A new model of surface drift currents is constructed using the full nonlinear equations of motion. This model includes the balance between Coriolis forces due to the mean and wave-induced motions and the surface wind stresses. The approach used in the analysis is similar to the work by Craik & Leibovich (1976) and Leibovich (1977), but the emphasis is on the mean motion rather than the small-scale time-dependent part of the Langmuir circulation. The final result indicates that surface currents can be generated by both the direct wind stresses, as in the classical Ekman model, and the Stokes drift, derived from the surface wave motion, in an interrelated fashion depending on a wave Ekman number E defined as \[ E = \Omega/\nu_ek^2_0, \] where Ω is the angular velocity of the earth's rotation, νe, the eddy viscosity and k0, the wavenumber of the surface wave at the spectral peak. When E [Lt ] 1, the Langmuir mode dominates. When E [Gt ] 1, inertial motion results. The classical Ekman drift current is a special case even under the restriction E ≃ 1. On the basis of these results, a new model of the surface-layer movements for future large-scale ocean circulation studies is presented. For this new model both the wind stresses and the sea-state information are crucial inputs.

The inviscid centrifugal instability of slowly varying flows is shown to be asymptotically associated with the lowest-order spatial dependence of the basic flow satisfying Rayleigh's criterion. This result requires special attention for basic flows which reverse their direction. At the instant of reversal the growth rate of the disturbance bifurcates and the choice of the proper branch requires that viscous effects be taken into account within a conveniently small neighbourhood of the branch point. Previous results by Rosenblat (1968) are shown to be incorrect. Such results were based on overlooking the need for viscous effects to be accounted for within a neighbourhood of the bifurcation point. This led to a wrong choice of the path to be followed at bifurcation.

This paper is a summary of the Second Bat-Sheva Seminar on magnetohydrodynamic (MHD) Flows and turbulence. It was held in the University of the Negev, Israel, on 28-31 March 1978, with 64 participants from 7 countries. Reviews and research papers were presented on the general theory of MHD, MHD duct flows (with emphasis on novel aspects such as non-uniform fields and fluid properties, bends, free-surface effects and longitudinal diffusion), two-phase flows (especially those likely to occur in a liquid-metal generator), turbulence and instabilities, and electrically driven flows (with new results presented for the theory of laminar and turbulent flows in induction furnaces, and for the theory of thermo-electrically driven flows in transverse magnetic fields). One day of the conference was devoted to turbulence, mainly without magnetic fields, with reviews and new results presented on the theory and measurements of coherent structures, intermittency at high Reynolds number, methods of calculating shear flows, and measurement techniques. The seminar was a strange mixture of people and topics, which produced some interesting papers and some useful discussion.

The abridged Langrangian-history direct-interaction (ALHDI) approximation (Kraichnan 1966) and the strain-based abridged Lagrangian-history direct-interaction (SBALHDI) approximation (Kraichnan & Herring 1978) are integrated numerically for isotropic turbulence in two and three dimensions and compared with data. At moderate Reynolds numbers in three dimensions, comparison with the computer simulations by Orszag & Patterson (1972) shows that the ALHDI gives numerically excessive energy transfer in the dissipation range while the SBALHDI approximation displays satisfactory accuracy in all ranges. In two dimensions, both approximations are in reasonable agreement with the simulations of Herring et al. (1974), the ALHDI approximation showing the better accuracy of the two at low wavenumbers. At high wavenumbers the SBALHDI approximation again transfers less energy than the ALHDI approximation but the effect is less marked than in three dimensions and the two curves straddle the data. High Reynolds number integrations of both approximations in three dimensions agree well with the tidal-channel inertial- and dissipationrange data of Grant, Stewart & Moilliet (1962), the SBALHDI approximation yielding a somewhat larger value of Kolmogorov's constant than the ALHDI approximation. The origin of the difference in straining efficiency between the two approximations at high wavenumbers and of the dependence of this difference on dimensionality is exhibited by application to the stretching of small scales of a convected passive scalar field. In three dimensions the SBALHDI approximation gives markedly larger values of the constant in Batchelor's (1959) k−1 spectrum range than the ALHDI approximation and is in better agreement with experiment. The SBALHDI values of Batchelor's constant satisfy Gibson's (1968) lower bound while the ALHDI values do not.