Everything about Turbulence totally explained
In
fluid dynamics,
turbulence or
turbulent flow is a fluid regime characterized by chaotic,
stochastic property changes. This includes low
momentum diffusion, high momentum
convection, and rapid variation of
pressure and
velocity in space and time. Flow that isn't turbulent is called
laminar flow. The (
dimensionless)
Reynolds number characterizes whether flow conditions lead to laminar or turbulent flow; for example for pipe flow, a Reynolds number above about 4000 (A Reynolds number between 2100 and 4000 is known as transitional flow) will be turbulent. At very low speeds the flow is laminar, for example, the flow is smooth (though it may involve vortices on a large scale). As the speed increases, at some point the transition is made to turbulent flow. In turbulent flow, unsteady vortices appear on many scales and interact with each other.
Drag due to
boundary layer skin friction increases. The structure and location of boundary layer separation often changes, sometimes resulting in a reduction of overall drag. Because laminar-turbulent transition is governed by
Reynolds number, the same transition occurs if the size of the object is gradually increased, or the
viscosity of the fluid is decreased, or if the
density of the fluid is increased.
Turbulence causes the formation of eddies of many different length scales. Most of the kinetic energy of the turbulent motion is contained in the large scale structures. The energy "cascades" from these large scale structures to smaller scale structures by an inertial and essentially inviscid mechanism. This process continues, creating smaller and smaller structures which produces a hierarchy of eddies. Eventually this process creates structures that are small enough that molecular diffusion becomes important and viscous dissipation of energy finally takes place. The scale at which this happens is the
Kolmogorov length scale.
In two dimensional turbulence (as can be approximated in the atmosphere or ocean), energy actually flows to larger scales. This is referred to as the inverse energy cascade and is characterized by a
.
Since the experimental values obtained for the second order structure function only deviate slightly from the 2/3 value predicted by Kolmogorov theory, the value for
p is very near to 5/3 (differences are about 2%). Thus the "Kolmogorov -5/3 spectrum" is generally observed in turbulence. However, for high order structure functions the difference with the Kolmogorov scaling is significant, and the breakdown of the statistical self-similarity is clear. This behavior, and the lack of universality of the
constants, are related with the phenomenon of intermittency in turbulence. This is an important area of research in this field, and a major goal of the modern theory of turbulence is to understand what is really universal in the inertial range.
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