closure problem

From Glossary of Meteorology
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.


Copyright 2024 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact [email protected]. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.