Kolmogorov microscales
Encyclopedia
Kolmogorov
microscales are the smallest scale
s in turbulent flow
. They are defined by
where
is the average rate of energy dissipation per unit mass, and 
is the kinematic viscosity of the fluid.
In his 1941 theory, A. N. Kolmogorov introduced the idea that the smallest scales of turbulence
are similar for every turbulent flow) and depend only on
and 
. Accordingly, the Kolmogorov microscales are derived from these two quantities on dimensional grounds.
The Kolmogorov 1941 theory is a mean field theory
since it assumes that the relevant dynamical parameter is the mean energy dissipation rate. In fluid turbulence, the energy dissipation rate fluctuates in space and time, so it is possible to think of the microscales as quantities that also vary in space and time. However, standard practice is to use mean field values since they represent the typical values of the smallest scales in a given flow.
Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov was a Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity.-Early life:Kolmogorov was born at Tambov...
microscales are the smallest scale
Scale (ratio)
The scale ratio of some sort of model which represents an original proportionally is the ratio of a linear dimension of the model to the same dimension of the original. Examples include a 3-dimensional scale model of a building or the scale drawings of the elevations or plans of a building. In such...
s in turbulent flow
Turbulence
In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...
. They are defined by
| Kolmogorov length scale |  |
| Kolmogorov time scale |  |
| Kolmogorov velocity scale |  |
where
is the average rate of energy dissipation per unit mass, and is the kinematic viscosity of the fluid.In his 1941 theory, A. N. Kolmogorov introduced the idea that the smallest scales of turbulence
Turbulence
In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...
are similar for every turbulent flow) and depend only on
and . Accordingly, the Kolmogorov microscales are derived from these two quantities on dimensional grounds.The Kolmogorov 1941 theory is a mean field theory
Mean field theory
Mean field theory is a method to analyse physical systems with multiple bodies. A many-body system with interactions is generally very difficult to solve exactly, except for extremely simple cases . The n-body system is replaced by a 1-body problem with a chosen good external field...
since it assumes that the relevant dynamical parameter is the mean energy dissipation rate. In fluid turbulence, the energy dissipation rate fluctuates in space and time, so it is possible to think of the microscales as quantities that also vary in space and time. However, standard practice is to use mean field values since they represent the typical values of the smallest scales in a given flow.