This paper studies the influence of boundary conditions on a fluid medium of finite depth. We determine the frequencies and the modal shapes of the fluid. The fluid is assumed to be incompressible and viscous. A potential technique is used to obtain in three-dimensional cylindrical coordinates a general solution for a problem. The method consists in solving analytically partial differential equations obtained from the linearized Navier-Stokes equation. A finite element analysis is also used to check the validity of the present method. The results from the proposed method are in good agreement with numerical solutions. The effect of the fluid thickness on the Stokes eigenmodes is also investigated. It is found that frequencies are strongly influenced. 1. Introduction Flow modeling in confined domains leads mostly to Stokes models [1]. The use of this model in the field of microfluidics and nanofluidics [2, 3] and in the understanding the movement of microorganisms [4] currently in full swing. This recent years, several authors have focused on the modal analysis of this model. We can cite in particular the aspects related to problems arising from geophysics. These studies highlight the existence of slow wave or Stoneley waves [5–7]. Other authors [8, 9] have focused on the dynamic aspects in the context of fluid-structure interaction. The numeric aspects for coupled (or not) modal problem were discussed in [10–12]. The theory of potential flow of viscous fluid was introduced by [13]. All of his work on this topic is framed in terms of the effects of viscosity on the attenuation of small amplitude waves on a liquid-gas surface. The problem treated by Stokes was solved exactly using the linearized Navier-Stokes equations, without assuming potential flow, and was solved exactly by [14]. Reference [15] has identified the main events in the history of thought about potential flow of viscous fluids. The problem of Stokes flow in cylindrical domain has been investigated by several authors. References [16, 17] studied Stokes flow in a cylindrical container by an eigenfunction expansion procedure without the compressibility effect. Potential flows through different kinds of geometry have been studied by many investigators for several applications. For example in vascular fluid dynamics, [18] presented the role of curvature in the wave propagation and in the development of a secondary flow. Reference [19] has studied the flow and pressure dynamics of the cerebrospinal fluid flow. Three-dimensional CSF flow studies have also been reported [20]. The knowledge of
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