Shear Instability

Turbulence Production

Breaking of smallscale internal waves, particularly those near the inertial frequency f, are the main energy source for turbulence production in the stratified ocean interior. Internal waves become unstable on vertical scales of a meter or so 5-10% of the time when either (i) their vertical shear exceeds twice the stratification frequency {[(∂u/∂z)² + (∂v/∂z)²]^1/2 = V_z > 2N} or (ii) they lift heavy water over light to produce a density overturn. The former appears to dominate because near-inertial waves with large shear and little strain dominate the smallscale variance. This is known as Richardson number, or shear, instability. It is thought to take the form of a growing wave known as a Kelvin-Helmholtz billow which creates density overturns which then break down into turbulence proper (Fig. 1).

FIg. 1: Typical history of a turbulence patch from a growing instability (Kelvin-Helmholtz billow), breaking into turbulence which then decays. Also shown as the silhouettes are shear production u'w'U_z, buoyancy-flux w'b', dissipation rate ε, turbulent available potential energy APE' and background potential energy PE (a). Lower panels show the vertical path of a float through a heaving density field as it becomes turbulent (b), and in a density coordinate system (c) (from Sun et al. 1996 JPO).

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