Scaling Laws for the Length Scale of Energy‐Containing Eddies in a Sheared and Thermally Stratified Atmospheric Surface Layer

In the atmospheric surface layer (ASL), a characteristic wavelength marking the limit between energy‐containing and inertial subrange scales can be defined from the vertical velocity spectrum. This wavelength is related to the integral length scale of turbulence, used in turbulence closure approaches for the ASL. The scaling laws describing the displacement of this wavelength with changes in atmospheric stability have eluded theoretical treatment and are considered here. Two derivations are proposed for mildly unstable to mildly stable ASL flows ‐ one that only makes use of normalizing constraints on the vertical velocity variance along with idealized spectral shapes featuring production to inertial subrange regimes, while another utilizes a co‐spectral budget with a return‐to‐isotropy closure. The expressions agree with field experiments and permit inference of the variations of the wavelength with atmospheric stability. This methodology offers a new perspective for numerical and theoretical modelling of ASL flows and for experimental design.

Plain Language Summary

Turbulent flows in the atmosphere are composed of a large number of eddies whose sizes vary from kilometers to fractions of millimeters. The energy content in the vertical direction associated with each eddy size dictates the overall ability of turbulent motion to mix and transport particles (such as seeds, pollen, or spores), gases (such as carbon dioxide, ozone, methane, isoprene, etc...), energy (such as latent and sensible heat) and momentum from or to the underlying surface. Despite this multiplicity of eddy sizes, numerous experiments and simulation studies have shown that an effective or dominant eddy size may be sufficient to represent the overall mixing and transport properties of turbulent flows. This finding is a corner‐stone to representing the effects of turbulence on transport in Numerical Weather Prediction models. The work here explores how surface heating or cooling (i.e. near‐surface atmospheric stability) regulates this dominant or effective eddy size. The derivation makes use of well‐established constraints on the overall turbulent kinetic energy in the vertical direction, and highlights the parameters dictating this regulation.


stratified turbulence, turbulent boundary layer, atmospheric surface layer, return-to-isotropy, spectral budget

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Ayet Alex, Katul G. G. (2020). Scaling Laws for the Length Scale of Energy‐Containing Eddies in a Sheared and Thermally Stratified Atmospheric Surface Layer. Geophysical Research Letters. 47 (23). e2020GL089997 (10p.).,

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