Turbulence: Vertical Shear of the Horizontal Wind, Jet Streams, Symmetry Breaking, Scale Invariance and Gibbs Free Energy

Adrian F Tuck

doi:10.3390/atmos12111414

Abstract

The increase of the vertical scaling exponent of the horizontal wind Hv(s) with altitude from the surface of the Pacific Ocean to 13 km altitude, as observed by GPS dropsondes, is investigated. An explanation is offered in terms of the decrease of gravitational force and decrease of quenching efficiency of excited photofragments from ozone photodissociation with increasing altitude (decreasing pressure). Turbulent scaling is examined in both the vertical from dropsondes and horizontal from aircraft observations; the scaling exponents H for both wind speed and temperature in both coordinates are positively correlated with traditional measures of jet stream strength. Interpretation of the results indicates that persistence of molecular velocity after collision induces symmetry breaking emergence of hydrodynamic flow via the mechanism first modelled by Alder and Wainwright, enabled by the Gibbs free energy carried by the highest speed molecules. It is suggested that the combined effects have the potential to address the cold bias in numerical models of the global atmosphere.

Highlights

Atmospheric turbulence is a very large field, as an exploration on Web of Science with that as the search term will reveal—27 new hits in the first 11 days of June 2021, and many thousands since 1950
Persistence of velocity after collision and the emergence of hydrodynamic flow spontaneously break the continuous translational symmetry of the random molecular motion underlying the theory of Maxwell–Boltzmann distributions
That will devalue attempts to deploy higher symmetries to the atmosphere, such as Fourier analysis and wave formulations, which seek to impose a symmetry on the air that it does not have

Summary

Introduction

Atmospheric turbulence is a very large field, as an exploration on Web of Science with that as the search term will reveal—27 new hits in the first 11 days of June 2021, and many thousands since 1950 It affects most aspects of the atmosphere, from modelling for weather forecasting, through water transport, cloud formation, radiative transfer, biogeospheric exchanges, pollutant transport and deposition to such engineering activities as aviation, wind turbines, adaptive optics for astronomical telescopes and building construction. These processes are all involved in global heating and the evolution of macroweather, the climate and their modelling. As a consequence of the analysis, the cold bias in numerical models of the global atmosphere is potentially addressable

Observations of the Vertical Scaling of the Horizontal Wind Speed

IInntteerrpprreettattiioon of the Observed Turbulence

Findings

Conclusions