Closure problem

From Glossary of Meteorology

closure problem

A difficulty in turbulence theory caused by more unknowns than equations.

The closure problem of turbulence is alternately described as the requirement for an infinite number of equations, which would also be impossible to solve. This problem is apparently associated with the nonlinear nature of turbulence, and the traditional analytical approach of Reynolds averaging the governing equations to eliminate linear terms while retaining the nonlinear terms as statistical correlations of various orders (i.e., consisting of the product of multiple dependent variables). The closure problem is a long-standing unsolved problem of classical (Newtonian) physics. While no exact solution has been found to date, approximations called closure assumptions can be made to allow approximate solution of the equations for practical applications.

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