In
fluid dynamics
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...
, vortex stretching is the lengthening of
vortices
In fluid dynamics, a vortex (: vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in th ...
in three-dimensional fluid flow, associated with a corresponding increase of the component of
vorticity
In continuum mechanics, vorticity is a pseudovector (or axial vector) field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point an ...
in the stretching direction—due to the
conservation of angular momentum
Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total ang ...
.
Vortex stretching is associated with a particular term in the
vorticity equation
The vorticity equation of fluid dynamics describes the evolution of the vorticity of a particle of a fluid dynamics, fluid as it moves with its flow (fluid), flow; that is, the local rotation of the fluid (in terms of vector calculus this is the ...
. For example, vorticity transport in an incompressible inviscid flow is governed by
:
where ''D/Dt'' is the
material derivative
In continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field. The material de ...
. The source term on the right hand side is the vortex stretching term. It amplifies the vorticity
when the velocity is diverging in the direction parallel to
.
A simple example of vortex stretching in a viscous flow is provided by the
Burgers vortex.
Vortex stretching is at the core of the description of the turbulence
energy cascade from the large scales to the small scales in
turbulence
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to laminar flow, which occurs when a fluid flows in parallel layers with no disruption between ...
. In turbulence,
fluid elements are, on average, more lengthened than squeezed. In the end, this results in more vortex stretching than vortex squeezing. For
incompressible flow
In fluid mechanics, or more generally continuum mechanics, incompressible flow is a flow in which the material density does not vary over time. Equivalently, the divergence of an incompressible flow velocity is zero. Under certain conditions, t ...
—due to volume conservation of fluid elements—the lengthening implies thinning of the fluid elements in the directions perpendicular to the stretching direction. This reduces the radial length scale of the associated vorticity. Finally, at the small scales of the order of the
Kolmogorov microscales, the turbulence
kinetic energy
In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion.
In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...
is dissipated into heat through the action of
molecular
A molecule is a group of two or more atoms that are held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemistry, ...
viscosity.
[Tennekes & Lumley (1972) pp. 75–92.]
Notes
References
*
*
Fluid dynamics
Turbulence
{{fluiddynamics-stub