Frequency predictions from global stability in the Benard vortex street

In 1908, Henri Bénard published the results of his experiments performed in Lyon-France on the discovery of an alternate vortex street when a body of prismatic shape is displaced in a fluid at rest. Using optical methods and cinematography, Bénard obtained the value of the frequency of the vortex shedding for this bluff body, with different sizes, velocities of the body and viscosities of the fluid. The comparison of this results (in modern terms, the variation of the Strouhal number with the Reynolds number) with similar ones obtained after, with a cylinder, by Karman and Rubach (1912), Kruger (1914), Relf (1921) and Camichel (1927), provided, in the 30’s, discussions. In this talk, we are presenting for the first time, more than a century later, quantitative predictions of the Strouhal number evolution for the geometry used in the pioneering experiments of Bénard. Global linear stability study is applied using the time averaged or mean base flow behind this prismatic body. We are comparing these predictions with the original experimental results. Similar comparisons are presented for the case of the vortex shedding from cylinders observed in many historical experiments beginning with Strouhal’ ones in 1878.