This paper presents results obtained from a numerical solution to a stream function–vorticity formulation of the Navier–Stokes equations for the flow around a circular cylinder in planar oscillating flow at small Keulegan–Carpenter numbers (KC) in the subcritical Reynolds number (Re) range. The equations are solved by finite-difference methods. For very small KC ([les ] 1), the numerical results coincide with analytical solutions. As KC is increased, the incipient separation and instability leading to an asymmetrical flow with vortex shedding are predicted. Computed flow fields at small KC values are compared to flow visualizations, and good agreement is found for moderate β-values (≈ 250). The well-documented flow regimes with the transverse vortex street, single-, double- and three-pair shedding, are predicted by the model. Although the flow is not fully resolved for the highest Re values, comparisons of calculated drag and inertia coefficients with experimental data for three different values of the frequency parameter β in the range 196–1035 for 0 < KC < 26 show good agreement.

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The distribution of turbulence in the wave boundary layer is investigated. Turbulent kinetic energy, eddy viscosity, and other quantities predicted by use of standard one-equation and two-equation turbulence models are compared with experimental data. It is found that the two-equation model gives better results for the eddy viscosity, which is important in connection with the modelling of suspended sediment. The improvements, however, may not be sufficient to justify the extra work involved in a practical application. RESUME La distribution de turbulence dans la couche limite de la houle a été analysée. L'énergie cinétique turbulente, la viscosité turbulente et les autres quantités calculées par les modèles classiques de turbulence à une équation et à deux équations ont été comparées avec des résultats d'essais. On a trouvé que le modèle à deux équations donne de meilleurs résultats pour la viscosité turbulente, ce qui est important pour une modélisation correcte des sédiments en suspension. Cet avantage n'est cependant pas assez important pour justifier l'utilisation dans une application pratique.