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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 ...
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 ]
Thus for an incompressible inviscid fluid the specific internal energy is constant along the flow lines, also in a time-dependent flow. The pressure in an incompressible flow acts like a Lagrange multiplier , being the multiplier of the incompressible constraint in the energy equation, and consequently in incompressible flows it has no ...
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] (″) ″ =,
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
Then, even for an adiabatic, chemically-homogenous fluid, the density can vary when the pressure changes, e.g. with Bernoulli. For inviscid fluids, the viscosity tensor τ is zero. Thus for an inviscid, barotropic fluid with conservative body forces, the vorticity equation simplifies to
It is impossible to define a sharp point at which the thermal boundary layer fluid or the velocity boundary layer fluid becomes the free stream, yet these layers have a well-defined characteristic thickness given by and . The parameters below provide a useful definition of this characteristic, measurable thickness for the thermal boundary layer.
The condition can be expressed in a number of ways. One is that there cannot be an infinite change in velocity at the trailing edge. Although an inviscid fluid can have abrupt changes in velocity, in reality viscosity smooths out sharp velocity changes. If the trailing edge has a non-zero angle, the flow velocity there must be zero.