The spectral energy equations are developed for mechanical and thermal wall turbulence; that is, turbulence which obeys similarity relations (not dependent on viscosity) in which the only characteristic length is the distance to the wall. The terms which appear are given physical interpretations relating them to inhomogeneities of intensity and scale. Some tentative conclusions are put forward regarding the spectral energy budget of a more general similar (homogenizable) turbulence.
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J. L. Lumley (1964) studied this question.