Nonlinear Processes in Geophysical Fluid Dynamics

A Tribute to the Scientific Work of Pedro Ripa

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Thisvolumecontainsacollectionofpapersbyinternationalexpertsingeoph- ical ?uid dynamics, based upon presentations at a colloquium held in memory of Pedro Ripa on the ?rst anniversary of his untimely death. They review or present recent developments in hydrodynamic stability theory, Hamiltonian ?uid mechanics,balanceddynamics, waves,vortices,generaloceanographyand the physical oceanography of the Gulf ofCalifornia; all of them subjects in which Professor Ripamadeimportant contributions. His work, but also his friendly spiritandkindnesswerehighly regardedandappreciatedby colleagues and students alike around the world. This book is a tribute to his scienti?c legacy and constitutes a valuable reference for researchers and graduate s- dents interested in geophysical and general ?uid mechanics. Earlyin his career asa physicaloceanographer,Pedro Ripa made two la- mark contributions to geophysical ?uid dynamics. In 1981, he showed that the conservation of the potential vorticity is related to the invariance of the eq- tions of motion under the symmetry transformationsof the labels that identify the ?uid particles.
That is, potential vorticity conservation is a consequence, via Noether's theorem, of the particle re-labelling symmetry. Two years later he published a paper entitled "General stability conditions for zonal ?ows in a one-layer model on the beta-plane or the sphere", where he established nec- sary conditions for stability in the shallow water equations, nowadays known as "Ripa's Theorem. " This is one of the very few Arnol'd-like stability con- tions that goes beyond two-dimensional or quasi-geostrophic ?ow, and stands alongside other famous stability criteria in making the foundations of the ?eld.