Dynamics of Spatio-Temporal Cellular Structures: Henri by Innocent Mutabazi, Jose Eduardo Wesfreid, Etienne Guyon

By Innocent Mutabazi, Jose Eduardo Wesfreid, Etienne Guyon

The effect of Benard's discovery on twentieth century physics is important to any smooth study region reminiscent of fluid dynamics, nonlinear dynamics, and non-equilibrium thermodynamics, simply to identify a number of. This centenary overview indicates the vast scope and improvement together with smooth functions, edited and written by means of specialists within the field.

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Extra resources for Dynamics of Spatio-Temporal Cellular Structures: Henri Bénard Centenary Review

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26 Jos´e Eduardo Wesfreid of his 1908 papers [B12]. This is the reason why, for several years, B´enard argued indirectly, trying to demonstrate that von K´ arm´an’s and Rubach’s theoretical results were idealistic and far from real conditions. An example can be found in the paper he published in 1926 entitled, “About the Inaccuracy for Fluids in Real Conditions of the K´ arm´ an’s Theoretical Laws Regarding Alternated Vortex Stability”[B29]. Actually, B´enard experimentally showed that the dimensionless frequencies measured with the Strouhal number S, vary with the velocity of the object, whereas von K´ arm´ an’s result could imply that Strouhal number is constant.

The subject had become a wide topic of investigation in hydrodynamics. H. Camichel, M. Teissie-Solier, L. Escande, and T. Dupin were specifically working on vortices emitted by circular cylinders. In 1928, B´enard published two other papers [B37, B38] in which he compared his observations with those of the Toulouse group, particularly on the similar properties of the law of frequency of the vortex shedding as a function of the Reynolds’ number, that is to say, the nondimensional value of the fluid velocity.

Bourri`eres published this experiment in 1939, with a foreword by B´enard [36], in which the latter exposed the nonperiodic form the movement could take, from whatever initial conditions, and how these conditions led the system to a limit cycle, referring to the concept of self-oscillations due to Alexandr A. Andronov (1901-1952) [37]. As it is known, one of great achievements of Andronov, who belonged to the group on nonlinear dynamics formed in Moscow around Leonid I. Mandelstam (1879-1944), was to demonstrate, in the late 1920s, the connection between Poincar´e’s limit cycles and a whole range of practical oscillatory processes.

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