scholarly journals The Horizontal Spectrum of Vertical Velocities near the Tropopause from Global to Gravity Wave Scales

2019 ◽  
Vol 76 (12) ◽  
pp. 3847-3862 ◽  
Author(s):  
Ulrich Schumann
Keyword(s):  
Kinetic Energy ◽  
Gravity Wave ◽  
Energy Exchange ◽  
Energy Spectra ◽  
Stratified Turbulence ◽  
Free Atmosphere ◽  
Aircraft Measurement ◽  
Small Scales ◽  
Field Campaigns ◽  
Measurement Validity

Abstract Vertical motions are fundamental for atmospheric dynamics. Compared to horizontal motions, the horizontal spectrum of vertical velocity w is less well known. Here, w spectra are related to spectra of horizontal motions in the free atmosphere near the tropopause from global to gravity wave scales. At large scales, w is related to vertically averaged horizontal divergent motions by continuity. At small scales, the velocity energy spectra reach anisotropy as in stably stratified turbulence. Combining these limits approximates the w spectrum from global to small scales. The w spectrum is flat at large scales when the divergent spectrum shows a −2 slope, reaches a maximum at mesoscales after transition to −5/3 slopes, and then approaches a fraction of horizontal kinetic energy. The ratio of vertical kinetic energy to potential energy increases quadratically with wavenumber at large scales. It exceeds unity at small scales in stratified turbulence. Global and regional simulations and two recent aircraft measurement field campaigns support these relationships within 30% deviations. Energy exchange between horizontal and vertical motions may contribute to slope changes in the spectra. The model allows for checking measurement validity. Isotropy at large and small scales varies between the datasets. The fraction of divergent energy is 40%–70% in the measurements, with higher values in the stratosphere. Spectra above the tropopause are often steeper over mountains than over oceans, partly with two −5/3 subranges. A total of 80% of w variance near the tropopause occurs at scales between about 0.5 and 80 km.

scholarly journals A solution of nonlinear equation for the gravity wave spectra from Adomian decomposition method: a first approach

2013 ◽  
Vol 28 (4) ◽  
pp. 357-363
Author(s):  
Antonio Gledson Goulart ◽  
Davidson Martins Moreira ◽  
Luiz Cláudio Pimentel ◽  
Jesus Salvador Pérez Guerrero
Keyword(s):  
Kinetic Energy ◽  
Nonlinear Equation ◽  
Gravity Wave ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Energy Spectra ◽  
Wave Spectra ◽  
Linear Solution ◽  
Adomian Decomposition ◽  
Nonlinear Nature

In this paper, the equation for the gravity wave spectra in mean atmosphere is analytically solved without linearization by the Adomian decomposition method. As a consequence, the nonlinear nature of problem is preserved and the errors found in the results are only due to the parameterization. The results, with the parameterization applied in the simulations, indicate that the linear solution of the equation is a good approximation only for heights shorter than ten kilometers, because the linearization the equation leads to a solution that does not correctly describe the kinetic energy spectra.

How white is the sky? 

2021 ◽  
Author(s):  
Nedjeljka Žagar ◽  
Žiga Zaplotnik ◽  
Valentino Neduhal
Keyword(s):  
Kinetic Energy ◽  
Gravity Wave ◽  
Power Law ◽  
Gravity Waves ◽  
Global Analysis ◽  
Vertical Motion ◽  
Energy Spectra ◽  
Horizontal Wind ◽  
Unified Framework ◽  
Inertia Gravity Waves

<p>The energy spectrum of atmospheric horizontal motions has been extensively studied in observations and numerical simulations. Its canonical shape includes a transition from the -3 power law at synoptic scale to -5/3 power law at mesoscale. The transition is taking place at scales around 500 km that can be seen as the scale where energy associated with quasi-linear inertia-gravity waves exceeds the balanced (or Rossby wave) energy. In contrast to the horizontal spectrum, the spectrum of kinetic energy of vertical motions is poorly known since the vertical motion is not an observed quantity of the global observing system and vertical kinetic energy spectra from non-hydrostatic models are difficult to validate.</p> <p>Traditionally, vertical velocities associated with the Rossby and gravity waves have been treated separately using the quasi-geostrophic omega equations and polarization relations for the stratified Boussinesq fluid in the (x,z) plane, respectively. In the tropics, the Rossby and gravity  wave regimes are difficult to separate and their frequency gap, present in the extra-tropics, is filled with the Kelvin and mixed Rossby-gravity waves. A separate treatment of the Rossby and gravity wave regimes makes it challenging to quantify energies of their vertical motions and vertical momentum fluxes. A unified treatment and wave interactions is performed by high-resolution non-hydrostatic models but their understanding requires the toolkit of theory. </p> <p>This contribution presents a unified framework for the derivation of vertical velocities of the Rossby and inertia-gravity waves and associated kinetic energy spectra. Expressions for the Rossby and gravity wave vertical velocities are derived using the normal-mode framework in the hydrostatic atmosphere that can be considered applicable up to the scale around 10 km. The derivation involves the analytical evaluation of divergence of the horizontal wind associated with the Rossby and inertia-gravity eigensolutions of the linearized primitive equations. The new framework is applied to the global analysis data of the ECMWF system. Results confirm that the tropical vertical kinetic energy spectra associated with inertia-gravity waves are on average indeed white. Deviations from the white spectrum are discussed for latitude and altitude bands.</p>

Energy spectra of stably stratified turbulence

2012 ◽  
Vol 698 ◽  
pp. 19-50 ◽  
Author(s):  
Y. Kimura ◽  
J. R. Herring
Keyword(s):  
Power Law ◽  
Large Scale ◽  
Wave Spectrum ◽  
Structure Functions ◽  
Direct Numerical Simulations ◽  
Energy Spectra ◽  
Stratified Turbulence ◽  
Uhlenbeck Process ◽  
Small Scales ◽  
Incompressible Turbulence

AbstractWe investigate homogeneous incompressible turbulence subjected to a range of degrees of stratification. Our basic method is pseudospectral direct numerical simulations at a resolution of $102{4}^{3} $. Such resolution is sufficient to reveal inertial power-law ranges for suitably comprised horizontal and vertical spectra, which are designated as the wave and vortex mode (the Craya–Herring representation). We study mainly turbulence that is produced from randomly large-scale forcing via an Ornstein–Uhlenbeck process applied isotropically to the horizontal velocity field. In general, both the wave and vortex spectra are consistent with a Kolmogorov-like ${k}^{\ensuremath{-} 5/ 3} $ range at sufficiently large $k$. At large scales, and for sufficiently strong stratification, the wave spectrum is a steeper ${ k}_{\perp }^{\ensuremath{-} 2} $, while that for the vortex component is consistent with ${ k}_{\perp }^{\ensuremath{-} 3} $. Here ${k}_{\perp } $ is the horizontally gathered wavenumber. In contrast to the horizontal wavenumber spectra, the vertical wavenumber spectra show very different features. For those spectra, a clear ${ k}_{z}^{\ensuremath{-} 3} $ dependence for small scales is observed while the large scales show rather flat spectra. By modelling the horizontal layering of vorticity, we attempt to explain the flat spectra. These spectra are linked to two-point structure functions of the velocity correlations in the horizontal and vertical directions. We can observe the power-law transition also in certain of the two-point structure functions.

Atmospheric Kinetic Energy Spectra from Global High-Resolution Nonhydrostatic Simulations

2014 ◽  
Vol 71 (11) ◽  
pp. 4369-4381 ◽  
Author(s):  
William C. Skamarock ◽  
Sang-Hun Park ◽  
Joseph B. Klemp ◽  
Chris Snyder
Keyword(s):  
High Resolution ◽  
Kinetic Energy ◽  
Constant Pressure ◽  
Energy Spectra ◽  
Vertical Resolution ◽  
Stratified Turbulence ◽  
Model Resolution ◽  
Constant Height ◽  
Velocity Variance ◽  
Model Filter

Abstract Kinetic energy (KE) spectra derived from global high-resolution atmospheric simulations from the Model for Prediction Across Scales (MPAS) are presented. The simulations are produced using quasi-uniform global Voronoi horizontal meshes with 3-, 7.5-, and 15-km mean cell spacings. KE spectra from the MPAS simulations compare well with observations and other simulations in the literature and possess the canonical KE spectra structure including a very-well-resolved shallow-sloped mesoscale region in the 3-km simulation. There is a peak in the vertical velocity variance at the model filter scale for all simulations, indicating the underresolved nature of updrafts even with the 3-km mesh. The KE spectra reveal that the MPAS configuration produces an effective model resolution (filter scale) of approximately 6Δx. Comparison with other published model KE spectra highlight model filtering issues, specifically insufficient filtering that can lead to spectral blocking and the production of erroneous shallow-sloped mesoscale tails in the KE spectra. The mesoscale regions in the MPAS KE spectra are produced without use of kinetic energy backscatter, in contrast to other results reported in the literature. No substantive difference is found in KE spectra computed on constant height or constant pressure surfaces. Stratified turbulence is not resolved with the vertical resolution used in this study; hence, the results do not support recent conjecture that stratified turbulence explains the mesoscale portion of the KE spectrum.

scholarly journals Revisiting Bolgiano–Obukhov scaling for moderately stably stratified turbulence

2019 ◽  
Vol 875 ◽  
pp. 961-973 ◽  
Author(s):  
Shadab Alam ◽  
Anirban Guha ◽  
Mahendra K. Verma
Keyword(s):  
Kinetic Energy ◽  
Nauk Sssr ◽  
Direct Consequence ◽  
Passive Scalar ◽  
Inertial Range ◽  
Stratified Turbulence ◽  
Scalar Turbulence ◽  
Akad Nauk Sssr ◽  
Small Scales ◽  
Quantitative Condition

According to the celebrated Bolgiano–Obukhov (Bolgiano, J. Geophys. Res., vol. 64 (12), 1959, pp. 2226–2229; Obukhov, Dokl. Akad. Nauk SSSR, vol. 125, 1959, p. 1246) phenomenology for moderately stably stratified turbulence, the energy spectrum in the inertial range shows a dual scaling: the kinetic energy follows (i) ${\sim}k^{-11/5}$ for $k<k_{B}$, and (ii) ${\sim}k^{-5/3}$ for $k>k_{B}$, where $k_{B}$ is the Bolgiano wavenumber. The $k^{-5/3}$ scaling, akin to passive scalar turbulence, is a direct consequence of the assumption that buoyancy is insignificant for $k>k_{B}$. We revisit this assumption, and using the constancy of kinetic and potential energy fluxes and simple theoretical analysis, we find that the $k^{-5/3}$ spectrum is absent. This is because the velocity field at small scales is too weak to establish a constant kinetic energy flux as in passive scalar turbulence. A quantitative condition for the existence of the second regime is also derived in the paper.

Stratified turbulence forced in rotational and divergent modes

2007 ◽  
Vol 586 ◽  
pp. 83-108 ◽  
Author(s):  
E. LINDBORG ◽  
G. BRETHOUWER
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Dynamic Process ◽  
Boussinesq Equations ◽  
Inertial Range ◽  
Energy Spectra ◽  
Stratified Turbulence ◽  
Frequency Spectra ◽  
Forward Energy ◽  
Simulation Results

We perform numerical box simulations of strongly stratified turbulence. The equations solved are the Boussinesq equations with constant Brunt–Väisälä frequency and forcing either in rotational or divergent modes, or, with another terminology, in vortical or wave modes. In both cases, we observe a forward energy cascade and inertial-range scaling of the horizontal kinetic and potential energy spectra. With forcing in rotational modes, there is approximate equipartition of kinetic energy between rotational and divergent modes in the inertial range. With forcing in divergent modes the results are sensitive to the vertical forcing wavenumber kfv. If kfv is sufficiently large the dynamics is very similar to the dynamics of the simulations which are forced in rotational modes, with approximate equipartition of kinetic energy in rotational and divergent modes in the inertial range. Frequency spectra of rotational, divergent and potential energy are calculated for individual Fourier modes. Waves are present at low horizontal wavenumbers corresponding to the largest scales in the boxes. In the inertial range, the frequency spectra exhibit no distinctive peaks in the internal wave frequency. In modes for which the vertical wavenumber is considerably larger than the horizontal wavenumber, the frequency spectra of rotational and divergent modes fall on top of each other. The simulation results indicate that the dynamics of rotational and divergent modes develop on the same time scale in stratified turbulence. We discuss the relevance of our results to atmospheric and oceanic dynamics. In particular, we review a number of observational reports indicating that stratified turbulence may be a prevalent dynamic process in the ocean at horizontal scales of the order of 10 or 100 m up to several kilometres.

Kinetic energy spectra of divergent wind in the atmosphere

Tellus ◽  
1981 ◽  
Vol 33 (1) ◽  
pp. 102-104 ◽  
Author(s):  
Tsing-Chang Chen ◽  
Joseph J. Tribbia
Keyword(s):  
Kinetic Energy ◽  
Energy Spectra ◽  
Divergent Wind

scholarly journals Correlation between Buoyancy Flux, Dissipation and Potential Vorticity in Rotating Stratified Turbulence

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 157
Author(s):  
Duane Rosenberg ◽  
Annick Pouquet ◽  
Raffaele Marino
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Potential Vorticity ◽  
Isotropic Turbulence ◽  
Joint Probability ◽  
Buoyancy Flux ◽  
Turbulent Regime ◽  
Stratified Turbulence ◽  
Low Dissipation ◽  
Linear And Nonlinear

We study in this paper the correlation between the buoyancy flux, the efficiency of energy dissipation and the linear and nonlinear components of potential vorticity, PV, a point-wise invariant of the Boussinesq equations, contrasting the three identified regimes of rotating stratified turbulence, namely wave-dominated, wave–eddy interactions and eddy-dominated. After recalling some of the main novel features of these flows compared to homogeneous isotropic turbulence, we specifically analyze three direct numerical simulations in the absence of forcing and performed on grids of 10243 points, one in each of these physical regimes. We focus in particular on the link between the point-wise buoyancy flux and the amount of kinetic energy dissipation and of linear and nonlinear PV. For flows dominated by waves, we find that the highest joint probability is for minimal kinetic energy dissipation (compared to the buoyancy flux), low dissipation efficiency and low nonlinear PV, whereas for flows dominated by nonlinear eddies, the highest correlation between dissipation and buoyancy flux occurs for weak flux and high localized nonlinear PV. We also show that the nonlinear potential vorticity is strongly correlated with high dissipation efficiency in the turbulent regime, corresponding to intermittent events, as observed in the atmosphere and oceans.

Kinetic energy spectra in thermionic emission from small tungsten cluster anions: Evidence for nonclassical electron capture

2010 ◽  
Vol 132 (10) ◽  
pp. 104307 ◽  
Author(s):  
Bruno Concina ◽  
Bruno Baguenard ◽  
Florent Calvo ◽  
Christian Bordas
Keyword(s):  
Kinetic Energy ◽  
Electron Capture ◽  
Thermionic Emission ◽  
Energy Spectra ◽  
Cluster Anions

Turbulent kinetic energy spectra and cascades in the polar atmosphere of Saturn

2021 ◽  
Author(s):  
Peter L. Read ◽  
Arrate Antuñano ◽  
Simon Cabanes ◽  
Greg Colyer ◽  
Teresa del Rio-Gaztelurrutia ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
High Latitude ◽  
Deep Convection ◽  
Baroclinic Instability ◽  
Polar Vortex ◽  
Energy Spectra ◽  
Horizontal Wind ◽  
Polar Regions ◽  
Zonal Wavenumber ◽  
Cloud Tops

&lt;p&gt;The regions of Saturn&amp;#8217;s cloud-covered atmosphere polewards of 60&lt;sup&gt;o&lt;/sup&gt; latitude are dominated in each hemisphere near the cloud tops by an intense, cyclonic polar vortex surrounded by a strong, high latitude eastward zonal jet. In the north, this high latitude jet takes the form of a remarkably regular zonal wavenumber m=6 hexagonal pattern that has been present at least since the Voyager spacecraft encounters with Saturn in 1980-81, and probably much longer. The origin of this feature, and the absence of a similar feature in the south, has remained poorly understood since its discovery. In this work, we present some new analyses of horizontal wind measurements at Saturn&amp;#8217;s cloud tops polewards of 60 degrees in both the northern and southern hemispheres, previously published by Antu&amp;#241;ano et al. (2015) using images from the Cassini mission, in which we compute kinetic energy spectra and the transfer rates of kinetic energy (KE) and enstrophy between different scales. 2D KE spectra are consistent with a zonostrophic regime, with a steep&amp;#160;(~n&lt;sup&gt;-5&lt;/sup&gt;) spectrum for the mean zonal flow (n is the total wavenumber) and a shallower Kolmogorov-like KE spectrum (~n&lt;sup&gt;-5/3&lt;/sup&gt;)&amp;#160;for the residual (eddy) flow, much as previously found for Jupiter&amp;#8217;s atmosphere (Galperin et al. 2014; Young &amp; Read 2017). Three different methods are used to compute the energy and enstrophy transfers, (a) as latitude-dependent zonal spectral fluxes, (b) as latitude-dependent structure functions and (c) as spatially filtered energy fluxes. The results of all three methods are largely in agreement in indicating a direct (forward) enstrophy cascade across most scales, averaged across the whole domain, an inverse kinetic energy cascade to large scales and a weak direct KE cascade at the smallest scales. The pattern of transfers has a more complex dependence on latitude, however. But it is clear that the m=6 North Polar Hexagon (NPH) wave was transferring KE into its zonal jet at 78&lt;sup&gt;o&lt;/sup&gt; N (planetographic) at a rate of &amp;#8719;&lt;sub&gt;E&lt;/sub&gt; &amp;#8776; 1.8 x 10&lt;sup&gt;-4&lt;/sup&gt; W kg&lt;sup&gt;-1&lt;/sup&gt;&amp;#160;at the time the Cassini images were acquired. This implies that the NPH was not maintained by a barotropic instability at this time, but may have been driven via a baroclinic instability or possibly from deep convection. Further implications of these results will be discussed.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;References&lt;/p&gt;&lt;p&gt;Antu&amp;#241;ano, A., T. del R&amp;#237;o-Gaztelurrutia, A. S&amp;#225;nchez-Lavega, and R. Hueso (2015), Dynamics of Saturn&amp;#8217;s polar regions, J. Geophys. Res. Planets, 120, 155&amp;#8211;176, doi:10.1002/2014JE004709.&lt;/p&gt;&lt;p&gt;Galperin, B., R. M.B. Young, S. Sukoriansky, N. Dikovskaya, P. L. Read, A.&amp;#160;J. Lancaster &amp; D. Armstrong (2014) Cassini observations reveal a regime of zonostrophic macroturbulence on Jupiter, Icarus, 229, 295&amp;#8211;320.doi: 10.1016/j.icarus.2013.08.030&lt;/p&gt;&lt;p&gt;Young, R. M. B. &amp; Read, P. L. (2017) Forward and inverse kinetic energy cascades in Jupiter&amp;#8217;s turbulent weather layer, Nature Phys., 13, 1135-1140. Doi:10.1038/NPHYS4227&lt;/p&gt;&lt;div&gt; &lt;div&gt; &lt;div&gt;&amp;#160;&lt;/div&gt; &lt;/div&gt; &lt;div&gt; &lt;div&gt;&amp;#160;&lt;/div&gt; &lt;/div&gt; &lt;div&gt; &lt;div&gt;&amp;#160;&lt;/div&gt; &lt;/div&gt; &lt;div&gt; &lt;div&gt;&amp;#160;&lt;/div&gt; &lt;/div&gt; &lt;/div&gt;

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