Scale dependence of near-inertial wave’s concentration in anticyclones

Abstract

Near-inertial waves (NIWs), pervasive and dominating the mixing process in the upper ocean, are observed to concentrate in anticyclones. Based on the NIW amplitude equation derived by Young & Ben Jelloul, which captures dispersion and effects of vortical flow’s advection and refraction, this work analytically and numerically studies the influence of scale on the concentration of NIWs. For a sinusoidal background shear flow, the exact solutions expressed as periodic Mathieu functions are approximated by a Gaussian envelope with Hermite polynomial oscillations to determine the distance to the anticyclones. Two dimensionless parameters control NIW’s dynamics: (i) h/Ψ, where h is a constant capturing the strength of wave dispersion and Ψ is the magnitude of the background streamfunction capturing the ratio of dispersion to refraction; (ii) LΨ/LM, the ratio between the spatial scales of background flow and NIWs, where LΨ and LM, respectively, captures the relative strength between advection and refraction. The refraction by the background flow leads to the concentration in the regions with negative vorticity, dispersion controls the variance of the wave packet, and the advection shifts the center of NIWs away from the peak of negative vorticity, which is scale-dependent. When the refraction effect dominates, i. e., small LΨ/LM, NIWs concentrate in anticyclones, and this concentration becomes stronger as h/Ψ decreases; when the advection effect dominates, i.e., large LΨ/LM, the NIW’s concentration is less obvious. Numerical simulations with backgrounds of sinusoidal shear, vortex quadrupoles and random vortices confirm these results. Considering the similarity between the NIW amplitude equation and the Schrödinger equation, we propose a new perspective that the combined effect of uncertainty relation and energy conservation leads to large-scale NIW’s concentration in anticyclones.