ALBERT

Description: Mean drift currents due to spatially periodic surface waves in a viscous rotating fluid are investigated theoretically. The analysis is based on the Lagrangian description of motion. The fluid is homogeneous, the depth is infinite, and there is no continuous energy input at the surface. Owing to viscosity the wave field and the associated mass transport will attenuate in time. For the non-rotating case the present approach yields the time-decaying Stokes drift in a slightly viscous ocean. The analysis shows that the drift velocities are finite everywhere. In a rotating fluid it is found that the effect of viscosity implies a non-zero net mass transport associated with the waves, as opposed to the result of no net transport obtained from inviscid theory (Ursell 1950). © 1983, Cambridge University Press. All rights reserved.

Description: For convection in a porous medium the dependence of the Nusselt number on the Rayleigh number is examined to sixth order using an expansion for the Rayleigh number proposed by Kuo (1961). The results show very good agreement with experiment. Additionally, the abrupt change which is observed in the heat transport at a supercritical Rayleigh number may be explained by a breakdown of Darcy's law. © 1972, Cambridge University Press. All rights reserved.

Description: Mean drift currents due to damped, progressive, capillary-gravity waves at an air/water interface are investigated theoretically. The analysis is based on a Lagrangian description of motion. Both media are assumed to be semi-infinite, viscous, homogeneous fluids. The system rotates about the vertical axis with a constant angular velocity 1/2f, where f is the Coriolis parameter. Owing to viscous effects, the wave field attenuates in time or space. Linear analysis verifies the temporal decay rate reported by Dore (1978a). The nonlinear drift velocities are obtained by a series expansion of the solutions to second order in a parameter e, which essentially is proportional to the wave steepness. The effect of the air on the drift current in the water is shown to depend on the values of the frequency co, wavenumber k, density p, and kinematic viscosity v through one single dimensionless parameter Q defined by [formula omitted] where subscripts 1 and 2 refer to the air and the water, respectively. Dynamically, the increased shear near the interface due to the presence of the air leads to a higher value of the virtual wave stress (Longuet-Higgins 1969). This yields a tendency towards a higher (Eulerian) mean drift velocity as compared to the free-surface case. For temporally damped waves, this stress, due to increased damping, effectively acts over a shorter period of time. Accordingly, the mean current associated with such waves tends to be larger for short times and smaller for large times than that obtained with a vacuum above the water. For spatially damped waves, the virtual wave stress becomes independent of time. The Coriolis force is then needed to balance the wave stress in order to avoid infinitely large drift velocities as too. Furthermore, assessment of realistic values for the turbulent eddy viscosities in the air and the ocean is shown to bring the results closer to those obtained for a vacuum/water system. © 1990, Cambridge University Press. All rights reserved.

Description: The mean, steady-state particle velocity in gravity-driven glacial flow over sinusoidal, sloping ground is computed using a Lagrangian description of motion. A Newtonian viscous fluid approximation is used for the ice. The glacier surface is free to move and is not subject to any stresses. At the bottom, the ice is frozen to the ground. The non-linear interaction between the basic downslope Poiseuille flow and the bottom corrugations yields a mean Lagrangian perturbation velocity that is always directed in the upslope direction near the ground. The requirement of mass balance imposes a mean negative surface slope in the corrugated region and an associated downslope perturbation flow in the upper part of the glacier. The no-slip condition at the wavy bottom induces a strong velocity shear in the ice, and particularly at the base. Analysis shows that the shear heating associated with shortwave perturbations could, in the case of a marginally frozen ground, lead to melting and subsequent sliding at wave crests along the bottom, while the ice stays frozen at the troughs. It is suggested that for glaciers the resulting high strain rates could lead to crevassing.