Abstract—The characteristics of wave motion in a two-dimensional viscous fluid medium which is described by a bounded solution is obtained for the case in which the depth is essentially high. The distortion rising from the mixing of lamina irregular and turbulent mode of flow under a common transverse gradient is represented by the complex viscous term and relates to the Reynolds number Re, so that when the coefficient of viscosity v is larger, the Reynolds number is Zero.The governing equation include terms relating to the non-linear coupling in the plane for which viscosity is the dominant factor influencing the eddy driven current in the medium. The solution suggests a system of wave motion generated by gradual transition from the linear law of resistance for lamina flow to that of quadratic law for turbulent flow.

Index Terms—Viscosity, amplitude, finite, lamina, turbulent.

M. A. Orukari, Zuonaki Ongodiebi are with Department of Mathematics, Niger Delta University, P.M.B 071 Amassoma, Bayelsa State, Nigeria.

Cite:M. A. Orukari, Zuonaki Ongodiebi, "On the Finite Amplitude Oscillations in a Viscous Two-Dimensional Fluid," International Journal of Applied Physics and Mathematics vol. 11, no. 2, pp. 25-32, 2021.

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