By H. Oertel Jr. (auth.), H. L. Jordan, H. Oertel, K. Robert (eds.)
The German Aerospace study institution (DFVLR) has initiated a brand new sequence of seminars pertaining to primary difficulties in utilized engineering sciences. those seminars could be dedicated to interdisciplinary issues regarding the significant number of DFVLR actions within the fields of fluid mechanics, flight mechanics, suggestions and regulate, fabrics and struc tures, non-nuclear energetics, verbal exchange know-how, and distant sensing. the aim of the sequence is twofold, specifically, to deliver glossy principles and strategies to the eye of the DFVLR which will stimulate inner activi ties, and secondly, to promulgate DFVLR achievements wi skinny the foreign scientific/technical group. To this finish, renowned audio system from Germany and different nations could be invited to affix in a sequence of lectures and discussions on sure issues of mutual curiosity. the 1st colloquium of this sequence handled the dynamics of nonlinear platforms, specially in relation'to its software to fluid mechanics, relatively in transcritical flows. Of precise curiosity are questions in regards to the formation of nonlinear third-dimensional buildings in classical fluid mechanical balance difficulties, the actual technique of transition to turbulence, and the looks of chaotic suggestions. The scope of lectures reaches from self-organization in actual platforms to structural balance of third-dimensional vortex styles, the therapy of dissipative and conservative platforms, the formation of nonlinear buildings within the quarter of laminar-turbulent transition, and numerical simulation of cumulus cloud convection in meteorology. The seminar should still offer an perception into the level to which theoretical findings in Non linear Dynamics practice to the comprehension of fluid-mechanical problems.
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Additional resources for Nonlinear Dynamics of Transcritical Flows: Proceedings of a DFVLR International Colloquium, Bonn, Germany, March 1984
Springer, 1983. [2) H. HAKEN: Cooperative Effects, Progress in Synergetics, North Holland, 1974. [3) H. HAKEN: Cooperative Effects in Systems far from Thermal Equilibrium and in Non-physical System, Rev. Mod. , 47, 67 (1975). [4) H. HAKEN: Advanced Synergetics, Instability Hierarchies Organizing Systems and Devices, Springer, 1984. [5) M. V. BERRY: Regular and Irregular Motion, Topics in Nonlinear Dynamics, American Institute of Physics Conference Proceedings Series, 46, 1978. [6) P. P. ECKMANN: Iterated Maps on the Interval as Dynamical Systems, Birkhauser, 1980.
Then come the turbulent spots (4) and the fully developed turbulent boundary layer or channel flows (5). The hierarchy of the nonlinear formation of structures following one after the other is completed by further subharmonic routes to turbulence, all determined according to the magnitude of the variations. The basic fluid mechanical equations for the transi tions are expressed as follows, assuming incompressible flows: 29 2 CD o o 2 4 Poiseuille Flow Boundary Layer o f-~~~~~~~~~ I z -1~~~ L2 Y peak Shear Layers 0 volley peak BROWN , KLEISER [53,54] SOUND SECONDARY TS - INSTABILIT IES INSTAB ILI T IES TURBULENT TURBULENCE - -"" SPOTS LATERAL ...
Horizontal toroidal vortices form, superimposed upon the azimuthal flow, as sketched in Fig. 11. With further increase in the Reynolds number, at a second critical value the rolls start to oscillate periodically. Azimuthal travelling waves form, superimposed on the toroidal vortices. When the rotation rate is further increased, a double period of oscillations with half of the basic frequency is a possible oscillatory state. This is the FEIGENBAUM period doubling mechanism. Recent experimental studies 24 show, however, that different stable modulation patterns can occur in the quasi-periodic regime, and that the frequency f2 is different for different patterns.