On Properties Of Turbulence Models
Author(s)
T. H. Moulden
Abstract
Many applications of fluid mechanics are to turbulent flows. The practical computation
of such flows call upon turbulence models to provide the information
needed to close the mean motion equations. The present comments concern those
properties of turbulence models that may be obtained by direct study of the field
equations defining these models. The second moment model and the k ~ ε model
are the focus of attention and norm inequalities are written for these models. The
stability properties of the associated dynamical system are determined. Some difficulties
associated with obtaining norm estimates are also discussed.
Keywords: turbulence models, energy estimates.
1 Background
It is generally accepted that the Navier–Stokes equations describe the motion of
fluids under normal conditions of pressure and temperature. It is also accepted
that these same equations describe turbulent fluid motion (the \“sinuous motion”
described by Stokes and studied by Reynolds). A caution is necessary at this point
since the consistency of the Navier–Stokes equations has not been documented. In
particular, there is no complete existence, uniqueness and regularity results available
for these equations when provided with general boundary conditions.
Restrict attention to constant density fluid motion. Due to the lack of a complete
theory for the constant density Navier–Stokes equations:
∂vi
∂xi
= 0 (1)
∂vi
∂t
+ ∂(vivj)
∂xj
+ ∂p
∂xi
= ν∇2(vi) + fi (2)
noted above, it cannot be expected that a complete theory exists for the mean
motion equations used to treat turbulent flow. Here v(x, t) is the instantaneous
Keywords
turbulence models, energy estimates
Related Book
Other papers in this volume
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