Harvard Climate Seminar
The Department of Earth and Planetary Sciences and the Paulson School of Engineering and Applied Sciences present "Baroclinic Instability over Topography: Unstable at Any Wavenumber" with Joe Pedlosky, Woods Hole Oceanographic Institute.
Abstract: The instability of an inviscid, baroclinic vertically sheared current of uniform potential vorticity, flowing along a uniform topographic slope, becomes linearly unstable at all wave numbers if the flow is in the direction of propagation of topographic waves. The parameter region of instability in the plane of scaled topographic slope versus wavenumber then extends to arbitrarily large wavenumbers at large slopes. The weakly nonlinear treatment of the problem reveals the existence of a nonlinear enhancement of the instability close to one of the two boundaries of this parametrically narrow unstable region. Since the domain of instability becomes exponentially narrow for large wavenumber it is unclear how applicable the results of the asymptotic, weakly nonlinear theory is since it must be limited to a region of small supercriticality. This question is pursued in that parameter domain through the use of a truncated model in which the approximations of weakly nonlinear theory are avoided. This more complex model demonstrates that the linearly most unstable wave in the narrow wedge in parameter space is nonlinearly stable and that the region of nonlinear destabilization is limited to a tiny region near one of the critical curves rendering both the linear and nonlinear growth essentially negligible. [Background reading]
Joe Pedlosky is a physical oceanographer at the Woods Hole Oceanographic Institution. He studied aeronautical engineering at MIT as an undergraduate and there fell in love with fluid dynamics. A life changing experience with at the Geophysical Fluid Dynamics program in the summer of 1960 put him on the path to a Ph.D. in meteorology at MIT under the supervision of Jule Charney. After his degree he taught in the applied math group at MIT from 1964-1968 when he moved to the Geosciences Department at the University of Chicago where he was involved in work in meteorology, oceanography and mantle dynamics (sea-floor spreading). In 1979 he transferred to the Woods Hole Oceanographic Institution where he continues as Emeritus Scientist. His work has centered on stability theory, ocean general circulation, and wave theory. He is an elected member of the National Academy of Sciences and the recipient of several professional awards including the Sverdrup medal from the American Meteorological Society and the Ewing medal from the American Geophysical Union.