Third Order Cnoidal Wave Solutions in Shallow Water and its Horizontal and Vertical Fluid Velocity Components

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Year:
2016
Type of Publication:
Article
Keywords:
Navier Stokes Equation, Jacobi Elliptic Function, Cnoidal Wave, Elliptic Parameter, Velocity Components
Authors:
Parvin; Sultana; Sarker
Journal:
IJISM
Volume:
4
Number:
5
Pages:
164-174
Month:
Sept
ISSN:
2347-9051
Abstract:
Third order cnoidal wave solutions in shallow water are developed where waves progress steadily without any change of form. Shallow water wave problems are solved at the bottom and at the free surface. The boundary conditions are also taken from Navier-Stokes equation of motion. Using these boundary conditions, three nonlinear ordinary differential equations are derived which can be solved using series expansion method. Taking Jacobi elliptic function, third order cnoidal wave solutions have been established from which wave elevation, horizontal wave velocity and acceleration due to gravity for cnoidal wave are expressed. Assuming Taylor expansion for the stream function about the bed, the fluid velocity components are derived in terms of Jacobi elliptic function
Full text: IJISM_330_FINAL.pdf

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