It is well known that the nonlinearity of fluid mechanics equations makes all the dynamic equations of turbulent flows nonclosed. If we add the equations for the new unknowns (higher-order moments), then the number of the unknowns in the equations will increase faster than the number of the equations themselves. Therefore the equations of turbulent flows cannot be solved without the use of some supplementary speculative closure hypotheses. There is an enormous amount of literature devoted to the different closure methods (i.e. various semiempirical model equations of turbulence), their applications to specific turbulent flows, and comparison of the results obtained with the results of other theories and with experiments (see, e.g., Launder & Spalding 1972, Rotta 1973, Reynolds 1976). Of course, none of the semiempirical theories is strict, and they include a number of empirical constants and lead to different conclusions. However, there are also results pertaining to turbulent flow that may be obtained with the aid of general physical reasoning without any use of dynamic equations and closure hypotheses. Similarity and dimensional arguments are, apparently, the most important general methods for obtaining meaningful results without solving the dynamical equations (Bridgman 1932, Sedov 1959):This review is devoted to
Annual Review of Fluid Mechanics – Annual Reviews
Published: Jan 1, 1979
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