Nonlinear faraday waves in a parametrically excited circular cylindrical container

Abstract

In the cylindrical coordinate system, a singular perturbation theory of multiplescale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder, which is subject to a vertical oscillation. It is assumed that the fluid in the circular cylindrical vessel is inviscid , incompressible and the motion is irrotational, a nonlinear amplitude equation with cubic and vertically excited terms of the vessel was derived by expansion of two-time scales withoutconsidering the effect of surface tension. It is shown by numerical computation that different free surface standing wave patterns will be formed in different excited frequencies and amplitudes. The contours of free surface waves are agreed well with the experimental results which were carried out several years ago.

Capillary effect on vertically excited surface wave in circular cylindrical vessel

“…Although theoretical contours agree well with those of experiment, the excited frequencies have large discrepancy. For example, the theoretical excited frequencies for (8,4) and (9,6) modes are 16.71 Hz and 19.66 Hz respectively, while the experimental forced frequencies for those two modes are 50 Hz and 52 Hz. When the effect of surface tension is considered in the paper, the theoretical forced frequencies are 21.10 Hz and 28.67 Hz respectively for above two modes.…”

“…The physical modeling is the same as Fig.1 in Ref. [8]. The meanings of parameters are the same as those in Ref.…”

“…However, when forced frequency is high (e.g., larger than 10 Hz), the influence of surface tension is significant. References [8,9] have compared their theoretical flowing patterns with those of experiment in ideal fluids without taking the effect of surface tension into account. Although theoretical contours agree well with those of experiment, the excited frequencies have large discrepancy.…”

“…The meanings of parameters are the same as those in Ref. [8]. It is assumed that the fluid is inviscid, incompressible and the motion is irrotational, there must exist a velocity potential function φ(r, θ, z, t), and satisfy the following governing equation:…”

“…[8], is obtained from Euler equation in inviscid fluid including the effect of surface tension. The difference of two amplitude equations is that the latter includes the effect of surface tension.…”