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

Select Volume / Issue:

• Volume 4,Issue 5, Sept. 2016

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 [Bibtex]