scholarly journals Electron inertia and quasi-neutrality in the Weibel instability

2017 ◽  
Vol 83 (3) ◽  
Author(s):  
Enrico Camporeale ◽  
Cesare Tronci
Keyword(s):  
Unsolved Problem ◽  
Plasma Frequency ◽  
Skin Depth ◽  
Mean Flow ◽  
Length Scales ◽  
Weibel Instability ◽  
Electron Inertia ◽  
Kinetic Effects ◽  
Flow Inertia ◽  
Kinetic Treatment

While electron kinetic effects are well known to be of fundamental importance in several situations, the electron mean-flow inertia is often neglected when length scales below the electron skin depth become irrelevant. This has led to the formulation of different reduced models, where electron inertia terms are discarded while retaining some or all kinetic effects. Upon considering general full-orbit particle trajectories, this paper compares the dispersion relations emerging from such models in the case of the Weibel instability. As a result, the question of how length scales below the electron skin depth can be neglected in a kinetic treatment emerges as an unsolved problem, since all current theories suffer from drawbacks of different nature. Alternatively, we discuss fully kinetic theories that remove all these drawbacks by restricting to frequencies well below the plasma frequency of both ions and electrons. By giving up on the length scale restrictions appearing in previous works, these models are obtained by assuming quasi-neutrality in the full Vlasov–Maxwell system.

scholarly journals The influence of idealized surface heterogeneity on virtual turbulent flux measurements

2018 ◽  
Vol 18 (7) ◽  
pp. 5059-5074 ◽  
Author(s):  
Frederik De Roo ◽  
Matthias Mauder
Keyword(s):  
Energy Budget ◽  
Turbulent Flux ◽  
Surface Heterogeneity ◽  
Surface Fluxes ◽  
Convective Conditions ◽  
Mean Flow ◽  
Flux Divergence ◽  
Length Scales ◽  
Flux Measurements ◽  
The Mean

Abstract. The imbalance of the surface energy budget in eddy-covariance measurements is still an unsolved problem. A possible cause is the presence of land surface heterogeneity, which affects the boundary-layer turbulence. To investigate the impact of surface variables on the partitioning of the energy budget of flux measurements in the surface layer under convective conditions, we set up a systematic parameter study by means of large-eddy simulation. For the study we use a virtual control volume approach, which allows the determination of advection by the mean flow, flux-divergence and storage terms of the energy budget at the virtual measurement site, in addition to the standard turbulent flux. We focus on the heterogeneity of the surface fluxes and keep the topography flat. The surface fluxes vary locally in intensity and these patches have different length scales. Intensity and length scales can vary for the two horizontal dimensions but follow an idealized chessboard pattern. Our main focus lies on surface heterogeneity of the kilometer scale, and one order of magnitude smaller. For these two length scales, we investigate the average response of the fluxes at a number of virtual towers, when varying the heterogeneity length within the length scale and when varying the contrast between the different patches. For each simulation, virtual measurement towers were positioned at functionally different positions (e.g., downdraft region, updraft region, at border between domains, etc.). As the storage term is always small, the non-closure is given by the sum of the advection by the mean flow and the flux-divergence. Remarkably, the missing flux can be described by either the advection by the mean flow or the flux-divergence separately, because the latter two have a high correlation with each other. For kilometer scale heterogeneity, we notice a clear dependence of the updrafts and downdrafts on the surface heterogeneity and likewise we also see a dependence of the energy partitioning on the tower location. For the hectometer scale, we do not notice such a clear dependence. Finally, we seek correlators for the energy balance ratio in the simulations. The correlation with the friction velocity is less pronounced than previously found, but this is likely due to our concentration on effectively strongly to freely convective conditions.

Differential Equation Specification of Integral Turbulence Length Scales

2012 ◽  
Author(s):  
Richard Jefferson-Loveday ◽  
Paul Tucker ◽  
V. Nagabhushana Rao ◽  
John Northall
Keyword(s):  
Differential Equation ◽  
Reynolds Number ◽  
Dirichlet Boundary Conditions ◽  
Recirculation Region ◽  
Mean Flow ◽  
Length Scales ◽  
Measured Velocity ◽  
Drag Coefficients ◽  
Rans Models ◽  
Turbulence Length

A Hamilton-Jacobi differential equation is used to naturally and smoothly (via Dirichlet boundary conditions) set turbulence length scales in separated flow regions based on traditional expected length scales. Such zones occur for example in rim-seals. The approach is investigated using two test cases, flow over a cylinder at a Reynolds number of 140,000 and flow over a rectangular cavity at a Reynolds number of 50,000. The Nee-Kovasznay turbulence model is investigated using this approach. Predicted drag coefficients for the cylinder test-case show significant (15%) improvement over standard steady RANS and are comparable with URANS results. The mean flow-field also shows a significant improvement over URANS. The error in reattachment length is improved by 180% compared with the steady RANS k–ω model. The wake velocity profile at a location downstream shows improvement and the URANS profile is inaccurate in comparison. For the cavity case the HJ-NK approach is generally comparable with the other RANS models for measured velocity profiles. Predicted drag coefficients are compared with large eddy simulation. The new approach shows a 20–30% improvement in predicted drag coefficients compared with standard one and two equation RANS models. The shape of the recirculation region within the cavity is also much improved.

scholarly journals Characterizing the Energetics of Vortex-Scale and Sub-Vortex-Scale Asymmetries during Tropical Cyclone Rapid Intensity Changes

2019 ◽  
Vol 77 (1) ◽  
pp. 315-336
Author(s):  
Saiprasanth Bhalachandran ◽  
Daniel R. Chavas ◽  
Frank D. Marks Jr. ◽  
S. Dubey ◽  
A. Shreevastava ◽  
...  
Keyword(s):  
Tropical Cyclone ◽  
Kinetic Energy ◽  
Mean Flow ◽  
Length Scales ◽  
Asymmetric Structures ◽  
Multiple Length Scales ◽  
Precise Understanding ◽  
Intensity Changes ◽  
Resolution Model ◽  
The Mean

Abstract Our collective understanding of azimuthally asymmetric features within the coherent structure of a tropical cyclone (TC) continues to improve with the availability of more detailed observations and high-resolution model outputs. However, a precise understanding of how these asymmetries impact TC intensity changes is lacking. Prior attempts at investigating the asymmetric impacts follow a mean–eddy partitioning that condenses the effect of all the asymmetries into one term and fails to highlight the differences in the role of asymmetries at different scales. In this study, we present a novel energetics-based approach to analyze the asymmetric impacts at multiple length scales during periods of rapid intensity changes. Using model outputs of TCs under low and high shear, we compute the different energy pathways that enhance/suppress the growth of multiscale asymmetries in the wavenumber (WN) domain. We then compare and contrast the energetics of the mean-flow field (WN 0) with that of the persistent, coherent vortex-scale asymmetric structures (WNs 1 and 2) and the more local, transient, sub-vortex-scale asymmetries (WNs ≥ 3). We find in our case studies that the dominant mechanisms of growth/decay of the asymmetries are the baroclinic conversion from available potential to kinetic energy at individual scales of asymmetries and the transactions of kinetic energy between the asymmetries of various length scales, rather than the barotropic mean–eddy transactions as is typically assumed. Our case study analysis further shows that the growth/decay of asymmetries is largely independent of the mean. Certain aspects of eddy energetics can potentially serve as early-warning indicators of TC rapid intensity changes.

Experiments on turbulence in a rotating fluid

1975 ◽  
Vol 68 (4) ◽  
pp. 639-672 ◽  
Author(s):  
A. Ibbetson ◽  
D. J. Tritton
Keyword(s):  
Rotation Rate ◽  
Rotation Axis ◽  
Turbulence Energy ◽  
Length Scale ◽  
Grid Turbulence ◽  
Rotating Fluid ◽  
Mean Flow ◽  
Length Scales ◽  
Wide Range ◽  
Energy Sink

Experiments have been carried out to investigate the effect of rotation of the whole system on decaying turbulence, generally similar to grid turbulence, generated in air in an annular container on a rotating table. Measurements to determine the structure of the turbulence were made during its decay, mean quantities being determined by a mixture of time and ensemble averaging. Quantities measured (as functions of time after the turbulence generation) were turbulence intensities perpendicular to and parallel to the rotation axis, spectra of these two components with respect to a wavenumber perpendicular to the rotation axis, and some correlation coefficients, selected to detect differences in length scales perpendicular and parallel to the rotation axis. The intensity measurements were made for a wide range of rotation rates; the other measurements were made at a single rotation rate (selected to give a Rossby number varying during the decay from about 1 to small values) and, for comparison, at zero rotation. Subsidiary experiments were carried out to measure the spin-up time of the system, and to determine whether the turbulence produced any mean flow relative to the container.A principal result is that increasing the rotation rate produces faster decay of the turbulence; the nature of the additional energy sink is an important part of the interpretation. Other features of the results are as follows: the measurements with-outrotation can be satisfactorily related to wind-tunnel measurements; even with rotation, the ratio of the intensities in the two directions remains substantially constant; the normalized spectra for the rotating and the non-rotating cases show surprising similarity but do contain slight systematic differences, consistent with the length scales indicated by the correlations; rotation produces a large increase in the length scale parallel to the rotation axis and a smaller increase in that perpendicular to it; the turbulence produces no measurable mean flow.A model for the interpretation of the results is developed in terms of the action of inertial waves in carrying energy to the boundaries of the enclosure, where it is dissipated in viscous boundary layers. The model provides satisfactory explanations of the overall decay of the turbulence and of the decay of individual spectral components. Transfer of energy between wavenumbers plays a much less significant role in the dynamics of decay than in a non-rotating fluid. The relationship of the model to the interpretation of the length-scale difference in terms of the Taylor-Proudman theorem is discussed.The model implies that the overall dimensions of the system enter in an important way into the dynamics. This imposes a serious limitation on the application of the results to the geophysical situations at which experiments of this type are aimed.The paper includes some discussion of the possibility of energy transfer from the turbulence to a mean motion (the ‘vorticity expulsion’ hypothesis). It is possible, on the basis of the observations, to exclude this process as the additional turbulence energy sink. But this does not provide any evidence either for or against the hypothesis in the conditions for which it has been postulated.

Differential Equation Specification of Integral Turbulence Length Scales

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Richard J. Jefferson-Loveday ◽  
Paul G. Tucker ◽  
John D. Northall ◽  
V. Nagabhushana Rao
Keyword(s):  
Differential Equation ◽  
Reynolds Number ◽  
Dirichlet Boundary Conditions ◽  
Recirculation Region ◽  
Mean Flow ◽  
Length Scales ◽  
Measured Velocity ◽  
Drag Coefficients ◽  
Rans Models ◽  
Turbulence Length

A Hamilton–Jacobi differential equation is used to naturally and smoothly (via Dirichlet boundary conditions) set turbulence length scales in separated flow regions based on traditional expected length scales. Such zones occur for example in rim-seals. The approach is investigated using two test cases, flow over a cylinder at a Reynolds number of 140,000 and flow over a rectangular cavity at a Reynolds number of 50,000. The Nee–Kovasznay turbulence model is investigated using this approach. Predicted drag coefficients for the cylinder test-case show significant (15%) improvement over standard steady RANS and are comparable with URANS results. The mean flow-field also shows a significant improvement over URANS. The error in re-attachment length is improved by 180% compared with the steady RANS k-ω model. The wake velocity profile at a location downstream shows improvement and the URANS profile is inaccurate in comparison. For the cavity case, the HJ–NK approach is generally comparable with the other RANS models for measured velocity profiles. Predicted drag coefficients are compared with large eddy simulation. The new approach shows a 20–30% improvement in predicted drag coefficients compared with standard one and two equation RANS models. The shape of the recirculation region within the cavity is also much improved.

Wave dynamics of an electrojet: generalized Farley–Buneman instability

2007 ◽  
Vol 73 (5) ◽  
pp. 701-713
Author(s):  
JAMES F. McKENZIE
Keyword(s):  
Growth Rates ◽  
Acoustic Waves ◽  
Plasma Frequency ◽  
Electron Cyclotron ◽  
Positive Energy ◽  
Lower Hybrid ◽  
Ion Acoustic Wave ◽  
Electron Inertia ◽  
Ion Plasma ◽  
Ion Acoustic

AbstractIn this paper we generalize the classical Farley–Buneman (FB) instability to include space-charge effects and finite electron inertia. The former effect makes the ion-acoustic wave dispersive with the usual resonance appearing at the ion plasma frequency, but other than that the structure of the FB instability remains intact. However, the inclusion of the latter, finite electron inertia, gives rise to the propagating electron-cyclotron mode, albeit modified by collisions. In the presence of differential electron streaming relative to the ions, the interaction between this mode, attempting to propagate against the stream, but convected forward by the stream, and a forward propagating ion-acoustic mode, gives rise to a new instability distinct from the FB instability. The process may be thought of in terms of the coupling between negative energy waves (electron-cyclotron waves attempting to propagate against the stream) and positive energy waves (forward propagating ion-acoustic waves). In principle, the instability simply requires super-ion acoustic streaming electrons and the corresponding growth rates are of the order of one half of the lower hybrid frequency, which are faster than the corresponding FB growth rates. For conditions appropriate to the middle day-side E-region this instability excites a narrow band of frequencies just below the ion plasma frequency. Its role in the generation of electrojet irregularities may be as important as the classical FB instability.

scholarly journals Statistical evidence of anasymptotic geometric structure to the momentum transporting motions in turbulent boundary layers

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160084 ◽  
Author(s):  
Caleb Morrill-Winter ◽  
Jimmy Philip ◽  
Joseph Klewicki
Keyword(s):  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Turbulent Boundary Layers ◽  
Wall Turbulence ◽  
Sensor Data ◽  
Joint Analysis ◽  
Large Reynolds Number ◽  
Mean Flow ◽  
Length Scales ◽  
The Mean

The turbulence contribution to the mean flow is reflected by the motions producing the Reynolds shear stress (〈− uv 〉) and its gradient. Recent analyses of the mean dynamical equation, along with data, evidence that these motions asymptotically exhibit self-similar geometric properties. This study discerns additional properties associated with the uv signal, with an emphasis on the magnitudes and length scales of its negative contributions. The signals analysed derive from high-resolution multi-wire hot-wire sensor data acquired in flat-plate turbulent boundary layers. Space-filling properties of the present signals are shown to reinforce previous observations, while the skewness of uv suggests a connection between the size and magnitude of the negative excursions on the inertial domain. Here, the size and length scales of the negative uv motions are shown to increase with distance from the wall, whereas their occurrences decrease. A joint analysis of the signal magnitudes and their corresponding lengths reveals that the length scales that contribute most to 〈− uv 〉 are distinctly larger than the average geometric size of the negative uv motions. Co-spectra of the streamwise and wall-normal velocities, however, are shown to exhibit invariance across the inertial region when their wavelengths are normalized by the width distribution, W ( y ), of the scaling layer hierarchy, which renders the mean momentum equation invariant on the inertial domain. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

scholarly journals The influence of idealized surface heterogeneity on virtual turbulent flux measurements

2017 ◽  
Author(s):  
Frederik De Roo ◽  
Matthias Mauder
Keyword(s):  
Boundary Layer ◽  
Energy Budget ◽  
Turbulent Flux ◽  
Surface Heterogeneity ◽  
Surface Fluxes ◽  
Surface Energy Budget ◽  
Parameter Study ◽  
Mean Flow ◽  
Length Scales ◽  
Large Eddy

Abstract. The imbalance of the surface energy budget in eddy-covariance measurements is still an unsolved problem. A possible cause is the presence of land surface heterogeneity. The influence of surface heterogeneities on the atmospheric boundary layer has been intensively investigated since two decades. Previous studies found that heterogeneities of the boundary-layer scale or larger are most effective in influencing the boundary layer turbulence. Subsequent large-eddy simulations showed that also the turbulent fluxes are influenced by large-scale organized structures in the boundary layer. However, the precise influence of the surface characteristics on the energy imbalance of measurements in the surface layer and its partitioning is still unknown. To investigate the influence of surface variables on all the components of the flux budget under convective conditions, we set up a systematic parameter study by means of large-eddy simulation. For the study we use a virtual control volume approach, which allows the determination of advection by the mean flow, flux-divergence and storage terms of the energy budget at the virtual measurement site, in addition to the standard turbulent flux. We focus on the heterogeneity of the surface fluxes and keep the topography flat. The surface fluxes vary locally in intensity and these patches have different length scales. Intensity and length scales can vary for the two horizontal dimensions but follow an idealized chessboard pattern. Our main focus lies on heterogeneities of length scales of the kilometer scale, and length scales of one order of magnitude smaller. For heterogeneities of these two types, we investigate the average response of the fluxes at a number of virtual towers, when varying the heterogeneity length within the length scale and when varying the contrast between the different patches. For each simulation, virtual measurement towers were positioned at functionally different positions (e.g. downdraft region, updraft region, at border between domains, etc.). Furthermore, we seek correlators for the energy balance ratio and the energy residual in the simulations. Besides the expected correlation with measurable atmospheric quantities such as the friction velocity, boundary-layer depth and temperature and moisture gradients, we have also found an unexpected correlation with the temperature difference between sonic temperature and surface temperature.

One-Equation Near-Wall Turbulence Modeling With the Aid of Direct Simulation Data

1993 ◽  
Vol 115 (2) ◽  
pp. 196-205 ◽  
Author(s):  
W. Rodi ◽  
N. N. Mansour ◽  
V. Michelassi
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Equation Model ◽  
Wall Turbulence ◽  
Mean Flow ◽  
Simulation Data ◽  
Length Scales ◽  
Velocity Scale ◽  
Layer Flow ◽  
Near Wall

The length scales appearing in the relations for the eddy viscosity and dissipation rate in one-equation models were evaluated from direct numerical (DNS) simulation data for developed channel and boundary-layer flow at two Reynolds numbers each. To prepare the ground for the evaluation, the distribution of the most relevant mean-flow and turbulence quantities is presented and discussed, also with respect to Reynolds-number influence and to differences between channel and boundary-layer flow. An alternative model is examined in which (v′2)1/2 is used as velocity scale instead of k1/2. With this velocity scale, the length scales now appearing in the model follow closely a linear relationship near the wall. The resulting length-scale relations together with a DNS based relation between v′2/k and y* = k1/2y/v form a new one-equation model for use in near-wall regions. The new model was tested as near wall component of a two-layer model by application to developed-channel, boundary-layer and backward-facing-step flows.

scholarly journals Two-Layer Baroclinic Eddy Heat Fluxes: Zonal Flows and Energy Balance

2007 ◽  
Vol 64 (9) ◽  
pp. 3214-3231 ◽  
Author(s):  
Andrew F. Thompson ◽  
William R. Young
Keyword(s):  
Heat Flux ◽  
Eddy Diffusivity ◽  
Bottom Friction ◽  
Heat Fluxes ◽  
Mixing Length ◽  
Mean Flow ◽  
Length Scales ◽  
Zonal Jets ◽  
Eddy Heat Flux ◽  
Velocity Jump

Abstract The eddy heat flux generated by statistically equilibrated baroclinic turbulence supported on a uniform, horizontal temperature gradient is examined using a two-layer β-plane quasigeostrophic model. The dependence of the eddy diffusivity of temperature, Dτ, on external parameters such as β, bottom friction κ, the deformation radius λ, and the velocity jump 2U, is provided by numerical simulations at 110 different points in the parameter space β* = βλ2/U and κ* = κλ/U. There is a special “pivot” value of β*, βpiv* ≈ 11/16, at which Dτ depends weakly on κ*. But otherwise Dτ has a complicated dependence on both β* and κ*, highlighted by the fact that reducing κ* leads to increases (decreases) in Dτ if β is less than (greater than) βpiv*. Existing heat-flux parameterizations, based on Kolmogorov cascade theories, predict that Dτ is nonzero and independent of κ* in the limit κ* → 0. Simulations show indications of this regime provided that κ* ≤ 0.04 and 0.25 ≤ β* ≤ 0.5. All important length scales in this problem, namely the mixing length, the scale of the energy containing eddies, the Rhines scale, and the spacing of the zonal jets, converge to a common value as bottom friction is reduced. The mixing length and jet spacing do not decouple in the parameter regime considered here, as predicted by cascade theories. The convergence of these length scales is due to the formation of jet-scale eddies that align along the eastward jets. The baroclinic component of these eddies helps force the zonal mean flow, which occurs through nonzero Reynolds stress correlations in the upper layer, as opposed to the barotropic mode. This behavior suggests that the dynamics of the inverse barotropic cascade are insufficient to fully describe baroclinic turbulence.

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