1. Some of this material, in a much condensed form, will appear inThe Structure of Atmospheric Turbulenceby J. L. Lumley and H. A. Panofsky (Interscience Publishers, Inc., New York, 1964).
2. See, for example, A. A. Townsend, “Remarks on the Malkus theory of turbulent flow,”Mėcanique de la Turbulence(Editions du Centre National de la Recherche Scientifique, Paris, 1962), p. 167.
3. The concept of energy entering and leaving wave number space at different wave numbers from other parts of physical space is not paradoxical—it is not different in spirit from the usual case in which energy enters at low wavenumbers, is transferred to high, and leaves thence to heat. Nor does the consideration of scale changes contradict the similarity hypothesis—just as the laws of mechanics acquire extra terms in a rotating framework, so the equations of motion acquire new terms when written in stretched coordinates.
4. Although the solutions are not expected to be similar in the wavenumber range in which this term is large, it is meaningful to consider the (similar) form of this term in the wavenumber range in which it is not dynamically important; by so doing, some light is shed on the mechanism involved.