The drag and lift forces acting on a rotating rigid sphere in a homogeneous linear shear flow are numerically studied by means of a three-dimensional numerical simulation. The effects of both the fluid shear and rotational speed of the sphere on the drag and lift forces are estimated for particle Reynolds numbers of 1 6 Re p 6 500.The results show that the drag forces both on a stationary sphere in a linear shear flow and on a rotating sphere in a uniform unsheared flow increase with increasing the fluid shear and rotational speed. The lift force on a stationary sphere in a linear shear flow acts from the low-fluid-velocity side to the high-fluid-velocity side for low particle Reynolds numbers of Re p < 60, whereas it acts from the high-velocity side to the low-velocity side for high particle Reynolds numbers of Re p > 60. The change of the direction of the lift force can be explained well by considering the contributions of pressure and viscous forces to the total lift in terms of flow separation. The predicted direction of the lift force for high particle Reynolds numbers is also examined through a visualization experiment of an iron particle falling in a linear shear flow of a glycerin solution. On the other hand, the lift force on a rotating sphere in a uniform unsheared flow acts in the same direction independent of particle Reynolds numbers. Approximate expressions for the drag and lift coefficients for a rotating sphere in a linear shear flow are proposed over the wide range of 1 6 Re p 6 500. † Present address:

Surface-renewal motions in the interfacial region below a gas-liquid interface were experimentally investigated in relation to bursting motions in the wall region. To estimate the frequency of the appearance of surface-renewal eddies, mass-transport experiments with methylene-blue solution, together with velocity measurements, were done in an open-channel flow. The instantaneous concentration of methylene-blue tracer emitted from a point source positioned in the buffer layer was measured at the free surface downstream from the source by an optical probe. Instantaneous streamwise velocity was measured using a laser-Doppler velocimeter at a position in the buffer region. Frequencies of both surface-renewal and bursting events were computed from these concentration and velocity signals using a conditional-averaging method. In order to clarify whether the surface-renewal eddies actually dominate mass transfer across the gas-liquid interface, gas-absorption experiments were added. Carbon dioxide was absorbed into the water flow across the calm free surface and its mass-transfer coefficient on the liquid side was measured under the same flow conditions as used in the above mass-transport experiments. The results show that the surface-renewal motions originate in the bursting motions which vigorously occur in the buffer region. That is, the decelerated fluid which is strongly lifted towards the outer layer by bursting almost always arrives at the free surface and renews the free surface. The frequency of the surface renewal, as well as the bursting frequency, is uniquely determined by the wall variables or the outer-flow variables and the Reynolds number. Mass transfer across the gas-liquid interface is dominated by the large-scale surface-renewal eddies, and the mass-transfer coefficient on the liquid side is proportional to the square-root of the surface-renewal frequency.

Turbulence structure in an open-channel flow with a zero-shear gas–liquid interface was numerically investigated by a three-dimensional direct numerical simulation (DNS) based on a fifth-order finite-difference formulation, and the relationship between scalar transfer across a zero-shear gas–liquid interface and organized motion near the interface was discussed. The numerical predictions of turbulence quantities were also compared with the measurements by means of a two-color laser Doppler velocimeter. The results by the DNS show that the vertical motion is restrained in the interfacial region and there the turbulence energy is redistributed from the vertical direction to the streamwise and spanwise directions through the pressure fluctuation. The large-scale eddies are generated by bursting phenomena in the wall region and they are lifted up toward the interfacial region. Then, the eddies renew the interface and promote the scalar transfer across the gas–liquid interface. Both the damping effect and the generation process of the surface-renewal motions predicted by the DNS explain well the experimental results deduced in previously published studies. Furthermore, the predicted bursting frequency and mass transfer coefficient are in good agreement with the measurements.

The mass transfer mechanism across a sheared air–water interface without bubble entrainment due to wave breaking was experimentally investigated in terms of the turbulence structure of the organized motions in the interfacial region in a wind-wave tank. The transfer velocity of the carbon dioxide (CO2) on the water side was measured through reaeration experiments of CO2, and the fluid velocities in the air and water flows were measured using both a hot-wire anemometer and a laser-Doppler velocimeter. The results show that the mass transfer across a sheared air–water interface is more intensively promoted in wind shear, compared to an unsheared interface. However, the effect of the wind shear on the mass transfer tends to saturate in the high-shear region in the present wind-wave tank, where the increasing rate of mass transfer velocity with the wind shear decreases rapidly. The effect of the wind shear on the mass transfer can be well explained on the basis of the turbulence structure near the air–water interface. That is, surface-renewal eddies are induced on the water side through the high wind shear on the air–water interface by the strong organized motion generated in the air flow above the interface, and the renewal eddies control the mass transfer across a sheared interface. The mass transfer velocity is correlated with the frequency of the appearance of the surface-renewal eddies, as it is in open-channel flows with unsheared interfaces, and it increases approximately in proportion to the root of the surface-renewal frequency. The surface-renewal frequency increases with increasing the wind shear, but for high shear the rate of increase slows. This results in the saturated effect of the wind shear on the mass transfer in the high-shear region in the present wind-wave tank. The mass transfer velocity can be well estimated by the surface-renewal eddy-cell model based on the concept of the time fraction when the surface renewal occurs.

.[1] Momentum transfer across the wind-driven breaking air-water interface under strong wind conditions was experimentally investigated using a high-speed wind-wave tank together with field measurements at normal wind speeds. An eddy correlation method was utilized to measure roughness length and drag coefficient from wind velocity components measured by laser Doppler and phase Doppler anemometers. As a result, a new model for the roughness length and drag coefficient was proposed for predicting momentum transfer across the sea surface under both normal and strong wind conditions using the universal relationship between energy and significant frequency of wind waves normalized by the roughness length. The model shows that the roughness length and drag coefficient are uniquely determined at all wind speeds by energy and significant frequency of wind waves, and they can be given against U 10 only from the measurements of the wave parameters and one-point mean air velocity in the logarithmic law region. Citation: Takagaki, N., S. Komori, N. Suzuki, K. Iwano, T. Kuramoto, S. Shimada, R. Kurose, and K. Takahashi (2012), Strong correlation between the drag coefficient and the shape of the wind sea spectrum over a broad range of wind speeds, Geophys.