弱非線形表面波の粘性Potential流解析とHelmholtz分解

概要

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Since a seminal paper of Benjamin &; Feir (Journal of Fluid Mechanics (1967), 27, 417-430), it has been shown that the nonlinear self-modulation of a quasi-monochromatic wave train is governed by the so-called nonlinear Schrodinger equation and that the stability characteristics of a uniform wave train may be determined by the known properties of background dispersive wave systems. It was shown that the gravity waves on a liquid layer are modulationally stable or unstable according as kh is smaller or greater than 1.363, where k is the wave number and h the liquid depth. In addition to this, quite recently, much attention is paid to revisit the nonlinear Schrodinger equation, in order to account for viscous dissipation. According to Kawahara's work (J. Phys. Soc. Japan 38 (1975), pp.265-270) in which it is shown that the stability characteristics of a uniform wave train are critically affected by the effect of capillarity, this paper is presented to study effects of viscous dissipation on weakly nonlinear surface waves from the point of viscous potential flow analysis.
沼津工業高等専門学校の論文
2008-01-31