Near - Inertial Waves in Shear

Internal Waves

For his Ph.D. research, Eric Kunze showed theoretically (Kunze JPO 1985; Fig. 1) and observationally (Kunze and Sanford 1984, 1986; Kunze 1986; Kunze and Lueck JPO 1986) that near-inertial waves are sensitive to rotation of the water (vorticity) as well as Earth’s rotation (Coriolis frequency). Near-inertial waves can be trapped in the negative vorticity regions of subinertial ocean currents such as found in fronts (Fig. 1) and eddies (Fig. 2). Trapped waves will encounter turning points where they reflect in the horizontal and critical-layers in the vertical (Figs. 1). At critical layers, their vertical wavelengths shrink, amplitudes increase and instabililty resulting in turbulence production expected (Fig. 3).

Fig. 1: Ray paths for near-inertial waves originating at the surface and propagating perpendicular to a southward frontal jet either from the west (a) or east (b). Waves originating in the negative vorticity side of the jet (–10-0 km) are trapped in the region of negative vorticity, reflecting from turning points in the horizontal and stalling at a critical layer in the vertical at the base of the region. Thin contours represent lines of constant velocity (isotachs) (from Kunze JPO 1985).

Fig. 2: Schematic illustrating a trapped near-inertial wave in the negative vorticity core of a Gulf Stream warm-core ring. As the wave approaches the base of the region of negative vorticity, its propagation is stalled at a critical layer where its vertical wavelength shrinks and its amplitude increases (solid and dotted profiles). Trapped near-energy energy can either be transferred to the ring’s anticyclonic flow (i), radiate away in untrapped waves (ii), or be lost to turbulence (iii). Observations suggests that turbulence is the energy sink (Fig. 4; Kunze et al. JPO 1995).

Fig. 3: Illustration of the behavior of ray paths (left panel) and velocity amplitudes (right panel) as a near-inertial wave approaches its critical layer at 380-m depth. In the right panel, the dashed wavy curve corresponds to north velocity and the solid wavy curve to east velocity so that the wave velocity vector is rotating clockwise with depth. This is a signature of downward energy propagation for near-inertial waves in the North hemisphere ().

 

Fig. 4: Comparison of vertical energy-flux CgzE (dots) with vertically integrated turbulent dissipation rate anomaly (black curve with gray uncertainties) as a function of depth in the negative-vorticity core of a Gulf Stream warm-core ring. The vertical convergence of the energy-flux is such as to match the turbulent dissipation rate, suggesting that trapped near-inertial wave energy is lost to turbulence (Fig. 2) (Kunze et al. JPO 1995).

Fig. 5: Observations of down- (CW) and upgoing (ACW) near-inertial energy across a southward flowing meander of the North Pacific Subtropical Front. Dramatically elevated downgoing energy is evident on the warm (negative vorticity) side of the front (from Kunze and Sanford JPO 1984).

Fig. 6: Vorticity normalized by Coriolis frequency ζ/f (upper panel), and down- (CW) and upgoing (ACW) near-inertial energy (lower panel) in a Gulf Stream warm-core ring. Downgoing energy is elevated in the region of negative vorticity (Kunze JPO 1986).

Fig. 7: Depth profiles of temperature T, east velocity u and north velocity v (leftmost panel), temperature T, salinity S and density σt (middle panel) and vertical shear magnitude (uz2 + vz2)1/2, buoyancy frequency N and inverse 20-m Richardson number Ri–1 = (uz2 + vz2)/N2 (right panel). The energetic velocity signature rotating clockwise with depth between 450-600 m (left panel) is a signature of a downgoing near-inertial wave stalling at its critical depth. Unstable 20-m Richardson numbers (right panel) are associated with this feature, implying shear instability and turbulence production (Kunze JPO 1986).

Fig 8: Sections of down- (CW) and upgoing (CCW) near-inertial energy in the upper (a) and lower (b) parts of the water column, azimuthal velocity vθ (c) and profile cross-section of isopycnals and near-inertial energy (d) in a Gulf Stream warm-core ring. Downgoing energy is elevated between 500-700 m depth at the base of the negative vorticity core of the ring (Kunze and Lueck JPO 1986).

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