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STRUCTURE OF THREE-DIMENSIONAL STATIONARY ISOBARIC DOUBLE WAVES IN AN IDEAL INCOMPRESSIBLE FLUID. PART 2. SOLUTION OF REDUCED SYSTEM AND LOCAL CLASSIFICATION OF DOUBLE WAVES

V. E. Shemarulin
VANT. Ser.: Mat. Mod. Fiz. Proc 2016. Вып.4. С. 26-39.

Studies of the structure of isobaric three-dimensional stationary waves in an ideal incompressible fluid are coming to an end. In the first part of the work, the system of functional equations implicitly defining these waves was reduced to an equivalent system, which is more convenient for research. The present part shows that the solutions of the reduced system have a simple geometric structure and provides an explicit description of the diversity of local solutions of this system. As a result, all isobaric three-dimensional stationary double waves are proven to be clusters of flow regions of thee major types: shear, conical and tangential. Shear flows are the well known flows in parallel planes; for each plane, in parallel right lines. Conical flows are the flows along sets of tangent semiplanes of arbitrary convex conical surfaces; for each semiplane, in right lines parallel to the generatrix of the conical surface belonging to the semiplane. Tangential flows are the flows along sets of tangent surfaces (surfaces generated by right tangents of arbitrary space curves) governed by certain convexity conditions (ensuring that there are no intersections of tangent semiplanes); for each semiplane, in right lines parallel to the generatrix of the tangent surface (tangent to the curve) belonging to the semiplane. A similar explicit description of the structure of isobaric three-dimensional steady-state simple waves and two-dimensional non-steady-state isobaric flows has been given by the author before.
Thus, the present work finalizes the local classification of isobaric flows of an ideal incompressible fluid for the case of three independent variables: three space variables or two space variables and time.

Keywords: isobaric flows, three-dimensional stationary double waves, local flow classification, shear, conical and tangential flows.








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