Global sonde datasets do not support a mesoscale transition in the turbulent energy cascade

TL;DR

This study uses global sonde datasets to challenge the traditional view of distinct atmospheric turbulence regimes across scales, instead supporting a unified anisotropic turbulence model with consistent scaling properties.

Contribution

The paper provides empirical evidence from global sonde data that contradicts the assumed scale breaks in atmospheric turbulence, supporting a single anisotropic turbulence framework.

Findings

Horizontal wind structure function has a Hurst exponent of ~0.6, inconsistent with gravity waves or 3D turbulence.

Horizontal wind structure function has a Hurst exponent of ~0.4 at larger scales, inconsistent with quasi-geostrophic dynamics.

Data supports a unified anisotropic turbulence model with specific Hurst exponents across scales.

Abstract

Conceptual and theoretical models describing the dynamics of the atmosphere often assume a hierarchy of dynamic regimes, each operating over some limited range of spatial scales. The largest scales are presumed to be governed by quasi-two-dimensional geostrophic turbulence, mesoscale dynamics by gravity waves, and the smallest scales by 3D isotropic turbulence. In theory, this hierarchy should be observable as clear scale breaks in turbulent kinetic energy spectra as one physical mechanism transitions to the next. Here, we show that this view is not supported by global dropsonde and radiosonde datasets of horizontal winds. Instead, the structure function for horizontal wind calculated for vertical separations between 200 m and 8 km has a Hurst exponent of $H_v \approx 0.6$, which is inconsistent with either gravity waves ($H_v = 1$) or 3D turbulence ($H_v = 1/3$). For horizontal separations between 200 km and 1800 km, the Hurst exponent is $H_h \approx 0.4$, which is inconsistent with quasi-geostrophic dynamics ($H_h = 1$). We argue that sonde observations are most consistent with a lesser known "Lovejoy-Schertzer" model for stratified turbulence where, at all scales, the dynamics of the atmosphere obey a single anisotropic turbulent cascade with $H_v=3/5$ and $H_h =1/3$. While separation scales smaller than 200 m are not explored here due to measurement limitations, the analysis nonetheless supports a single cohesive theoretical framework for describing atmospheric dynamics, one that might substitute for the more traditional hierarchy of mechanisms that depends on spatial scale.