ONSET OF CONVECTION IN A ROTATING SEMIINFINITE FLUID - THEORY AND EXPERIMENT

We look at the development of the first plumes that emerge from a conv ectively unstable boundary layer by modelling the process as the insta bility of a fluid with a time-dependent mean density field The fluid i s semi-infinite, rotating, dissipative - characterized by the ratio of its viscosity to thermal diffusivity (Prandtl number Pr = nu/kappa) - and initially homogeneous. A constant destabilizing hear flux is appl ied at the boundary and the stability of the evolving density field is investigated both mathematically and in laboratory experiments. Using a ''natural convective'' scaling, we show that the behaviour of the n on-dimensional governing equations depends on Pr and the parameter gam ma = f(nu/B)(1/2), where f is the Coriolis parameter and B is the appl ied buoyancy flux. For the ocean, gamma approximate to 0.1, whilst for the atmosphere gamma approximate to 0.01. In the absence of rotation, the behaviour of the differential equations is independent of B, depe nding only on Pr. The boundary-layer Rayleigh number (Ra-bl) is also i ndependent of B. We show that Ra-bl, evaluated at the onset of rapid v ertical motion, depends on the form of the perturbation. Due to the ti me-dependence of the mean density field, analytic instability analysis is difficult, so we use a numerical technique. The governing equation s are transformed to a stretched vertical coordinate and their stabili ty investigated for a particular form of perturbation function. The mo del predictions are, for the ocean: instability time similar to 2 - 4 h, density difference similar to 0.002 - 0.013 kg m(-3), boundary-laye r thickness similar to 50 - 75 m and horizontal scale similar to 200 - 300 m; and for the atmosphere: instability time similar to 10 min, te mperature difference similar to 2.0 - 3.0 degrees C, boundary-layer th ickness similar to 400 - 500 m and horizontal scale similar to 1.5 - 2 .0 km. Laboratory experiments are performed to compare with the numeri cal predictions. The time development of the mean field closely matche s the assumed analytic form. Furthermore, the model predictions of the instability timescale agree well with the laboratory measurements. Th is supports the other predictions of the model, such as the lengthscal es and buoyancy anomaly.