Free Surface Boundary Ideal Fluid Navier -Stokes Equation
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The free surface boundary ideal fluid Navier -Stokes equation is a mathematical equation that describes the motion of an incompressible fluid with a free surface. The equation is named after the French mathematician Claude-Louis Navier and the Irish mathematician George Stokes, who independently developed the equation in the 19th century.
The Navier-Stokes equation is a partial differential equation that describes the conservation of mass, momentum, and energy in a fluid. The equation is a complex system of equations that are difficult to solve analytically. However, numerical methods have been developed to solve the Navier-Stokes equation for specific cases.
The free surface boundary condition is a condition that is imposed on the Navier-Stokes equation at the boundary of the fluid. The condition states that the normal stress at the boundary is zero. This condition is equivalent to the condition that the fluid is in equilibrium with the surrounding air.
The Navier-Stokes equation with a free surface boundary condition is a powerful tool for modeling fluid flows. The equation can be used to model a wide variety of flows, including waves, jets, and drops. The equation is also used in a variety of engineering applications, such as the design of aircraft and ships.
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