Sur les petites oscillations d'un profil sous une ligne libre. I. Détermination du potential complexe et de la ligne libre. (On small oscillations of a profile under a free line. I. Determination of the complex potential and the free lines) (Q1057714)

The problem of small harmonic oscillations of a profile under a free line in a heavy fluid has been solved by Kotchin [\textit{J. V. Wehausen} and \textit{E. V. Laitone}, Surface waves, in: \textit{S. Flügge} (ed.), Encyclopedia of physics. Vol. IX: Fluid dynamics III (1960; Zbl 0102.407)]. In this paper the problem is considered again by adjusting a method used by \textit{H. Lamb} [Hydrodynamics, Cambridge, University Press, 6th ed. (1932); see review of the 2nd German ed. (1931; Zbl 0001.36304)] for the uniform translation and by using the results of \textit{G. Couchet} [Les profils en aérodynamique instationnaire et la condition de Joukowski, Ed. A. Blanchard, Paris (1976)] for the unsteady motions. Kotchin's results are found again but, in addition, explicit expressions are given for the H-functions introduced by this author, of the complex potential and of the equation of the free line.