Reynolds decomposition
In fluid dynamics and turbulence theory, a Reynolds decomposition is a mathematical technique used to separate a field into its mean and fluctuating components. == Decomposition == A Reynolds decomposition of a field u {\displaystyle \mathbf {u} } (e.g., a velocity field) is given by u ( x , t ) = u ( x , t ) ¯ + u ′ ( x , t ) , {\displaystyle \mathbf {u} (\mathbf {x} ,t)={\overline {\mathbf {u} (\mathbf {x} ,t)}}+\mathbf {u} '(\mathbf {x} ,t),} where u ¯ {\displaystyle {\overline {\mathbf {u} }}} denotes the mean of u {\displaystyle \mathbf {u} } (which can be a time, space, or ensemble average), and u ′ {\displaystyle \mathbf {u} '} denotes the fluctuations from that mean.