Formulation of Averaged Lagrangian Velocities for the Surface Wave Motion in a Layered Fluid

Select Volume / Issue:

• Volume 12, Issue 6, Nov. 2024

Year:

2024

Type of Publication:

Article

Keywords:

Navier Stokes Equations of Motion, Lagrangian and Averaged Lagrangian Velocities, Shear Currents

Authors:

Mst. Shahana Parvin; Md. Ashrafuzzaman Khan

Journal:

IJISM

Volume:

12

Number:

6

Pages:

36-45

Month:

November

ISSN:

2347-9051

Abstract:

The Navier-Stokes equations are the nonlinear partial differential equations describing fluid motion derived from the application of Newton’s second law of fluid motion. To derive the solution of Navier-Stokes equations of motion which gives the notion of velocity field components with different densities [S. Parvin and S. Sultana (2024)] and its application on many branches of fluid dynamics. For the irrotational wave motion, the Lagrangian formulation is straight forward and follows from a Lagrangian functional which is the difference between the kinetic energy and the potential energy of the system. When the velocity decomposition consists of a potential part and a shear current in two different densities, the vorticity is constant. Lagrangian velocity is formulated with a shear current and without a shear current in both densities. The averaged Lagrangian velocities are also derived in both cases.

Full text: IJISM_1013_FINAL.pdf [Bibtex]