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In fluid dynamics, turbulence modeling is the construction and use of a mathematical model to predict the effects of turbulence. Turbulent flows are commonplace in most real-life scenarios. Turbulent flows are commonplace in most real-life scenarios.
For homogeneous turbulence (i.e., statistically invariant under translations of the reference frame) this is usually done by means of the energy spectrum function E(k), where k is the modulus of the wavevector corresponding to some harmonics in a Fourier representation of the flow velocity field u(x):
The total time interval simulated is generally proportional to the turbulence time scale given by τ = L u ′ . {\displaystyle \tau ={\frac {L}{u'}}.} Combining these relations, and the fact that h {\displaystyle h} must be of the order of η {\displaystyle \eta } , the number of time-integration steps must be proportional to L / ( C η ...
Large eddy simulation of a turbulent gas velocity field.. Large eddy simulation (LES) is a mathematical model for turbulence used in computational fluid dynamics.It was initially proposed in 1963 by Joseph Smagorinsky to simulate atmospheric air currents, [1] and first explored by Deardorff (1970). [2]
A variety of models exist for gusts [3] but only two, the Dryden and von Kármán models, are generally used for continuous gusts in flight dynamics applications. [2] [4] Both of these models define gusts in terms of power spectral densities for the linear and angular velocity components parameterized by turbulence length scales and intensities.
The mean velocities ¯ are determined by either time averaging, spatial averaging or ensemble averaging, depending on the flow under study. Further ′ denotes the fluctuating (turbulence) part of the velocity. We consider a homogeneous fluid, whose density ρ is taken to be a constant.
There are various ways to define the Greenwood frequency, but all the definitions attempt to represent the frequency at which the turbulence distortion of the image is changing. The reciprocal of the Greenwood frequency is sometimes known as the Greenwood or atmospheric time constant (τ 0). Since the distortions are approximately constant over ...
where ε is the average rate of dissipation of turbulence kinetic energy per unit mass, and; ν is the kinematic viscosity of the fluid.; Typical values of the Kolmogorov length scale, for atmospheric motion in which the large eddies have length scales on the order of kilometers, range from 0.1 to 10 millimeters; for smaller flows such as in laboratory systems, η may be much smaller.