A conceptual framework for analysing the energetics of density-stratified Boussinesq fluid flows is discussed. The concept of gravitational available potential energy is used to formulate an energy budget in which the evolution of the background potential energy, i.e. the minimum potential energy attainable through adiabatic motions, can be explicitly examined. For closed systems, the background potential energy can change only due to diabatic processes. The rate of change of background potential energy is proportional to the molecular diffusivity. Changes in the background potential energy provide a direct measure of the potential energy changes due to irreversible diapycnal mixing. For open systems, background potential energy can also change due to boundary fluxes, which can be explicitly measured. The analysis is particularly appropriate for evaluation of diabatic mixing rates in numerical simulations of turbulent flows. The energetics of a shear driven mixing layer is used to illustrate the analysis.

We have performed three-dimensional linear stability analysis, based on Floquet theory, to study the stability of finite amplitude internal gravity waves. This analysis has been used to compute instability growth rates over a range of wave amplitudes and propagation angles, especially waves above and below overturning amplitude, and identifies several new characteristics of wave instability. Computation of instability eigenfunctions has allowed us to analyze the energetics of the instability and to clarify the paths of energy transfer from the base wave to the instability. We find that the presence of wave overturning has no qualitative effect on the wave instability, except for the limiting case when the wavenumber vector is vertical. Instabilities which are nearly two-dimensional are closely related to second-order wave–wave interactions. But the three-dimensional instabilities, more prominent at higher wave amplitudes, may be caused by higher order resonance interactions. The energetics of the instabilities range from being shear driven to being driven by ‘‘density gradient’’ production (the potential energy analog of ‘‘shear’’ production); this characteristic is strongly dependent on wave propagation angle and the three-dimensionality of the instability.

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A 90-year-old woman presented with 2 masses on the right lower eyelid. Excisional biopsy revealed 1 lesion to be Merkel cell carcinoma and the other to be invasive squamous cell carcinoma. The patient also had a prior history of basal cell carcinoma in the same eyelid. This case emphasizes the importance of careful pathologic examination of all eyelid lesions regardless of previous history.

The spreadsheet-based IOL power prediction model calculated an ideal distribution of IOLs to order for humanitarian cataract surgery. It is generalizable to missions of any size and should help planners minimize costs while ensuring excellent refractive outcomes.