Spectra, Spatial Scales, and Predictability in a Quasigeostrophic Model

2009 ◽  
Vol 66 (10) ◽  
pp. 3115-3130 ◽  
Author(s):  
Rebecca E. Morss ◽  
Chris Snyder ◽  
Richard Rotunno
Keyword(s):  
Growth Rate ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Spatial Scales ◽  
Error Growth ◽  
Surface Perturbation ◽  
Kinetic Energy Spectrum ◽  
Quasigeostrophic Model ◽  
Perturbation Growth

Abstract Results from homogeneous, isotropic turbulence suggest that predictability behavior is linked to the slope of a flow’s kinetic energy spectrum. Such a link has potential implications for the predictability behavior of atmospheric models. This article investigates these topics in an intermediate context: a multilevel quasigeostrophic model with a jet and temperature perturbations at the upper surface (a surrogate tropopause). Spectra and perturbation growth behavior are examined at three model resolutions. The results augment previous studies of spectra and predictability in quasigeostrophic models, and they provide insight that can help interpret results from more complex models. At the highest resolution tested, the slope of the kinetic energy spectrum is approximately at the upper surface but −3 or steeper at all but the uppermost interior model levels. Consistent with this, the model’s predictability behavior exhibits key features expected for flow with a shallower than −3 slope. At the highest resolution, upper-surface perturbation spectra peak below the energy-containing scales, and the error growth rate decreases as small scales saturate. In addition, as model resolution is increased and smaller scales are resolved, the peak of the upper-surface perturbation spectra shifts to smaller scales and the error growth rate increases. The implications for potential predictive improvements are not as severe, however, as in the standard picture of flows exhibiting a finite predictability limit. At the highest resolution, the model also exhibits periods of much faster-than-average perturbation growth that are associated with faster growth at smaller scales, suggesting predictability behavior that varies with time.

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.

Hybrid Eulerian–Lagrangian simulations for polymer–turbulence interactions

2013 ◽  
Vol 717 ◽  
pp. 535-575 ◽  
Author(s):  
Takeshi Watanabe ◽  
Toshiyuki Gotoh
Keyword(s):  
Energy Spectrum ◽  
Energy Dissipation ◽  
Kinetic Energy ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Polymer Concentration ◽  
Hybrid Approach ◽  
Weissenberg Number ◽  
Polymer Additives ◽  
Kinetic Energy Spectrum

AbstractThe effects of polymer additives on decaying isotropic turbulence are numerically investigated using a hybrid approach consisting of Brownian dynamics simulations for an enormous number of dumbbells (of the order of 10 billion,$O(1{0}^{10} )$) and direct numerical simulations of turbulence making full use of large-scale parallel computations. Reduction of the energy dissipation rate and modification of the kinetic energy spectrum in the dissipation range scale were observed when the reaction term due to the polymer additives was incorporated into the equation of motion for the solvent fluid. An increase in the polymer concentration or Weissenberg number${W}_{i} $yielded significant modifications of the turbulence statistics at small scales, such as a suppression of the local energy dissipation fluctuations. A power-law decay of the kinetic energy spectrum$E(k, t)\sim {k}^{- 4. 7} $was observed in the wavenumber range below the Kolmogorov length scale when${W}_{i} = 25$. The generation of intense vortices was suppressed by the polymer additives, consistent with previous studies using the constitutive equations. The field structures of the trace of the polymer stress depended on the intensity of its fluctuation: sheet-like structures were observed for the intermediate intensity region and filamentary structures were observed for the intense region. The results obtained with few polymers and large replicas could approximate those with many polymers and smaller replicas as far as the large-scale statistics were concerned.

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 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.

Decrypting the charge-resolved kinetic-energy spectrum in the Coulomb explosion of argon clusters

2012 ◽  
Vol 85 (2) ◽  
Author(s):  
R. Rajeev ◽  
K. P. M. Rishad ◽  
T. Madhu Trivikram ◽  
V. Narayanan ◽  
T. Brabec ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
Coulomb Explosion ◽  
Kinetic Energy Spectrum ◽  
Argon Clusters
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