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A new method for computing the rate at which turbulent mixing builds potential energy in the ocean is described. The traditional approach has focused on the rate of change of the background potential energy associated with an adiabatically leveled state. We argue that when examining mixing events, so‐called “Thorpe” sorting yields a useful and local measure of diabatically generated potential energy and exhibits some advantages relative to adiabatic leveling. Among these, the open question about the leveling domain is avoided, the fate of kinetic energy during a mixing event is clearly defined, and the computational load associated with the leveling is relieved. The resultant kinetic energy equation leads to a natural definition of mixing efficiency and turbulent diffusivity in terms of sign definite viscous and diffusive contributions. Applications to 2‐D Kelvin Helmholtz instability demonstrate the utility of the procedure. We find an integrated efficiency of ≈ 0.15 for a Prandtl number of 1, and of ≈ 0.08 for a Prandtl number of 10. The larger is comparable to the classical value of 0.2 used frequently by the mixing community and smaller than that found in some recent simulations.

An important characteristic of geophysically turbulent flows is the transfer of energy between scales. Balanced flows pass energy from smaller to larger scales as part of the well‐known upscale cascade, while submesoscale and smaller scale flows can transfer energy eventually to smaller, dissipative scales. Much effort has been put into quantifying these transfers, but a complicating factor in realistic settings is that the underlying flows are often strongly spatially heterogeneous and anisotropic. Furthermore, the flows may be embedded in irregularly shaped domains that can be multiply connected. As a result, straightforward approaches like computing Fourier spatial spectra of nonlinear terms suffer from a number of conceptual issues. In this paper, we develop a method to compute cross‐scale energy transfers in general settings, allowing for arbitrary flow structure, anisotropy, and inhomogeneity. We employ Green's function approach to the kinetic energy equation to relate kinetic energy at a point to its Lagrangian history. A spatial filtering of the resulting equation naturally decomposes kinetic energy into length‐scale‐dependent contributions and describes how the transfer of energy between those scalestakes place. The method is applied to a doubly periodic simulation of vortex merger, resulting in the demonstration of the expected upscale energy cascade. Somewhat novel results are that the energy transfers are dominated by pressure work, rather than kinetic energy exchange, and dissipation is a noticeable influence on the larger scale energy budgets. We also describe, but do not employ here, a technique for developing filters to use in complex domains.