By M. Dubois, F. Daviaud, M. Bonetti (auth.), F. H. Busse, L. Kramer (eds.)
This quantity comprises papers contributed to the NATO complicated study Workshop "Nonlinear Evolution of Spatio-Temporal buildings in Dissipative non-stop structures" held in Streitberg, Fed. Rep. Germany, Sept. 24 via 30, 1989. the aim of the relatively lengthy identify has been to concentration awareness on a very fruitful path of analysis in the wide box coated by way of phrases like Nonlinear Dynamics or Non-Equilibrium platforms. After physicists were occupied for a number of a long time regularly with the microscopic constitution of topic, fresh years have witnessed a resurgence of curiosity in macroscopic styles and dynamics. study on those latter phenomena has now not been dormant, in fact, considering that fluid dynamicists drawn to the foundation of turbulence, meteorologists learning climate styles and various different scientists have persisted to develop the certainty of the buildings appropriate to their disciplines. the new development within the dynamics of nonl inear platforms wi th few levels of freedom and the invention of common legislation similar to the Feigenbaum scaling of period-doubling cascades has given upward thrust to new hopes for the knowledge of universal rules underlying the spontaneous formation of constructions in prolonged non-stop systems.
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Extra info for Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems
76. The data were obtained for a top-plate modulation. The lines represent fits to the data as in Figure 9. 15 f- -0. O • • b • . 50 a'· i a o ........ aD -0. so c ; . • -1. 00 . 00 a. I~:rr) Figure 11. 35 (filled circles). Dependence on the modulation amplitude of the results in (a) and (b) is suggested in (c), where /) = (1 + E,)L'.. 41 characteristic vertical viscous diffusion time. 0,. :!. 70. :!. 70 are shown in Figure ll(a) where Ec is a reduced critical Rayleigh number 0 At very low frequencies of modulation the conducting state is severely destabilized relative to steady rotation at 0..
1987, Phys. Rev. A, 36, 4870. , 1923, Phil. Trans. Roy. Soc. A, 223, 289. , 1968, "Instabilities of Some Time Dependent Flows," D. Phil. Thesis, MIT. , 1987, Phys. Rev. , 58, 2543. , 1988, Phys. Rev. , 60, 700. , 1989, Phys. Rev. A, 40, 7197. 43 SIDEBAND INSTABILITY OF WAVES WITH PERIODIC BOUNDARY CONDITIONS B. Janiaud, E. Guyon, D. Bensimon and V. Croquette LPS-ENS, 24 rue Lhomond, 75231 Paris cedex 05 ABSTRACT The sideband instability for traveling waves is studied experimentally under periodic boundary conditions.
Now, on substituting the stream function (1), the Navier-Stokes equations, in the form of the vorticity equation, reduce to the ordinary differential equation, VF1V + FF" - F'r = o. (2) In a fertile paper on two-dimensional unsteady flow near a stagnation point of separation at 0, Proudman and Johnson (1962) assumed the similarity form ~(x, y, t) = xf(y, t). (3) Then the x- and y- components of the velocity of the fluid are u = xfy, V = - f, respectively. H. Busse and L. Kramer Plenum Press, New York, 1990 51 (4) although Proudman and Johnson in fact stated only the integral of (4) with respect to y rather than (4) explicitly.
Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems by M. Dubois, F. Daviaud, M. Bonetti (auth.), F. H. Busse, L. Kramer (eds.)