The Critical Richardson Number and Limits of Applicability of Local Similarity Theory in the Stable Boundary Layer

By A. Grachev, Edgar L. Andreas, Christopher W. Fairall, P. Guest. Boundary-layer Meteorology, 2012

253 citations recorded by the source corpus.

Measurements of atmospheric turbulence made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to determine the limits of applicability of Monin–Obukhov similarity theory (in the local scaling formulation) in the stable atmospheric boundary layer. Based on the spectral analysis of wind velocity and air temperature fluctuations, it is shown that, when both the gradient Richardson number, Ri, and the flux Richardson number, Rf, exceed a ‘critical value’ of about 0.20–0.25, the inertial subrange associated with the Richardson–Kolmogorov cascade dies out and vertical turbulent fluxes become small. Some small-scale turbulence survives even in this supercritical regime, but this is non-Kolmogorov turbulence, and it decays rapidly with further increasing stability. Similarity theory is based on the turbulent fluxes in the high-frequency part of the spectra that are associated with energy-containing/flux-carrying eddies. Spectral densities in this high-frequency band diminish as the Richardson–Kolmogorov energy cascade weakens; therefore, the applicability of local Monin–Obukhov similarity theory in stable conditions is limited by the inequalities Ri < Ricr and Rf < Rfcr. However, it is found that Rfcr  =  0.20–0.25 is a primary threshold for applicability. Applying this prerequisite shows that the data follow classical Monin–Obukhov local z-less predictions after the irrelevant cases (turbulence without the Richardson–Kolmogorov cascade) have been filtered out.

Subfields: Atmospheric Science, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/2a963d298ab912fffeeffd7495b35d9462b1dd05

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atmospheric Science

1. Larry Mahrt
2. A. Grachev
3. B. Grisogono
4. Jielun Sun
5. B. Galperin
6. R. Banta
7. D. Vickers

In Global and Planetary Change

1. Larry Mahrt
2. A. Grachev
3. Jielun Sun
4. B. Grisogono
5. B. Galperin
6. R. Banta
7. D. Vickers

Citations in the corpus

• Stably Stratified Atmospheric Boundary Layers (2014, background): “Additionally, the inertial subrange may not be detectable in Fourier spectra, pointing to the failure of Kolmogorov similarity theory, or perhaps failure to observe sufficiently small scales (Grachev et al. 2013).”
• Review of wave‐turbulence interactions in the stable atmospheric boundary layer (2015, methodology): “…et al., 1984; Grisogono, 1994b; Strang and Fernando, 2001; Andreas, 2002; Zilitinkevich and Baklanov, 2002; Fernando, 2003; Troy and Koseff , 2005; Achatz, 2007; Galperin et al., 2007; Mauritsen and Svensson, 2007; Zilitinkevich and Esau, 2007; Sun, 2011; Sun et al., 2012; Grachev et al., 2013].”