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For a stationary process in the wave‐number range investigated (the buoyancy subrange of stably stratified flow) under the assumption of local homogeneity of the flow, two governing spectral equations derived from equations of motion and energy are solved by means of a generalized eddy‐viscosity approximation. Asymptotic solutions are obtained in the buoyancy subrange, where the local production and local dissipation of turbulence energy are negligible when compared with the inertial transfer and vertical heat‐flux terms when the flow conditions satisfy the frequency criterion [(g/T0)(d‐Γ‐/dz)]1/2≪[N/ε(g/T0)2]1/2 . The power law for the velocity and temperature spectra is not universal but varies with the flow conditions in the way ϕ(k) ∼ kn and ϕTT(k) ∼ km, where −11/5 ≥ n ≥ −3 and −1 ≥ m ≥ −7/5.

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