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In
fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...
, 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 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 and traveling along wit ...
in the stretching direction—due to the conservation of angular momentum. Vortex stretching is associated with a particular term in the vorticity equation. For example, vorticity transport in an incompressible inviscid flow is governed by : = \left(\vec \cdot \vec\right) \vec, 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 \vec when the velocity is diverging in the direction parallel to \vec. A simple example of vortex stretching in a viscous flow is provided by the
Burgers vortex In fluid dynamics, the Burgers vortex or Burgers–Rott vortex is an exact solution to the Navier–Stokes equations governing viscous flow, named after Jan Burgers and Nicholas Rott. The Burgers vortex describes a stationary, self-similar flow. An ...
. Vortex stretching is at the core of the description of the turbulence
energy cascade In continuum mechanics, an energy cascade involves the transfer of energy from large scales of motion to the small scales (called a direct energy cascade) or a transfer of energy from the small scales to the large scales (called an inverse energy ...
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 a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
. In general, in turbulence fluid elements are more lengthened than squeezed, on average. 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 ( isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. An e ...
—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 energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accel ...
is dissipated into heat through the action of
molecular A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
viscosity.Tennekes & Lumley (1972) pp. 75–92.


Notes


References

* * Fluid dynamics Turbulence {{fluiddynamics-stub