Waves

Near-Inertial Waves    |     Near-Inertial Waves in Shear

Internal waves or internal gravity waves resemble surface gravity waves in that they rely on a gravitational restoring force to induce oscillations across a density contrast. While surface waves ride a sharp density step between air and water, internal wave propagate in the much weaker continuous density stratification of the ocean (stratosphere and lakes too) (upper left in Fig. 1 below). As a result, internal waves propagate vertically as well as horizontally (upper central, Fig. 3) and have longer periods. While surface waves have periods of seconds, internal waves have periods ranging from about 1 hour (the buoyancy frequency N which depends on the density stratification and typically weakens with depth, upper right) to about 1 day (the Coriolis frequency f which varies with latitude from zero at the equator to 2π/(12 h) at the poles, upper right) (Fig. 2). The strongest energy and currents are found at the longest periods (near-inertial waves) and in internal waves generated by interaction of tidal currents with bottom topography. The distribution of energy with wave period and wavelength is remarkably uniform in the ocean. Unlike surface waves, in the vertical plane, the crests and troughs (phase) travel perpendicular to the energy (middle right) rather like a sidewinder rattlesnake. These waves can break to produce turbulence and mixing when either their shear exceeds twice the stratification (∂u/∂z > 2N, lower left and right) or when their vertical motions lift heavy water over light to create an unstable density profile (middle central). The former appears to be more important.

Fig. 1: Cartoon explaining ocean internal waves and internal wave breaking.

Fig. 2: Log-log frequency spectra for vertical velocity w from a subsurface float (Sun et al. JPO 1994) as compared to a kinematic model (GM). Variance is largest between the Coriolis frequency f and the buoyancy frequency N.

Fig. 3: Propagation of crests and troughs (bottom panel) and phase (central panel) as a function of distance (Kunze and Sanford JPO 1984).

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