Using a two-dimensional nonlinear numerical simulation of a (viscous) stratified shear layer, strong instabilities resulted from the resonant interaction of a long linearly neutrally stable wave and the corresponding fastest growing wave. This linearly fastest growing wave, with optimal initial conditions, grows initially at a rate five times that predicted by linear theory. With other initial conditions, the linearly fastest growing wave may actually decay. The possibility of this type of interaction is suggested by the weakly nonlinear theory (cf. Maslowe, 1977). This coupled system of fourth order nonl inear partial differential equations was solved using a modified pseudospectral scheme for the spatial variables, incorporating the use of fast Fourier transforms to calculate spatial derivatives, and a second order Adams-Bashforth scheme for the temporal derivatives . / Dans cette etude, en utilisant une simulation numerique nonlineaire a deux dimensions d'une couche stratifiee, decollee et visqueuse, on obtint des resultats interessants a partir des cas correspondant a l'interaction resonnante d'une onde longue a stabilite neutre et d'une onde courte qui croit la plus rapidement selon la theorie lineaire. En utilisant certaines conditions initiales, l'onde courte croit initialement a un taux cinq fois superieur a celui predit par la theorie lineaire. Avec d'autres conditions initiales l'onde courte decroit. La possibilite de ce genre d'interaction est predite par la theorie faiblement nonlineaire (voir Maslowe, 1977). Ce systeme couple aux equations nonlineaires du quatrieme ordre aux derivees partielles, est resolu par une methode pseudo-spectrale modifiee, pour les variables spatiales, et une methode Adams-Bashforth du second ordre pour les derivees temporelles. fr

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Thesis (Ph. D.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, and the Woods Hole Oceanographic Institution), 2003. / Includes bibliographical references (p. 145-148). / Oceanic observations indicate that abyssal mixing is localized in regions of rough topography. How locally mixed fluid interacts with the ambient fluid is an open question. Laboratory experiments explore the interaction of mechanically induced boundary mixing and an interior body of linearly stratified rotating fluid. Turbulence is generated by a vertically oscillating horizontal bar, located at middepth along the tank wall. The turbulence forms a region of mixed fluid which quickly reaches a steady state height and collapses into the interior. The mixed layer thickness ... is independent of the Coriolis frequency f. N is the buoyancy frequency, co is the bar frequency, and the constant, Y=1 cm, is empirically determined by bar mechanics. In initial experiments, the bar is exposed on three sides. Mixed fluid intrudes directly into the interior as a radial front of uniform height, rather than as a boundary current. Mixed fluid volume grows linearly with time ... The circulation patterns suggest a model of unmixed fluid being laterally entrained with velocity, e Nhm, into the sides of a turbulent zone with height hm and width Lf ... where Lf is an equilibrium scale associated with rotational control of bar-generated turbulence. In accord with the model, outflux is constant, independent of stratification and restricted by rotation ... Later experiments investigate the role of lateral entrainment by confining the sides of the mixing bar between two walls, forming a channel open to the basin at one end. A small percentage of exported fluid enters a boundary current, but the bulk forms a cyclonic circulation in front of the bar. As the recirculation region expands to fill the channel, it restricts horizontal entrainment into the turbulent zone. The flux of mixed fluid decays with time. / (cont.) ... The production of mixed fluid depends on the size of the mixing zone as well as on the balance between turbulence, rotation and stratification. As horizontal entrainment is shut down, longterm production of mixed fluid may be determined through much weaker vertical entrainment. Ultimately, the export of mixed fluid from the channel is restricted to the weak boundary current. / by Judith R. Wells. / Ph.D.