Closure problem: Difference between revisions
From Glossary of Meteorology
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<div class="definition"><div class="short_definition">A difficulty in [[turbulence]] theory caused by more unknowns than equations.</div><br/> <div class="paragraph">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.</div><br/> </div> | <div class="definition"><div class="short_definition">A difficulty in [[turbulence]] theory caused by more unknowns than equations.</div><br/> <div class="paragraph">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|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.</div><br/> </div> | ||
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Latest revision as of 15:37, 25 April 2012
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.
