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.

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 Influence of Gravity Waves on the Slope of the Kinetic Energy Spectrum in Simulations of Idealized Midlatitude Cyclones

2019 ◽  
Vol 76 (7) ◽  
pp. 2103-2122 ◽  
Author(s):  
Maximo Q. Menchaca ◽  
Dale R. Durran
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
Gravity Waves ◽  
Surface Stress ◽  
Advective Transport ◽  
Flux Divergence ◽  
Mountain Waves ◽  
Wave Induced ◽  
The Impact ◽  
The Waves

Abstract The influence of gravity waves generated by surface stress and by topography on the atmospheric kinetic energy (KE) spectrum is examined using idealized simulations of a cyclone growing in baroclinically unstable shear flow. Even in the absence of topography, surface stress greatly enhances the generation of gravity waves in the vicinity of the cold front, and vertical energy fluxes associated with these waves produce a pronounced shallowing of the KE spectrum at mesoscale wavelengths relative to the corresponding free-slip case. The impact of a single isolated ridge is, however, much more pronounced than that of surface stress. When the mountain waves are well developed, they produce a wavenumber to the −5/3 spectrum in the lower stratosphere over a broad range of mesoscale wavelengths. In the midtroposphere, a smaller range of wavelengths also exhibits a −5/3 spectrum. When the mountain is 500 m high, the waves do not break, and their KE is entirely associated with the divergent component of the velocity field, which is almost constant with height. When the mountain is 2 km high, wave breaking creates potential vorticity, and the rotational component of the KE spectrum is also strongly energized by the waves. Analysis of the spectral KE budgets shows that the actual spectrum is the result of continually shifting balances of direct forcing from vertical energy flux divergence, conservative advective transport, and buoyancy flux. Nevertheless, there is one interesting example where the −5/3-sloped lower-stratospheric energy spectrum appears to be associated with a gravity-wave-induced upscale inertial cascade.

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

scholarly journals Ageostrophic instability in rotating, stratified interior vertical shear flows

2014 ◽  
Vol 755 ◽  
pp. 397-428 ◽  
Author(s):  
Peng Wang ◽  
James C. McWilliams ◽  
Claire Ménesguen
Keyword(s):  
Energy Source ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Gravity Waves ◽  
Shear Flows ◽  
Vertical Shear ◽  
Mean Flow ◽  
Efficient Energy Transfer ◽  
The Mean ◽  
Inertia Gravity Waves

AbstractThe linear instability of several rotating, stably stratified, interior vertical shear flows $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\overline{U}(z)$ is calculated in Boussinesq equations. Two types of baroclinic, ageostrophic instability, AI1 and AI2, are found in odd-symmetric $\overline{U}(z)$ for intermediate Rossby number ($\mathit{Ro}$). AI1 has zero frequency; it appears in a continuous transformation of the unstable mode properties between classic baroclinic instability (BCI) and centrifugal instability (CI). It begins to occur at intermediate $\mathit{Ro}$ values and horizontal wavenumbers ($k,l$) that are far from $l= 0$ or $k = 0$, where the growth rate of BCI or CI is the strongest. AI1 grows by drawing kinetic energy from the mean flow, and the perturbation converts kinetic energy to potential energy. The instability AI2 has inertia critical layers (ICL); hence it is associated with inertia-gravity waves. For an unstable AI2 mode, the coupling is either between an interior balanced shear wave and an inertia-gravity wave (BG), or between two inertia-gravity waves (GG). The main energy source for an unstable BG mode is the mean kinetic energy, while the main energy source for an unstable GG mode is the mean available potential energy. AI1 and BG type AI2 occur in the neighbourhood of $A-S= 0$ (a sign change in the difference between absolute vertical vorticity and horizontal strain rate in isentropic coordinates; see McWilliams et al., Phys. Fluids, vol. 10, 1998, pp. 3178–3184), while GG type AI2 arises beyond this condition. Both AI1 and AI2 are unbalanced instabilities; they serve as an initiation of a possible local route for the loss of balance in 3D interior flows, leading to an efficient energy transfer to small scales.

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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