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The Navier–Stokes equations (/ n æ v ˈ j eɪ s t oʊ k s / nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades ...
Projected streamlines of the Sullivan vortex on the axial -plane; is the origin.. In fluid dynamics, the Sullivan vortex is an exact solution of the Navier–Stokes equations describing a two-celled vortex in an axially strained flow, that was discovered by Roger D. Sullivan in 1959.
This equation is called the mass continuity equation, or simply the continuity equation. This equation generally accompanies the Navier–Stokes equation. In the case of an incompressible fluid, Dρ / Dt = 0 (the density following the path of a fluid element is constant) and the equation reduces to:
Burgers vortex layer or Burgers vortex sheet is a strained shear layer, which is a two-dimensional analogue of Burgers vortex. This is also an exact solution of the Navier–Stokes equations, first described by Albert A. Townsend in 1951. [8] The velocity field (,,) expressed in the Cartesian coordinates are
In mathematics, the Navier–Stokes equations are a system of nonlinear partial differential equations for abstract vector fields of any size. In physics and engineering, they are a system of equations that model the motion of liquids or non-rarefied gases (in which the mean free path is short enough so that it can be thought of as a continuum mean instead of a collection of particles) using ...
Oseen looked for a solution for the Navier–Stokes equations in cylindrical coordinates (,,) with velocity components (,,) of the form =, = (,), = where is the circulation of the vortex core.
The equation of motion for Stokes flow can be obtained by linearizing the steady state Navier–Stokes equations.The inertial forces are assumed to be negligible in comparison to the viscous forces, and eliminating the inertial terms of the momentum balance in the Navier–Stokes equations reduces it to the momentum balance in the Stokes equations: [1]
The Batchelor vortex is an approximate solution to the Navier–Stokes equations obtained using a boundary layer approximation. The physical reasoning behind this approximation is the assumption that the axial gradient of the flow field of interest is of much smaller magnitude than the radial gradient.