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

Abstract : 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 modeling of ASL flows and for experimental design.