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 laws – they 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 Hwav/2. Using geostationary IR radiances, we estimate the parameters, finding that Hwav ≈ 0.17 ± 0.04 (the classical value = 2).
Highlights
The atmosphere is a highly turbulent system with the ratio of nonlinear to linear terms – the Reynolds number (Re) – typically of the order ≈ 1012
Based on the classical laws of turbulence, they involve extensions to account for intermittency and anisotropy. Their success underlines the fundamental role of scale symmetries in constraining the high-Re dynamics. All this motivates the following question: are atmospheric waves scaling turbulent phenomena? If this is the case, we may logically expect anomalous wave propagators that could readily have dispersion relations identical to or nearly indistinguishable from their classical counterparts, while simultaneously having nontrivial consequences for the dynamics and for our understanding – for example, we find that energy transport will be modified (Appendix B)
Theories explaining the turbulent aspects assume that the dynamics are strongly nonlinear and scaling; in contrast, the corresponding wave theories are generally linear or weakly nonlinear
Summary
The atmosphere is a highly turbulent system with the ratio of nonlinear to linear terms – the Reynolds number (Re) – typically of the order ≈ 1012. There is no doubt that atmospheric waves exist and play an important role in transferring energy and momentum These empirical facts only become problematic when we consider the numerous apparently successful studies comparing data with linear (or weakly nonlinear) theory, commonly (for gravity waves) with the Taylor–Goldstein equations or with the linearized shallow-water equations. In the last few years, (nonlinear) scaling theories of waves have become more compelling This is because empirical evidence and theoretical arguments have amassed to the effect that atmospheric dynamics give rise to emergent highReynolds-number scaling laws with different horizontal and vertical exponents. Based on the classical laws of turbulence, they involve extensions to account for (multifractal) intermittency and anisotropy Their success underlines the fundamental role of scale symmetries in constraining the high-Re dynamics. The reason is that with only scaling symmetries to guide us the possibilities are very broad, while on the empirical side over the scaling range accessible here (60–5000 km in space and 3–100 h in time) the turbulent part of the spectrum is by far the most dominant one, accounting for an empirical range of spectral densities of a factor ≈ 105, leaving the residual wave-like part to account for the remaining factor of 0.9 ± 0.5 in the dynamical spectral scaling range
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