Atmospheric waves as scaling, turbulent phenomena

Abstract

Abstract. It is paradoxical that, while atmospheric dynamics are highly nonlinear and turbulent, atmospheric waves are commonly modelled by linear or weakly nonlinear theories. We postulate that the laws governing atmospheric waves are in fact high-Reynolds-number (Re), emergent laws so that -in common with the emergent high-Re turbulent lawsthey are also constrained by scaling symmetries. We propose an effective turbulence-wave propagator which corresponds to a fractional and anisotropic extension of the classical wave equation propagator, with dispersion relations similar to those of inertial gravity waves (and Kelvin waves) yet with an anomalous (fractional) order H wav /2. Using geostationary IR radiances, we estimate the parameters, finding that H wav ≈ 0.17 ± 0.04 (the classical value = 2).

On Mars too expect macroweather

“…The use of turbulence laws up to planetary scales—even if nonclassical due to anisotropy and intermittency—may seem surprising in view of the usual approach to the large‐scale Martian circulation [ Hollingsworth and Barnes , ; Read and Lewis , ; see also Leovy , ] that relies on quasi‐linear analyses including diurnal tides, the interaction between planetary waves, and the topography. However, an analogous apparent contradiction appears in tropical meteorology, which—while often understood in similar type terms—nevertheless well respects high‐level statistical laws showing their compatibility with mechanistic, deterministic explanations [ Pinel et al ., ; Pinel and Lovejoy , ]. Here thanks to Martian reanalyses, we have directly confirmed the multiplicative nature of the dynamical fluxes as well as the rough Kolmogorov horizontal spectra (although with artifacts similar to those of terrestrial reanalyses [ Lovejoy and Schertzer , ]).…”

Scaling Analysis of the China France Oceanography Satellite Along‐Track Wind and Wave Data

“…Later, the horizontal anisotropy has been taken into account in the 23/9D model and verified by using the European Centre for Medium‐Range Weather Forecasts (ECMWF) reanalyzes data (Lovejoy & Schertzer, 2011). This model is also discussed and checked in more recent works (Lovejoy & Schertzer, 2013; Pinel & Lovejoy, 2014). The results show that this model is capable to explain numerous claims of transition phenomena, for instance the spurious −2.4 slope for aircraft collected data can be interpreted by the anisotropic 23/9D turbulence model, rather than the isotropic 3D or 2D turbulence models.…”