An investigation of the Helmholtz and wave-vortex decompositions on surface currents in a coastal region

Abstract

Recent efforts to observe sea surface height (SSH) fields at less than kilometer spatial resolution using various satellite missions have spurred interest in understanding how well balanced and unbalanced motions can describe the ocean surface current field at finer scales, particularly in coastal regions characterized by complex flows under multiple driving forces (e.g., tides, winds, and low-frequency signals). In this study, we investigated the Helmholtz physical decomposition and wave-vortex decomposition to delineate the balanced and unbalanced motions of coastal surface currents while considering their reasonable justifications individually. The observed and simulated coastal surface currents do not exhibit an evident decomposition of balanced and unbalanced motions when wave-vortex decomposition is applied. Wave-vortex decomposition may not always be valid in coastal regions in which (1) the isotropy, spatial homogeneity, temporal stationarity, and statistical zero-correlations of the current components may not be guaranteed, and (2) multiple geophysical signals and footprints of driving forces are present. In contrast, the stream function obtained from the Helmholtz physical decomposition can be used as a proxy for balanced motions when the variance of vertical currents is weak, except for near-inertial variance. We believe that the Helmholtz decomposition in the physical domain will provide better insights into the dynamical decomposition than that in the spectral domain and can be applied to the analysis of upper ocean dynamics, including the propagation of unbalanced motions and vertical and horizontal structures of ageostrophic currents. Based on our study, SSH fields that will be observed at a very high spatial resolution in upcoming satellite missions will complement ocean current fields at finer scales, particularly in coastal regions characterized by a complex flow geometry.