Energy spectra and energy pathways of submesoscale coastal surface currents

This paper describes submesoscale kinetic energy (KE) spectra and KE fluxes of coastal ocean currents observed from multiple platforms of satellite altimeters, shore-based high-frequency radars, and shipboard acoustic Doppler current profilers. One-dimensional wavenumber energy spectra of coastal currents decay with a slope of approximately $k^{-2}$ at a wavenumber ($k$) of 0.5 km$^{-1}$. The spatial covariance of surface currents, equivalent to two-dimensional wavenumber spectra, has an anisotropic exponential shape with decorrelation length scales of {\it O}(10) km close to the shore and {\it O}(100) km offshore and principal axes nearly parallel with the shoreline, exhibiting coastal boundary effects on surface currents. The exponentially decaying spatial covariance function is consistent with submesoscale wavenumber spectra of a $k^{-2}$ decay slope. Moreover, the KE fluxes of coastal surface currents show that zero-crossing wavenumbers, at which the forward and inverse cascades occur, appear at a length scale of {\it O}(1) km and vary with time within a range of {\it O}(1) km depending on the dominance of driving forces (e.g., tides and wind stress). The KE fluxes of statistically decomposed surface currents based on relationships between forcing and responses in the frequency domain exhibit unique separation length scales (inverse of zero-crossing wavenumbers) of {\it O}(1) km and reflect the characteristics of the responses to individual forcing and their interactions at all spatial scales.