A modal method for finite amplitude, nonlinear sloshing

Abstract

A modal method is used to calculate the two-dimensional sloshing motion of an inviscid liquid in a rectangular container. The full nonlinear problem is reduced to the solution of a system of nonlinear ordinary differential equations for the time varying coefficients in the expansions of the interface and the potential. The effects of capillarity are included in the formulation. The simplicity, generality and power of the method are exhibited not only by recovering the earlier results obtained, for example, by Penney and Price [1], Tadjbakhsh and Keller [2] and Faltinsen et al [3], but also by obtaining new and interesting results of the effects of capillarity and shallow depth, which would be difficult to obtain otherwise. For example, it is found that for the initial interface profile considered here, parasitic capillary waves, borne by the higher number wave modes, are generated for moderate capillarity but disappear for larger values of the parameter. The method can be extended to other simple geometries.

Classification of three-dimensional nonlinear sloshing in a square-base tank with finite depth

“…This way constitutes the main idea of the Perko-like scheme (Moore and Perko, 1964;Perko, 1969). Some recent modifications of this scheme have been developed by Chern et al (1999), La Rocca et al (2000), Ferrant and Le Touze (2001) and Shankar and Kidambi (2002). The advantage of the Perko-like scheme relative to the asymptotic modal technique is that corresponding truncated systems of ordinary differential equations take into account the full set of high-order wave components.…”

Resonant three-dimensional nonlinear sloshing in a square-base basin

“…where T is the forcing period. The system (2.15) together with (2.16) (or (2.17) may be truncated and implemented for numerical analysis of the fluid sloshing as in Perko-like methods (see, for instance, recent papers by La Rocca et al 1997;La Rocca, Sciortino & Boniforti 2000;Shankar & Kidambi 2002). For periodic forcing the numerical approach makes it also possible to treat the periodic steady-state solutions including bifurcation and stability analysis by employing appropriate codes given by Bader & Ascher (1987) and Hermann & Ullrich (1992).…”

The contact angle in inviscid fluid mechanics

“…In any case, the analysis of §2 shows that no extra contact angle condition can be prescribed for classical solutions. (h) It suffices now to mention that the old confusions persist into the new millenium, typical samples being [3,15,16,19].…”

“…The imperative to impose a contact angle condition at the contact line, not permitted in general by the classical inviscid formulation, appears to have come from experimental observations of real, viscous contact lines. It is well-known [6,16,13,18] that real, dynamic viscous contact lines display complex behaviour and are not at all well-understood with many parameters playing a role. It is in attempting to model this complicated behaviour in an inviscid framework that the need for contact angle conditions began to be felt and then applied.…”