A review is given on the similarity laws of wind waves and related problems, with special reference to our recent studies. Growing wind waves have statistical similarity laws. One of these is expressed as the 3/2-power law. Experimental evidence indicates that the boundary layers above and below wind waves are both turbulent boundary layers, which are similar to those on rough solid walls. Combination of the characteristics of turbulent boundary layers of air and water with the 3/2-power law requires that several characteristic velocities, which are concerned with the air-water boundary processes including wind waves, are all proportional to one another. Experimental observations are consistent with the above reasoning, together with the empirical value of the coefficient of the 3/2-power law. An interpretation of the physical situation is given as a concept of the breaking-adjustment of wind waves. The relation between the power law and the form of energy spectra of waves, and practical applications of the similarity laws are also given.

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There are two methods available to predict gas-particle two-phase flows : Eulerian and Lagrangian approaches. In the Eulerian method, various turbulence closure models are proposed in the same manner as in the single phase flow. In the Lagrangian method, particle-to-wall collision is important in the simulation, and irregular bouncing should be taken into consideration in horizontal wall-bounded flows. Interaction between particles and fluid is described by the PSI-Cell model.

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乱れの秩序構造の1つとして著者らが先に提示した円柱後流中のさじ形渦の形成について, それがカルマン渦の湾曲によって発生するというモデルに基づき, 数値解析を行った.基礎式としては非粘性理論に基づく渦糸の局所誘導方程式に背後の平均流の影響を考慮した方程式を用い, 初期に1本の渦糸にx-z平面 (x, z : 主流方向, スパン方向の座標) とθの角度をなす幅Zwの釣鐘状の境乱を与え, 以後その変形を解析した.まず, Zwを固定しθを変えて行った計算結果によると, 渦糸はθに依存せず最終的にはぼ一之平面と30°から45°の角度をなす構造に落ち着く.次にθを固定してZwを変えて行った結果によれば, 最終的な渦糸の変形幅はZwによらず4dから6d程度となった (d=円柱の直径).これらの結果から初期境乱の形によらず渦糸が下流で一定の構造を形成することが示された.

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著者らは既報において円柱後流でカルマン渦がちぎれ変形することによって円柱直径の8倍程度のスケールをもつさじ形の渦連鎖からなる秩序構造が形成されることを示した.本研究はレイノルズ数2100, 4200の円柱後流につき可視化と熱線流速計によるスパン方向の同時測定, スパン方向の相関, 条件付抽出法による構造に固定した流れ場の速度ベクトル, 構造内の乱れなどの測定から上記秩序構造の存在を確認し, 形成過程および内部構造を明らかにしたものである.

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The methods of obtaining exact solutions for nonlinear diffusion equations are surveyed. Included are linearization technique, bilinear transformation, Painlevé analysis and method of similarity solution. The equations considered are Burgers' type equations, Fisher's type equations, diffusion equations with integral terms and equations with density dependent diffusion. Explicit solutions are also shown for some of the equations.

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Magma is generated by partial melting of rocks and ascends due to its buoyancy in interstitial conduits through the country rock. When the country rock creeps, the magma conduits are deformable. A vertical cylindrical conduit that is deformable with time and space is considered for the present analysis, assuming that both country rock and magma are viscous fluids. Here the fluid representing the country rock has a significantly higher viscosity than magma. This analysis can be generalized to permeable flow with a network of deformable magma paths. The theory gives such a solution that a bulge of magma conduit propagates upward at a constant speed without change of wave form. Such a stationary wave resumes its form after collision with another wave so that it may be called magma soliton. The propagation velocity of a magma soliton increases with increasing amplitude. If magma flux is changed to a higher value at a certain depth, a new state of greater flux is established upward, creating new magma solitons at the moving tip. This process of soliton creation might be applicable for explaining the episodicity of volcanic eruptions.

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