Dynamical analysis of mesoscale eddy-induced ocean internal waves using linear theories

This study aims to explore generation mechanisms of the ocean internal wave using the dynamical analysis methods based on linear theories.Historical cruise measurements and recent synthetic aperture radar (SAR) observations of mesoscale eddies with diameter of several tens of kilometers to hundreds of kilometers show that the internal wave packets with wavelength of hundreds of meters to kilometer exist inside the mesoscale eddies.This coexistence phenomenon and inherent links between the two different scale processes are revealed in the solutions of governing equations and boundary conditions for the internal wave disturbance with a horizontally slowly variable amplitude in a cylindrical coordinate system.The theoretical solutions indicate that the instability of eddy current field provides the dynamical mechanism to internal wave generation.The derived dispersion relation indicates that the internal wave propagation is modified by the eddy current field structure.The energy equation of the internal waves clearly shows the internal wave energy increment comes from the eddy.The theoretical models are used to explain the observation of the mesoscale eddy-induced internal waves off the Norwegian coast.The two-dimensional waveform solution of the anticyclonic eddy-induced internal wave packet appears as ring-shaped curves, which contains the typical features of eddy stream lines.The comparison of theoretical solutions to the structure of the internal wave packets on SAR image shows a good agreement on the major features.