We have already investigated stably stratified flows (0<K=NH/πU≤3) past a two-dimensional hill in a channel of finite depth numerically by using a Direct Numerical Simulation (DNS) and a Large Eddy Simulation (LES) based on a finite-difference method, where N is the Brunt-Väisälä frequency, H, the domain depth, U, the approaching flow speed, and h, the hill's height. In these simulations, as the first step, we assumed a free-slip condition on the ground, both upstream and downstream of the hill, and a no slip condition was imposed only on the hill surface. Under this situation, it was expected that no shedding of large vortices from the hill occurs, because we wanted to clarify the behavior of upstream columnar disturbances and lee waves without any troublesome bound ary layer effects and any interactions with vortex shedding from the hill. The numerical results have clarified the mechanisms of the various flow unsteadiness around the hill.
As the next step, we have conducted a DNS where a no-slip condition is imposed on both the ground and the hill surface at a Reynolds number of 2000 in the present study. The velocity, perturbation velocity and vorticity fields around the hill are visualized.The time variations in the drag coefficient on the hill and in the upstream advancing columnar disturbances are shown. Using these numerical results, we have investigated the following phenomena in detail : one is the effect of stable stratification on the separated-reattached flow behind the hill, especially for the cases of 0≤K≤1 (weak stratification); the other is the flow unsteadiness around the hill for the cases of 1<K≤2 (strong stratification) as well as the previous numerical studies employing a free-slip condition on the ground except for the hill surface.

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Numerical computation is made for the two-dimensional stationally Bénard convection with temperature-dependent viscosity of exponential type. Cases with aspect ratios 1-10 and the ratios 1-e⁸ for viscosities at the lower and the upper boundaries are treated for the Rayleigh number 3000 and the Prandtl number 10⁸. In the cases with higher aspect ratios and viscosity ratios chaotic roll patterns were observed, where stationally cells with various horizontal scales were distributed randomly.

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In the present study, a time response of a conventional flush-mounted hot film gage for measuring wall shear stress is investigated. After the flush-mounted hot film probe is calibrated in a water tunnel, a streamwise velocity in the viscous sublayer of fully developed turbulent boundary layer flows above the flush-mounted hot film probe and the wall shear stress using the flush-mounted hot film probe are measured simultaneously. The time response of the flush-mounted hot film probe are examined from comparing with a cross-correlation and a phase lag between the wall shear stress from the velocity gradient in the viscous sublayer and wall shear stress measured using the flush-mounted hot film probe. As a result, it is evident that the flush-mounted hot film probe is useful for detecting organized motions in turbulent wall flows.

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A numerical model to compute wind speeds and sea-salt concentrations around pine forests at coast is presented, which is based on the κκ-ε model and contains a new parameter C_4ε in the source term of the E equation. This parameter represents a rate of conversion of the turbulence energy from the low frequncy band to the high frequncy one due to drag of trees. The system of equations is represented in a generalized coordinates fitting to topography. Numerical simulations almost agree to observed data with respect to their streamwise and vertical profiles. The present model, however, fails to simulate the maximum wind speeds observed at the top of a slope and above forests. Numerical simulation also shows that an extent of stagnant or reverse flow, and a rate of recover of wind speed behind a forest considerably depend on a value of parameter C_4ε.

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The effect of continental plates with large horizontal sizes on mantle convection is investigated by the use of a two-dimensional Boussinesq fluid model. A continental plate is realized as a rectangular zero-velocity region near the upper surface of the model domain with the aspect ratio of 12. Numerical results show that the convection cells extending over the regions below and outside the plate are horizontally elongated and upwellings exist below the center of the plate when Ra=10⁵ and 10⁶. However, in the case of Ra=10⁴, the aspect ratio of the convection cell is nearly 1 and an upwelling exists below the margin of the plate.
By applying the boundary layer theory to the case of convection beneath the plate, the maximum horizontal size of the convection cell is predicted. It is shown that the convection cells with larger horizontal scale can emerge for the larger Rayleigh numbers, which is consistent with the results of numerical experiments.
The results suggest that an upwelling of the convection cell extending over the margin of a superontinent can be generated beneath the center of the continent in the case of whole mantle convection, however, in the case of upper mantle convection, an upwelling appears beneath its margin.

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