Effects of enrichment of refined olive oil with phenolic compounds from olive leaves

The possibility of preparing olive oil, with the same nutritional value and stability characteristics found in virgin olive oil, by the enrichment of refined olive oil with olive leaf polyphenols was studied. To obtain antioxidant phenols similar to those found in virgin olive oil, these components were extracted from the leaves of several olive cultivars from the Northern region of Portugal, namely, Carrasca, Ripa, Negruche, Cordovil, Verdeal, Madural, and Bical cultivars, under several conditions. The concentration of a leaf extract required for addition to refined olive oil to obtain the same stability as virgin olive oil was determined. The extract from 1 kg of leaves was sufficient to fortify 50-320 L of refined olive oil to a similar stability as a virgin olive oil sample depending on the metal concentration of the oil, cultivar, and time of the year when the leaves were picked.

Lateral boundary contributions to wave-activity invariants and nonlinear stability theorems for balanced dynamics

The slow advective-timescale dynamics of the atmosphere and oceans is referred to as balanced dynamics. An extensive body of theory for disturbances to basic flows exists for the quasi-geostrophic (QG) model of balanced dynamics, based on wave-activity invariants and nonlinear stability theorems associated with exact symmetry-based conservation laws. In attempting to extend this theory to the semi-geostrophic (SG) model of balanced dynamics, Kushner & Shepherd discovered lateral boundary contributions to the SG wave-activity invariants which are not present in the QG theory, and which affect the stability theorems. However, because of technical difficulties associated with the SG model, the analysis of Kushner & Shepherd was not fully nonlinear. This paper examines the issue of lateral boundary contributions to wave-activity invariants for balanced dynamics in the context of Salmon's nearly geostrophic model of rotating shallow-water flow. Salmon's model has certain similarities with the SG model, but also has important differences that allow the present analysis to be carried to finite amplitude. In the process, the way in which constraints produce boundary contributions to wave-activity invariants, and additional conditions in the associated stability theorems, is clarified. It is shown that Salmon's model possesses two kinds of stability theorems: an analogue of Ripa's small-amplitude stability theorem for shallow-water flow, and a finite-amplitude analogue of Kushner & Shepherd's SG stability theorem in which the ‘subsonic’ condition of Ripa's theorem is replaced by a condition that the flow be cyclonic along lateral boundaries. As with the SG theorem, this last condition has a simple physical interpretation involving the coastal Kelvin waves that exist in both models. Salmon's model has recently emerged as an important prototype for constrained Hamiltonian balanced models. The extent to which the present analysis applies to this general class of models is discussed.