ALBERT

Description: The formation and evolution of a diffusive interface in a stable salt-stratified layer cooled from above is studied in a two-dimensional geometry by direct numerical simulation. For a typical example with realistic parameters, the evolution of the flow is computed up to the moment where three layers can be distinguished. Focus is on the development of the first mixed layer. The convective velocity scaling as proposed by Hunt (1984) and previously proposed expressions for the interfacial heat flux (Huppert 1971; Fernando 1989a) are shown to correspond well with the results of the simulation. The evolution of the first layer can be well described by an entrainment relation based on a local balance between kinetic and potential energy with mixing efficiency γ. The new entrainment relation is shown to fit the numerical results well and an interpretation of γ in terms of the overall energy balances of the flow is given. Previously, two rival mechanisms have been proposed that determine the final thickness of the first layer (Turner 1968; Fernando 1987). One of the distinguishing itures of both mechanisms is whether a transition in entrainment regime - as the first layer develops - is a necessary condition for the mixed layer to stop growing. Another the presence of a buoyancy jump over the interface before substantial convection the second layer occurs. From the numerical results, we find a significant buoyancy jump even before the thermal boundary layer ahead of the first layer becomes unstable. Moreover, the convective activity in the second layer is too small to be able to stop the growth of the first layer. We therefore favour the view proposed by Fernando (1987) that a transition in entrainment regime determines the thickness of the first layer. Following this, a new one-dimensional model of layer formation is proposed. Important expressions within this model are verified using the results of the numerical simulation. The model contains two constants which are determined from the numerical results. The results of the new model fit experimental results quite well and the parameter dependence of the thickness of the first layer is not sensitive to the values of the two constants.

Description: The bifurcation structure of thermohaline-driven flows is studied within one of the simplest zonally averaged models which captures thermohaline transport: a Boussinesq model of surface-forced thermohaline flow in a two-dimensional rectangular basin. Under mixed boundary conditions, i.e. prescribed surface temperature and fresh-water flux, it is shown that symmetry breaking originates from a codimension-two singularity which arises through the intersection of the paths of two symmetry-breaking pitchfork bifurcations. The physical mechanism of symmetry breaking of both the thermally and salinity dominated symmetric solution is described in detail from the perturbation structures near bifurcation. Limit cycles with an oscillation period in the order of the overturning time scale arise through Hopf bifurcations on the branches of asymmetric steady solutions. The physical mechanism of oscillation is described in terms of the most unstable mode just at the Hopf bifurcation. The occurrence of these oscillations is quite sensitive to the shape of the prescribed fresh-water flux. Symmetry breaking still occurs when, instead of a fixed temperature, a Newtonian cooling condition is prescribed at the surface. There is only quantitative sensitivity, i.e. the positions of the bifurcation points shift with the surface heat transfer coefficient. There are no qualitative changes in the bifurcation diagram except in the limit where both the surface heat flux and fresh-water flux are prescribed. The bifurcation structure at large aspect ratio is shown to converge to that obtained by asymptotic theory. The complete structure of symmetric and asymmetric multiple equilibria is shown to originate from a codimension-three bifurcation, which arises through the intersection of a cusp and the codimension-two singularity responsible for symmetry breaking.

Description: It is known that the breakup by surface tension of a cylindrical interface containing a viscous liquid can be dampeu by axial motion of the underlying liquid and that for an annular film the capillary instability can be completely suppressed (disturbances of all wavelengths decay) by certain axial velocity profiles. Here, using a linear stability analysis, it is shown that complete stabilization can also occur for thermocapillary-driven axial motions. However, the influence of thermocapillary instabilities typically shrinks the window in parameter space where stabilization is found, relative to the isothermal case. The influence of Reynolds, surface tension, Prandtl, and Biot parameters on limits of stabilization is calculated using continuation techniques. It is observed that windows of stabilization first open with topological changes of the neutral curves in parameter space. A long-wave analysis unfolds the nature of the singularities responsible for several of these topological changes. The analysis also leads to the physical mechanism responsible for (longwave) stabilization and in certain cases to necessary conditions for (long-wave) stabilization. © 1991, Cambridge University Press. All rights reserved.