On the Theory of Temperature Spectra in a Stably Stratified Fluid

It is shown that the Lumley-Phillips buoyancy subrange theory predicts the temperature spectrum to be proportional to k−3 at small scalar wavenumbers k—-consistent with oceanic experiments (although those experiments measure vertical wavenumber k3 rather than k). A previous derivation by Phillips does not apply to such small k. The predicted temperature spectrum is also shown proportional to the velocity spectrum in the buoyancy subrange. Although its predictions are consistent with experiments, the a priori validity of buoyancy subrange theory still remains in question.