scholarly journals Interaction of Upper-Tropospheric Turbulence and Gravity Waves as Obtained from Spectral and Structure Function Analyses

2008 ◽  
Vol 65 (8) ◽  
pp. 2676-2690 ◽  
Author(s):  
Chungu Lu ◽  
Steven E. Koch
Keyword(s):  
Structure Function ◽  
Gravity Waves ◽  
Function Analysis ◽  
Power Spectra ◽  
Physical Space ◽  
Energy Cascade ◽  
Small Scale ◽  
Order Structure ◽  
Scale Interactions ◽  
Inverse Energy Cascade

Abstract Spectral and structure function analyses of horizontal velocity fields observed in the upper troposphere and lower stratosphere during the Severe Clear Air Turbulence Collides with Air Traffic (SCATCAT) field program, conducted over the Pacific, were carried out in an effort to identify the scale interactions of turbulence and small-scale gravity waves. Because of the intermittent nature of turbulence, these analyses were conducted by clearly separating out the cases when turbulence did or did not occur in the data. In the presence of turbulence, transitional power spectra from k−2 to k−5/3 were found to be associated with gravity waves and turbulence, respectively. The second-order structure function analysis was able to translate these spectral slopes into r and r 2/3 scaling, consistent with the Monin and Yaglom conversion law, in physical space, which presented clearer pictures of scale interactions between turbulence and gravity waves. The third-order structure function analysis indicated the existence of a narrow region of inverse energy cascade from the scales of turbulence up to the gravity waves scales. This inverse energy cascade region was linked to the occurrence of Kelvin–Helmholtz instability and other wave-amplifying mechanisms, which were conjectured to lead to the breaking of small-scale gravity waves and the ensuing generation of turbulence. The multifractal analyses revealed further scale breaks between gravity waves and turbulence. The roughness and intermittent properties were also calculated for turbulence and gravity waves, respectively. Based on these properties, turbulence and gravity waves in a bifractal parameter space were mapped. In this way, their physical and statistical attributes were clearly manifested and understood.

Inverse energy cascade in ocean macroscopic turbulence:      Energy transfer rate ε and Richardson-Obhukov  constant g from an surface drifter experiment in the Benguela upwelling system

2021 ◽  
Author(s):  
Julia Draeger-Dietel ◽  
Alexa Griesel
Keyword(s):  
Energy Transfer ◽  
Probability Distribution ◽  
Structure Function ◽  
Transfer Rate ◽  
Energy Cascade ◽  
Order Structure ◽  
Energy Transfer Rate ◽  
Inverse Energy Cascade ◽  
Surface Drifter ◽  
Benguela Upwelling

<p>We derive the energy transfer rate ε from the 3<sup>rd</sup> order relative (longitudinal)  velocity structure function <Δu<sub>l</sub><sup>3</sup>>=(3/2)εs from ocean surface drifter trajectories in the turbulent mixed layer of the Benguela upwelling region off the coast of Namibia.  Combination with the  mean squared pair separation<s<sup>2</sup>(t)> =gεt<sup>3 </sup>reveals the Richardson-Obhukov constant g≅0.5, which is remarkably close to the one measured in  controlled two-dimensional turbulent flows in laboratory. We verify the  two coupled  cascades of energy (upscale/inverse) and enstrophy (downwscale) by  the  theoretically predicted  slope 1  for <Δu<sub>l</sub><sup>3</sup>> for inertial scales (above the injection scale) and slope 2 for  the 2<sup>nd</sup> order structure function <Δu<sub>l</sub><sup>2</sup>> for non-local scales (below the injection scale) respectively. We detect  additional 'ballistic contributions' in the central regime of the corresponding probability distribution P(st) of relative separations s for fixed time t, leading to an additional  power law factor s<sup>-α</sup> with  α ≅ 5/3. The algebraic decay with 1<α <2 revives  to the relevance of Levy distributions in the stochastic description of the turbulent transport process in contrast to former claims. Our findings  of a positively skewed   probability distribution P(Δu<sub>l</sub>s) of relative longitudinal velocity Δu<sub>l</sub>  for inertial scales s renews the question of intermittency in the  inverse energy cascade.</p>

scholarly journals Inverse Energy Cascade in Advanced MHD Turbulence (the RNG Method)

1993 ◽  
Vol 157 ◽  
pp. 255-261
Author(s):  
N. Kleeorin ◽  
I. Rogachevskii
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Magnetic Field Effect ◽  
Magnetic Reynolds Number ◽  
Energy Cascade ◽  
Small Scale ◽  
Magnetic Fluctuations ◽  
Mhd Turbulence ◽  
Inverse Energy Cascade ◽  
Large Scale Magnetic Field

The nonlinear (in terms of the large-scale magnetic field) effect of the modification of the magnetic force by an advanced small-scale magnetohydrodynamic (MHD) turbulence is considered. The phenomenon is due to the generation of magnetic fluctuations at the expense of hydrodynamic pulsations. It results in a decrease of the elasticity of the large-scale magnetic field.The renormalization group (RNG) method was employed for the investigation of the MHD turbulence at the large magnetic Reynolds number. It was found that the level of the magnetic fluctuations can exceed that obtained from the equipartition assumption due to the inverse energy cascade in advanced MHD turbulence.This effect can excite an instability of the large-scale magnetic field due to the energy transfer from the small-scale turbulent pulsations. This instability is an example of the inverse energy cascade in advanced MHD turbulence. It may act as a mechanism for the large-scale magnetic ropes formation in the solar convective zone and spiral galaxies.

scholarly journals Structure function analysis and intermittency in the atmospheric boundary layer

2008 ◽  
Vol 15 (6) ◽  
pp. 915-929 ◽  
Author(s):  
J. M. Vindel ◽  
C. Yagüe ◽  
J. M. Redondo
Keyword(s):  
Structure Function ◽  
Velocity Structure ◽  
Function Analysis ◽  
Inertial Range ◽  
Order Structure ◽  
Turbulence Structure ◽  
Scaling Exponent ◽  
Local Similarity ◽  
Velocity Structure Function ◽  
Velocity Increments

Abstract. Data from the SABLES98 experimental campaign (Cuxart et al., 2000) have been used in order to study the relationship of the probability distribution of velocity increments (PDFs) to the scale and the degree of stability. This connection is demonstrated by means of the velocity structure functions and the PDFs of the velocity increments. Using the hypothesis of local similarity, so that the third order structure function scaling exponent is one, the inertial range in the Kolmogorov sense has been identified for different conditions, obtaining the velocity structure function scaling exponents for several orders. The degree of intermittency in the energy cascade is measured through these exponents and compared with the forcing intermittency revealed through the evolution of flatness with scale. The role of non-homogeneity in the turbulence structure is further analysed using Extended Self Similarity (ESS). A criterion to identify the inertial range and to show the scale independence of the relative exponents is described. Finally, using least-squares fits, the values of some parameters have been obtained which are able to characterize intermittency according to different models.

Infrared Reynolds number dependency of the two-dimensional inverse energy cascade

2011 ◽  
Vol 667 ◽  
pp. 463-473 ◽  
Author(s):  
ANDREAS VALLGREN
Keyword(s):  
Reynolds Number ◽  
Cascade Range ◽  
Energy Cascade ◽  
Energy Spectra ◽  
Small Scale ◽  
Two Dimensional ◽  
Inverse Energy Cascade ◽  
Linear Friction ◽  
Non Local ◽  
Reynolds Number Dependency

High-resolution simulations of forced two-dimensional turbulence reveal that the inverse cascade range is sensitive to an infrared Reynolds number, Reα = kf/kα, where kf is the forcing wavenumber and kα is a frictional wavenumber based on linear friction. In the limit of high Reα, the classic k−5/3 scaling is lost and we obtain steeper energy spectra. The sensitivity is traced to the formation of vortices in the inverse energy cascade range. Thus, it is hypothesized that the dual limit Reα → ∞ and Reν = kd/kf → ∞, where kd is the small-scale dissipation wavenumber, will lead to a steeper energy spectrum than k−5/3 in the inverse energy cascade range. It is also found that the inverse energy cascade is maintained by non-local triad interactions.

Structure function analysis of plasma density fluctuations during total loss of lock of GPS signal events

2020 ◽  
Author(s):  
Hossein Ghadjari ◽  
David Knudsen ◽  
Susan Skone
Keyword(s):  
Structure Function ◽  
Plasma Density ◽  
Large Scale ◽  
Function Analysis ◽  
Density Fluctuations ◽  
Total Loss ◽  
Small Scale ◽  
Self Similarity ◽  
Radio Signals ◽  
Swarm Mission

<p>Ionospheric irregularities are fluctuations or structures of plasma density that affect the propagation of radio signals. Whenever large-scale irregularities break up into meso and small-scale irregularities, these processes become similar to a turbulence cascade. In order to have a better comparison between this and plasma density irregularities, we study different orders of structure functions of plasma density of total loss of lock events measured with the faceplate measurements of plasma density and the GPS measurements from the Swarm mission. Total loss of lock of GPS signal is a physical proxy for severe degradation of GPS signals. In addition to different orders of structure-function, we study the existence of self-similarity or multifractality of plasma density of total loss of lock events to investigate any possible intermittent fluctuations. </p>

scholarly journals Spectral and Structure Function Estimates of Turbulence Dissipation Rates in a High-Flow Tidal Channel Using Broadband ADCPs

2017 ◽  
Vol 34 (1) ◽  
pp. 5-20 ◽  
Author(s):  
Justine M. McMillan ◽  
Alex E. Hay
Keyword(s):  
Structure Function ◽  
Dissipation Rate ◽  
Acoustic Doppler Current Profiler ◽  
Universal Constant ◽  
Flow Speed ◽  
High Flow ◽  
Small Scale ◽  
Order Structure ◽  
Tidal Channel ◽  
Current Profiler

AbstractSpectral and structure function methods are implemented to compute the dissipation rate ε from broadband, diverging-beam acoustic Doppler current profiler (ADCP) data collected at four sites in a high-flow tidal channel. This paper shows that middepth estimates of ε obtained from spectral and second-order structure function (SF2) methods are both lognormally distributed with comparable means and variances. Speed bin–averaged ε values agree to within 16%, depending on the site and tidal phase (ebb/flood). The close agreement between the two independent methods provides further support for the argument put forward by McMillan et al.: that is, that the factor-of-2 difference between shear probe and (spectral) ADCP estimates of ε was likely caused by spatial differences in turbulence levels. The agreement between the spectral and both second- and third-order structure function methods also supports the use of for the SF2 universal constant. Notably, however, the SF3 method was less robust for these data. Two additional aspects of the SF2 approach are examined in some detail: 1) the differences from upstream- and downstream-facing beams are shown to arise from the Reynolds stress and 2) the inability of the ADCP to resolve small-scale motions does not affect the estimates of ε but yields apparent Doppler noise levels that—counterintuitively—decrease with increasing flow speed and increasing dissipation rate. A modified SF2 method that accounts for the variance associated with the unresolved scales removes the flow speed dependence and yields noise level estimates that agree with the spectral values.

scholarly journals Aircraft measurements of gravity waves in the upper troposphere and lower stratosphere during the START08 Field Experiment

2015 ◽  
Vol 15 (4) ◽  
pp. 4725-4766 ◽  
Author(s):  
Fuqing Zhang ◽  
Junhong Wei ◽  
Meng Zhang ◽  
K. P. Bowman ◽  
L. L. Pan ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Lower Stratosphere ◽  
Power Spectra ◽  
Small Scale ◽  
Aircraft Measurements ◽  
Upper Troposphere ◽  
Long Wavelength ◽  
Airborne Measurements ◽  
Wide Range

Abstract. This study analyzes in situ airborne measurements from the 2008 Stratosphere–Troposphere Analyses of Regional Transport (START08) experiment to characterize gravity waves in the extratropical upper troposphere and lower stratosphere (ExUTLS) region. The focus is on the second research flight (RF02), which took place on 21–22 April 2008. This was the first airborne mission dedicated to probing gravity waves associated with strong upper-tropospheric jet-front systems. Based on spectral and wavelet analyses of the in situ observations, along with a diagnosis of the polarization relationships, clear signals of mesoscale variations with wavelengths ~50–500 km are found in almost every segment of the 8 h flight, which took place mostly in the lower stratosphere. The aircraft sampled a wide range of background conditions including the region near the jet core, the jet exit and over the Rocky Mountains. In contrast to the long wavelength mesoscale variations, smaller-scale wavelike oscillations below 50 km are found to be quite transient. In particular, aircraft measurements of several flight segments are dominated by signals with periods of ~20– ~60 s and wavelengths of ~5– ~15 km. We speculate that at least part of these nearly-periodic high-frequency signals are a result of intrinsic observational errors in the aircraft measurements or small-scale flight-altitude fluctuations that are difficult to fully characterize. Despite the presence of possibly spurious wave oscillations in several flight segments, the power spectra of horizontal winds and temperature averaged over the analyzed START08 flight segments follow closely the -5/3 power law.

scholarly journals Robustness of vortex populations in the two-dimensional inverse energy cascade

2018 ◽  
Vol 850 ◽  
pp. 844-874
Author(s):  
B. H. Burgess ◽  
R. K. Scott
Keyword(s):  
Vortex Formation ◽  
Energy Cascade ◽  
Scaling Theory ◽  
Small Scale ◽  
Two Dimensional ◽  
Number Density ◽  
Scale Invariant ◽  
Inverse Energy Cascade ◽  
Simulation Parameters ◽  
The Impact

We study how the properties of forcing and dissipation affect the scaling behaviour of the vortex population in the two-dimensional turbulent inverse energy cascade. When the flow is forced at scales intermediate between the domain and dissipation scales, the growth rates of the largest vortex area and the spectral peak length scale are robust to all simulation parameters. For white-in-time forcing the number density distribution of vortex areas follows the scaling theory predictions of Burgess & Scott (J. Fluid Mech., vol. 811, 2017, pp. 742–756) and shows little sensitivity either to the forcing bandwidth or to the nature of the small-scale dissipation: both narrowband and broadband forcing generate nearly identical vortex populations, as do Laplacian diffusion and hyperdiffusion. The greatest differences arise in comparing simulations with correlated forcing to those with white-in-time forcing: in flows with correlated forcing the intermediate range in the vortex number density steepens significantly past the predicted scale-invariant $A^{-1}$ scaling. We also study the impact of the forcing Reynolds number $Re_{f}$, a measure of the relative importance of nonlinear terms and dissipation at the forcing scale, on vortex formation and the scaling of the number density. As $Re_{f}$ decreases, the flow changes from one dominated by intense circular vortices surrounded by filaments to a less structured flow in which vortex formation becomes progressively more suppressed and the filamentary nature of the surrounding vorticity field is lost. However, even at very small $Re_{f}$, and in the absence of intense coherent vortex formation, regions of anomalously high vorticity merge and grow in area as predicted by the scaling theory, generating a three-part number density similar to that found at higher $Re_{f}$. At late enough stages the aggregation process results in the formation of long-lived circular vortices, demonstrating a strong tendency to vortex formation, and via a route distinct from the axisymmetrization of forcing extrema seen at higher $Re_{f}$. Our results establish coherent vortices as a robust feature of the two-dimensional inverse energy cascade, and provide clues as to the dynamical mechanisms shaping their statistics.

Turbulence and Gravity Waves within an Upper-Level Front

2005 ◽  
Vol 62 (11) ◽  
pp. 3885-3908 ◽  
Author(s):  
Steven E. Koch ◽  
Brian D. Jamison ◽  
Chungu Lu ◽  
Tracy L. Smith ◽  
Edward I. Tollerud ◽  
...  
Keyword(s):  
Structure Function ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Function Analysis ◽  
Numerical Models ◽  
Wide Spectrum ◽  
Potential Temperature ◽  
Scale Model ◽  
Air Turbulence ◽  
Upper Level

Abstract High-resolution dropwindsonde and in-flight measurements collected by a research aircraft during the Severe Clear-Air Turbulence Colliding with Aircraft Traffic (SCATCAT) experiment and simulations from numerical models are analyzed for a clear-air turbulence event associated with an intense upper-level jet/frontal system. Spectral, wavelet, and structure function analyses performed with the 25-Hz in situ data are used to investigate the relationship between gravity waves and turbulence. Mesoscale dynamics are analyzed with the 20-km hydrostatic Rapid Update Cycle (RUC) model and a nested 1-km simulation with the nonhydrostatic Clark–Hall (CH) cloud-scale model. Turbulence occurred in association with a wide spectrum of upward propagating gravity waves above the jet core. Inertia–gravity waves were generated within a region of unbalanced frontogenesis in the vicinity of a complex tropopause fold. Turbulent kinetic energy fields forecast by the RUC and CH models displayed a strongly banded appearance associated with these mesoscale gravity waves (horizontal wavelengths of ∼120–216 km). Smaller-scale gravity wave packets (horizontal wavelengths of 1–20 km) within the mesoscale wave field perturbed the background wind shear and stability, promoting the development of bands of reduced Richardson number conducive to the generation of turbulence. The wavelet analysis revealed that brief episodes of high turbulent energy were closely associated with gravity wave occurrences. Structure function analysis provided evidence that turbulence was most strongly forced at a horizontal scale of 700 m. Fluctuations in ozone measured by the aircraft correlated highly with potential temperature fluctuations and the occurrence of turbulent patches at altitudes just above the jet core, but not at higher flight levels, even though the ozone fluctuations were much larger aloft. These results suggest the existence of remnant “fossil turbulence” from earlier events at higher levels, and that ozone cannot be used as a substitute for more direct measures of turbulence. The findings here do suggest that automated turbulence forecasting algorithms should include some reliable measure of gravity wave activity.

Physical mechanism of the inverse energy cascade of two-dimensional turbulence: a numerical investigation

2009 ◽  
Vol 619 ◽  
pp. 1-44 ◽  
Author(s):  
Z. XIAO ◽  
M. WAN ◽  
S. CHEN ◽  
G. L. EYINK
Keyword(s):  
Energy Flux ◽  
Large Scale ◽  
Physical Mechanism ◽  
Energy Cascade ◽  
Small Scale ◽  
Local Energy ◽  
Two Dimensional ◽  
Turbulent Stress ◽  
Inverse Energy Cascade ◽  
The Mean

We report an investigation of inverse energy cascade in steady-state two-dimensional turbulence by direct numerical simulation (DNS) of the two-dimensional Navier–Stokes equation, with small-scale forcing and large-scale damping. We employed several types of damping and dissipation mechanisms in simulations up to 20482 resolution. For all these simulations we obtained a wavenumber range for which the mean spectral energy flux is a negative constant and the energy spectrum scales as k−5/3, consistent with the predictions of Kraichnan (Phys. Fluids, vol. 439, 1967, p. 1417). To gain further insight, we investigated the energy cascade in physical space, employing a local energy flux defined by smooth filtering. We found that the inverse energy cascade is scale local, but that the strongly local contribution vanishes identically, as argued by Kraichnan (J. Fluid Mech., vol. 47, 1971, p. 525). The mean flux across a length scale ℓ was shown to be due mainly to interactions with modes two to eight times smaller. A major part of our investigation was devoted to identifying the physical mechanism of the two-dimensional inverse energy cascade. One popular idea is that inverse energy cascade proceeds via merger of like-sign vortices. We made a quantitative study employing a precise topological criterion of merger events. Our statistical analysis showed that vortex mergers play a negligible direct role in producing mean inverse energy flux in our simulations. Instead, we obtained with the help of other works considerable evidence in favour of a ‘vortex thinning’ mechanism, according to which the large-scale strains do negative work against turbulent stress as they stretch out the isolines of small-scale vorticity. In particular, we studied a multi-scale gradient (MSG) expansion developed by Eyink (J. Fluid Mech., vol. 549, 2006a, p. 159) for the turbulent stress, whose contributions to inverse cascade can all be explained by ‘thinning’. The MSG expansion up to second order in space gradients was found to predict well the magnitude, spatial structure and scale distribution of the local energy flux. The majority of mean flux was found to be due to the relative rotation of strain matrices at different length scales, a first-order effect of ‘thinning’. The remainder arose from two second-order effects, differential strain rotation and vorticity gradient stretching. Our findings give strong support to vortex thinning as the fundamental mechanism of two-dimensional inverse energy cascade.

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