Spectral Kinetic-Energy Fluxes in the North Pacific: Definition Comparison and Normal- and Shear-Strain Decomposition

The spectral kinetic-energy flux is an effective tool to analyze the kinetic-energy transfer across a range of length scales, also known as the kinetic-energy cascade. Three methods to calculate spectral energy fluxes have been widely used, hereafter the ΠA, ΠF, and ΠQ definitions. However, the relations among these three definitions have not been examined in detail. Moreover, the respective contribution of the normal strain and shear strain of the flow field to kinetic-energy cascade has not been estimated before. Here, we use the kinetic energy equations to rigorously compare these definitions. Then, we evaluate the spectral energy fluxes, as well as its decomposition into the normal-strain and shear-strain components for the North Pacific, using a dynamically consistent global eddying state estimate. We find that the data must be preprocessed first to obtain stable results from the ΠF and ΠQ definitions, but not for the ΠA definition. For the upper 500 m of the North Pacific, in the wavenumber ranges with inverse kinetic-energy cascade, both the normal and shear-strain flow components contribute significantly to the spectral energy fluxes. However, at high wavenumbers, the dominant contributor to forward kinetic-energy cascade is the normal-strain component. These results should help shed light on the underlying mechanism of inverse and forward energy cascades.