Contributions of Moist Convection and Internal Gravity Waves to Building the Atmospheric −5/3 Kinetic Energy Spectra

2017 ◽  
Vol 74 (1) ◽  
pp. 185-201 ◽  
Author(s):  
Y. Qiang Sun ◽  
Richard Rotunno ◽  
Fuqing Zhang
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
Gravity Waves ◽  
Mesoscale Model ◽  
Lower Troposphere ◽  
Internal Gravity Waves ◽  
Moist Convection ◽  
Convective Systems ◽  
Kinetic Energy Spectrum ◽  
Advection Term

Abstract With high-resolution mesoscale model simulations, the authors have confirmed a recent study demonstrating that convective systems, triggered in a horizontally homogeneous environment, are able to generate a background mesoscale kinetic energy spectrum with a slope close to −5/3, which is the observed value for the kinetic energy spectrum at mesoscales. This shallow slope can be identified at almost all height levels from the lower troposphere to the lower stratosphere in the simulations, implying a strong connection between different vertical levels. The present study also computes the spectral kinetic energy budget for these simulations to further analyze the processes associated with the creation of the spectrum. The buoyancy production generated by moist convection, while mainly injecting energy in the upper troposphere at small scales, could also contribute at larger scales, possibly as a result of the organization of convective cells into mesoscale convective systems. This latter injected energy is then transported by energy fluxes (due to gravity waves and/or convection) both upward and downward. Nonlinear interactions, associated with the velocity advection term, finally help build the approximate −5/3 slope through upscale and/or downscale propagation at all levels.

scholarly journals The Mesoscale Kinetic Energy Spectrum of a Baroclinic Life Cycle

2009 ◽  
Vol 66 (4) ◽  
pp. 883-901 ◽  
Author(s):  
Michael L. Waite ◽  
Chris Snyder
Keyword(s):  
Life Cycle ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Gravity Waves ◽  
Linear Instability ◽  
Mature Stage ◽  
Flux Divergence ◽  
Full Spectrum ◽  
Kinetic Energy Spectrum ◽  
Inertia Gravity Waves

Abstract The atmospheric mesoscale kinetic energy spectrum is investigated through numerical simulations of an idealized baroclinic wave life cycle, from linear instability to mature nonlinear evolution and with high horizontal and vertical resolution (Δx ≈ 10 km and Δz ≈ 60 m). The spontaneous excitation of inertia–gravity waves yields a shallowing of the mesoscale spectrum with respect to the large scales, in qualitative agreement with observations. However, this shallowing is restricted to the lower stratosphere and does not occur in the upper troposphere. At both levels, the mesoscale divergent kinetic energy spectrum—a proxy for the inertia–gravity wave energy spectrum—resembles a −5/3 power law in the mature stage. Divergent kinetic energy dominates the lower stratospheric mesoscale spectrum, accounting for its shallowing. Rotational kinetic energy, by contrast, dominates the upper tropospheric spectrum and no shallowing of the full spectrum is observed. By analyzing the tendency equation for the kinetic energy spectrum, it is shown that the lower stratospheric spectrum is not governed solely by a downscale energy cascade; rather, it is influenced by the vertical pressure flux divergence associated with vertically propagating inertia–gravity waves.

Mesoscale Predictability in Moist Mid-Latitude Cyclones Is Not Sensitive to the Slope of the Background Kinetic Energy Spectrum

2021 ◽  
Author(s):  
Daniel J. Lloveras ◽  
Lydia H. Tierney ◽  
Dale R. Durran
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
Small Amplitude ◽  
Numerical Solutions ◽  
Physical Space ◽  
Homogeneous Turbulence ◽  
Moist Convection ◽  
Error Growth ◽  
Horizontal Scale ◽  
Kinetic Energy Spectrum

Abstract We investigate the sensitivity of mesoscale atmospheric predictability to the slope of the background kinetic energy spectrum E by adding initial errors to simulations of idealized moist midlatitude cyclones at several wavenumbers k for which the slope of E(k) is significantly different. These different slopes arise from 1) differences in the E(k) generated by cyclones growing in two different moist baroclinically unstable environments, and 2) differences in the horizontal scale at which initial perturbations are added, with E(k) having steeper slopes at larger scales. When small-amplitude potential temperature perturbations are added, the error growth through the subsequent 36-hour simulation is not sensitive to the slope of E(k) nor to the horizontal scale of the initial error. In all cases with small-amplitude perturbations, the error growth in physical space is dominated by moist convection along frontal boundaries. As such, the error field is localized in physical space and broad in wavenumber (spectral) space. In moist mid-latitude cyclones, these broadly distributed errors in wavenumber space limit mesoscale predictability by growing up-amplitude rather than by cascading upscale to progressively longer wavelengths. In contrast, the error distribution in homogeneous turbulence is broad in physical space and localized in wavenumber space, and dimensional analysis can be used to estimate the error growth rate at a specific wavenumber k from E(k). Predictability estimates derived in this manner, and from the numerical solutions of idealized models of homogeneous turbulence, depend on whether the slope of E(k) is shallower or steeper than k−3, which differs from the slope-insensitive behavior exhibited by moist mid-latitude cyclones.

scholarly journals Calculating Energy Spectra from Drifters

2016 ◽  
Author(s):  
Joseph H. LaCasce
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
Structure Function ◽  
Two Dimensions ◽  
Longitudinal Structure ◽  
Kinetic Energy Spectrum ◽  
Longitudinal Structure Function ◽  
Large Pair ◽  
Non Local ◽  
Lagrangian Data

The relations between the kinetic energy spectrum and the second order longitudinal structure function in two dimensions are derived, and several examples are considered. The forward conversion (from spectrum to structure function) is illustrated first with idealized power law spectra, representing turbulent inertial ranges. The forward conversion is also applied to the zonal kinetic energy spectrum of Nastrom and Gage (1985) and the result agrees well with the longitudinal structure function of Lindborg (1999). The inverse conversion (from structure function to spectrum) is tested with data from 2D turbulence simulations. When applied to the theoretical structure function (derived from the forward conversion of the spectrum), the result closely resembles the original spectrum, except at the largest wavenumbers. However the inverse conversion is much less successful when applied to the structure function obtained from pairs of particles in the flow. This is because the inverse conversion favors large pair separations, which are typically noisy with particle data. Fitting the structure function to a polynomial improves the result, but not sufficiently to distinguish the correct inertial range dependencies. Furthermore the inversion of non-local spectra is largely unsuccessful. Thus it appears that focusing on structure functions with Lagrangian data is preferable to estimating spectra.

Kinetic energy spectrum of large-and mesoscale atmospheric processes

Nature ◽  
1984 ◽  
Vol 310 (5972) ◽  
pp. 36-38 ◽  
Author(s):  
G. D. Nastrom ◽  
K. S. Gage ◽  
W. H. Jasperson
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
Atmospheric Processes ◽  
Kinetic Energy Spectrum

Characterization of Momentum Transport Associated with Organized Moist Convection and Gravity Waves

2010 ◽  
Vol 67 (10) ◽  
pp. 3208-3225 ◽  
Author(s):  
Todd P. Lane ◽  
Mitchell W. Moncrieff
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Tropical Convection ◽  
Momentum Transport ◽  
Moist Convection ◽  
Convective Systems ◽  
Convective Momentum Transport ◽  
Convective Organization ◽  
Wave Momentum

Abstract Tropical convection is inherently multiscalar, involving complex fields of clouds and various regimes of convective organization ranging from small disorganized cumulus up to large organized convective clusters. In addition to being a crucial component of the atmospheric water cycle and the global heat budget, tropical convection induces vertical fluxes of horizontal momentum. There are two main contributions to the momentum transport. The first resides entirely in the troposphere and is due to ascent, descent, and organized circulations associated with precipitating convective systems. The second resides in the troposphere, stratosphere, and farther aloft and is caused by vertically propagating gravity waves. Both the convective momentum transport and the gravity wave momentum flux must be parameterized in general circulation models; yet in existing parameterizations, these two processes are treated independently. This paper examines the relationship between the convective momentum transport and convectively generated gravity wave momentum flux by utilizing idealized simulations of multiscale tropical convection in different wind shear conditions. The simulations produce convective systems with a variety of regimes of convective organization and therefore different convective momentum transport properties and gravity wave spectra. A number of important connections are identified, including a consistency in the sign of the momentum transports in the lower troposphere and stratosphere that is linked to the generation of gravity waves by tilted convective structures. These results elucidate important relationships between the convective momentum transport and the gravity wave momentum flux that will be useful for interlinking their parameterization in the future.

scholarly journals Comment on "Reinterpreting aircraft measurement in anisotropic scaling turbulence" by Lovejoy et al. (2009)

2010 ◽  
Vol 10 (3) ◽  
pp. 1401-1402 ◽  
Author(s):  
E. Lindborg ◽  
K. K. Tung ◽  
G. D. Nastrom ◽  
J. Y. N. Cho ◽  
K. S. Gage
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
General Circulation ◽  
General Circulation Models ◽  
Measured Spectrum ◽  
Vertical Movements ◽  
Aircraft Measurement ◽  
Kinetic Energy Spectrum ◽  
Anisotropic Scaling ◽  
The 1960S

Abstract. Recently, Lovejoy et al. (2009) argued that the steep ~k−3 atmospheric kinetic energy spectrum at synoptic scales (≥1000 km) observed by aircraft is a spurious artefact of aircraft following isobars instead of isoheights. Without taking into account the earth's rotation they hypothesise that the horizontal atmospheric energy spectrum should scale as k−5/3 at all scales. We point out that the approximate k−3-spectrum at synoptic scales has been observed by a number of non-aircraft means since the 1960s and that general circulation models and other current models have successfully produced this spectrum. We also argue that the vertical movements of the aircraft are far too small to cause any strong effect on the measured spectrum at synoptic scales.

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