Considerations on the Theory of Temperature spectra in Stably Stratified Turbulence

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Abstract
In a recent note, Weinstock reconsiders an argument advanced twenty years earlier by Phillips concerning the buoyancy subrange theory of Lumley. Phillips pointed out that Lumley's theory ought to predict a certain form for temperature fluctuation spectra. Subsequent observations are inconsistent with the predicted spectral form. Weinstock argues that Phillips' analysis is incorrect and that Lumley's theory, suitably extended to treat temperature spectra, is consistent with observations. Here I will argue that both Lumley and Weinstock theories are incorrect. An alternative theory is described. Field and laboratory tests should be capable of discriminating between the two accounts. The outcome of such tests will bear upon significant practical matters. Abstract In a recent note, Weinstock reconsiders an argument advanced twenty years earlier by Phillips concerning the buoyancy subrange theory of Lumley. Phillips pointed out that Lumley's theory ought to predict a certain form for temperature fluctuation spectra. Subsequent observations are inconsistent with the predicted spectral form. Weinstock argues that Phillips' analysis is incorrect and that Lumley's theory, suitably extended to treat temperature spectra, is consistent with observations. Here I will argue that both Lumley and Weinstock theories are incorrect. An alternative theory is described. Field and laboratory tests should be capable of discriminating between the two accounts. The outcome of such tests will bear upon significant practical matters.

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