On the Evaluation of Seasonal Variability of the Ocean Kinetic Energy

The seasonal cycles of the mean kinetic energy (MKE) and eddy kinetic energy (EKE) are compared in an idealized flow as well as in a realistic simulation of the Gulf Stream (GS) region based on three commonly used definitions: orthogonal, nonorthogonal, and moving-average filtered decompositions of the kinetic energy (KE). It is shown that only the orthogonal KE decomposition can define the physically consistent MKE and EKE that precisely represents the KEs of the mean flow and eddies, respectively. The nonorthogonal KE decomposition gives rise to a residual term that contributes to the seasonal variability of the eddies, and therefore the obtained EKE is not precisely defined. The residual term is shown to exhibit more significant seasonal variability than EKE in both idealized and realistic GS flows. Neglecting its influence leads to an inaccurate evaluation of the seasonal variability of both the eddies and the total flow. The decomposition using a moving-average filter also results in a nonnegligible residual term in both idealized and realistic GS flows. This type of definition does not ensure conservation of the total KE, even if taking into account the residual term. Moreover, it is shown that the annual cycles of the three types of EKEs or MKEs have different phases and amplitudes. The local differences of the EKE cycles are very prominent in the GS off-coast domain; however, because of the spatial inhomogeneity, the area-mean differences may not be significant.