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Turbulence Structure of the Unstable Atmospheric Surface Layer and Transition to the Outer Layer

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Abstract

We present a new model of the structure of turbulence in the unstable atmospheric surface layer, and of the structural transition between this and the outer layer. The archetypal element of wall-bounded shear turbulence is the Theodorsen ejection amplifier (TEA) structure, in which an initial ejection of air from near the ground into an ideal laminar and logarithmic flow induces vortical motion about a hairpin-shaped core, which then creates a second ejection that is similar to, but larger than, the first. A series of TEA structures form a TEA cascade. In real turbulent flows TEA structures occur in distorted forms as TEA-like (TEAL) structures. Distortion terminates many TEAL cascades and only the best-formed TEAL structures initiate new cycles. In an extended log layer the resulting shear turbulence is a complex, self-organizing, dissipative system exhibiting self-similar behaviour under inner scaling. Spectral results show that this structure is insensitive to instability. This is contrary to the fundamental hypothesis of Monin--Obukhov similarity theory. All TEAL cascades terminate at the top of the surface layer where they encounter, and are severely distorted by, powerful eddies of similar size from the outer layer. These eddies are products of the breakdown of the large eddies produced by buoyancy in the outer layer. When the outer layer is much deeper than the surface layer the interacting eddies are from the inertial subrange of the outer Richardson cascade. The scale height of the surface layer, z s, is then found by matching the powers delivered to the creation of emerging TEAL structures to the power passing down the Richardson cascade in the outer layer. It is z s = u 3* /kεs, where u * is friction velocity, k is the von Kármán constant and εs is the rate of dissipation of turbulence kinetic energy in the outer layer immediately above the surface layer. This height is comparable to the Obukhov length in the fully convective boundary layer. Aircraft and tower observations confirm a strong qualitative change in the structure of the turbulence at about that height. The tallest eddies within the surface layer have height z s, so z s is a new basis parameter for similarity models of the surface layer.

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  1. School of GeoSciences, University of Edinburgh, Scotland, EH9 3JU, U.K.

    K.G. McNaughton

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McNaughton, K. Turbulence Structure of the Unstable Atmospheric Surface Layer and Transition to the Outer Layer. Boundary-Layer Meteorology 112, 199–221 (2004). https://doi.org/10.1023/B:BOUN.0000027906.28627.49

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