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In fluid dynamics, inviscid flow is the flow of an inviscid fluid which is a fluid with zero viscosity. [1] The Reynolds number of inviscid flow approaches infinity as the viscosity approaches zero. When viscous forces are neglected, such as the case of inviscid flow, the Navier–Stokes equation can be simplified to a form known as the Euler ...
Example of a parallel shear flow. In fluid dynamics, Rayleigh's equation or Rayleigh stability equation is a linear ordinary differential equation to study the hydrodynamic stability of a parallel, incompressible and inviscid shear flow. The equation is: [1] (″) ″ =,
In fluid dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity. [1] The Euler equations can be applied to incompressible and ...
In fluid mechanics, Kelvin's circulation theorem states: [1] [2] In a barotropic, ideal fluid with conservative body forces, the circulation around a closed curve (which encloses the same fluid elements) moving with the fluid remains constant with time. The theorem is named after William Thomson, 1st Baron Kelvin who published it in 1869.
Unlike an ideal inviscid fluid, a viscous flow past a cylinder, no matter how small the viscosity, will acquire a thin boundary layer adjacent to the surface of the cylinder. Boundary layer separation will occur, and a trailing wake will exist in the flow behind the cylinder. The pressure at each point on the wake side of the cylinder will be ...
A typical example of this flow is the forward stagnation point appearing in a flow past a sphere. Paul A. Libby (1974) [ 16 ] (1976) [ 17 ] extended Homann's work by allowing the solid wall to translate along its own plane with a constant speed and allowing constant suction or injection at the solid surface.
Take the simple example of a barotropic, inviscid vorticity-free fluid. Then, the conjugate fields are the mass density field ρ and the velocity potential φ. The Poisson bracket is given by {(), ()} = and the Hamiltonian by:
In this model the red fluid – initially on top, and afterwards below – represents a more dense fluid and the blue fluid represents one which is less dense. The Rayleigh–Taylor instability is another application of hydrodynamic stability and also occurs between two fluids but this time the densities of the fluids are different. [ 6 ]