## Abstract

Because of its non-conformity to Monin-Obukhov Similarity Theory (MOST), the effects of thermal stratification on scaling laws describing the streamwise turbulent intensity σ_{u} normalized by the turbulent friction velocity (u_{*}) continue to draw research attention. A spectral budget method has been developed to assess the variability of σ_{u}/u_{*} under unstable atmospheric stratification. At least three different length-scales-the distance from the ground (z), the height of the atmospheric boundary layer (δ) and the Obukhov length (L)-are all found to be controlling parameters in the variation of σ_{u}/u_{*}. Analytical models have been developed and supported by experiments for two limiting conditions: z/δ < 0.02, -z/L < 0.5 and 0.02 ≪ z/δ < 0.1, -z/L > 0.5. Under the first constraint, the turbulent kinetic energy spectrum is predicted to follow three regimes: k^{0}, k^{-1} and k^{-5/3}, divided in the last two regimes by a break-point at kz = 1, where k denotes the wave number. The quantity σ_{u}/u_{*} is shown to follow the much discussed logarithmic scaling, reconciled to Townsend's attached eddy hypothesis σu2/u*2=B1-A1log(z/δ), where the coefficients B_{1} and A_{1} are modified by MOST for mildly unstable stratification. Under the second constraint, the turbulent energy spectrum tends to become quasi-inertial, displaying k^{0} and k^{-5/3} with a break-point predicted to occur at 0.3 < kz < 1. The work here brings together well-established but seemingly unrelated theories of turbulence such as Kolmogorov's hypothesis, Townsend's attached eddy hypothesis, MOST and Heisenberg's eddy viscosity under a common framework.

Original language | English (US) |
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Pages (from-to) | 1699-1711 |

Number of pages | 13 |

Journal | Quarterly Journal of the Royal Meteorological Society |

Volume | 141 |

Issue number | 690 |

DOIs | |

State | Published - Jul 1 2015 |

## All Science Journal Classification (ASJC) codes

- Atmospheric Science