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| Theoretic solutions are studied to answer the laminar-turbulence transition conditions for one-directional flow. The geometrical equations, strain rate components, and motion equations are formulated by rational mechanics equipped with geometrical field description of instant deformation. The obtained two typical theoretic solutions of velocity section for constant flow is identical with the classical well-known results, as a important soundness-check for the theoretic treatment. The motion equation for general case is solved for high speed flow to get its theoretic solutions. The results show that: theoretically, the velocity field has four possible solution functions for given initial velocity profile, center line velocity function, and fluid feature parameter. As a natural result, the pressure also has four possible functions determined by corresponding velocity function. As an example, the velocity bifurcation near zero-velocity boundary is obtained. Hence, the spatial self-evolution equation of flow velocity for high speed flow may be exposed. |
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| Keywords:velocity bifurcations; self-evolution equation of velocity; pressure; motion equation; geometrical equation |
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