Time-Dependent Eddy-Mean Energy Diagrams and Their Application to the Ocean

Insight into the global ocean energy cycle and its relationship to climate variability can be gained by examining the temporal variability of eddy–mean flow interactions. A time-dependent version of the Lorenz energy diagram is formulated and applied to energetic ocean regions from a global, eddying state estimate. The total energy in each snapshot is partitioned into three components: energy in the mean flow, energy in eddies, and energy temporal anomaly residual, whose time mean is zero. These three terms represent, respectively, correlations between mean quantities, correlations between eddy quantities, and eddy-mean correlations. Eddy–mean flow interactions involve energy exchange among these three components. The temporal coherence about energy exchange during eddy–mean flow interactions is assessed. In the Kuroshio and Gulf Stream Extension regions, a suppression relation is manifested by a reduction in the baroclinic energy pathway to the eddy kinetic energy (EKE) reservoir following a strengthening of the barotropic energy pathway to EKE; the baroclinic pathway strengthens when the barotropic pathway weakens. In the subtropical gyre and Southern Ocean, a delay in energy transfer between different reservoirs occurs during baroclinic instability. The delaymechanism is identified using a quasigeostrophic, two-layermodel; part of the potential energy in large-scale eddies, gained from the mean flow, cascades to smaller scales through eddy stirring before converting to EKE. The delay time is related to this forward cascade and scales linearly with the eddy turnover time. The relation between temporal variations in wind power input and eddy–mean flow interactions is also assessed.