Transition from geostrophic turbulence to inertia–gravity waves in the atmospheric energy spectrum

Abstract

Midlatitude fluctuations of the atmospheric winds on scales of thousands of kilometers, the most energetic of such fluctuations, are strongly constrained by the Earth's rotation and the atmosphere's stratification. As a result of these constraints, the flow is quasi-2D and energy is trapped at large scales-nonlinear turbulent interactions transfer energy to larger scales, but not to smaller scales. Aircraft observations of wind and temperature near the tropopause indicate that fluctuations at horizontal scales smaller than about 500 km are more energetic than expected from these quasi-2D dynamics. We present an analysis of the observations that indicates that these smaller-scale motions are due to approximately linear inertia-gravity waves, contrary to recent claims that these scales are strongly turbulent. Specifically, the aircraft velocity and temperature measurements are separated into two components: one due to the quasi-2D dynamics and one due to linear inertia-gravity waves. Quasi-2D dynamics dominate at scales larger than 500 km; inertia-gravity waves dominate at scales smaller than 500 km. meteorology | atmospheric dynamics | geostrophic turbulence | inertia-gravity waves T he midlatitude high-and low-pressure systems visible in weather maps are associated with winds and temperature fluctuations that we experience as weather. These fluctuations arise from a baroclinic instability of the mean zonal winds at horizontal scales of a few thousand kilometers, commonly referred to as the synoptic scales (1-3). The combined effects of rotation and stratification constrain the synoptic-scale winds to be nearly horizontal and to satisfy geostrophic balance, a balance between the force exerted by the changes in pressure and the Coriolis force resulting from Earth's rotation. It is an open question whether the same constraints dominate in the mesoscale range (i.e., at scales of 10-500 km), or whether qualitatively different dynamics govern flows at these scales.The synoptic-scale flows are turbulent in the sense that nonlinear scale interactions, which lie at the core of the difficulty to predict the weather, exchange energy between different scales of motion (4-7). Under the constraints of rotation and stratification, the synoptic-scale winds are approximately 2D and nondivergent (8, 9). In 2D flows, nonlinear scale interactions tend to transfer energy to larger scales, that is, the synoptic-scale pressure anomalies often merge and form larger ones, contrary to nonlinear scale interactions in 3D flows, which tend to transfer energy to smaller scales (10). Little energy is thus transferred to scales smaller than those at which the synoptic-scale fluctuations are generated through instabilities. Theory and numerical simulations predict that the energy per unit horizontal wavenumber k decays as rapidly as k −3 at wavenumbers larger than the wavenumber corresponding to the instability scale (9, 11). This predicted kinetic energy spectrum is roughly consistent with synoptic-scale observations (9, 12).Long-range passeng...

The Dynamics of Mesoscale Winds in the Upper Troposphere and Lower Stratosphere

“…1). Unlike the structure functions shown by Lindborg (2015), the spectra presented in Callies et al (2014) exhibit a rough equipartition between the rotational and divergent components of horizontal kinetic energy over a wide mesoscale range, with a slight dominance of the divergent component at wavenumbers around k 5 2p/100 km. As confirmed by the wavevortex decomposition, this is consistent with inertiagravity waves dominating the mesoscale range.…”

“…The apparent discrepancy between the energy spectra of Callies et al (2014) and the structure functions of Lindborg (2015) can be fully explained by the relationship FIG. 1.…”

“…Conversely, if the flow is strongly nonlinearnot satisfying polarization and dispersion relations-one would expect the predicted energy to differ from the observed energy. In Callies et al (2014), we applied this procedure to the MOZAIC data and found that the observations in the mesoscale range are consistent with inertia-gravity waves. Lindborg (2015) also applied the Helmholtz decomposition-reformulated for structure functionsto the MOZAIC data.…”

“…In Callies et al (2014), we did not separate the data into altitude ranges but instead used all available flight tracks of sufficient length and data quality (cf. the appendix).…”

Submesoscale turbulence in the upper ocean

“…Callies, R. Ferrari, and O. Bühler (2014) Transition from geostrophic turbulence to inertia-gravity waves in the atmospheric energy spectrum. Proc.…”