kinetic energy density
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2021 ◽  
Vol 923 (1) ◽  
pp. 40
Author(s):  
Morgan Stores ◽  
Natasha L. S. Jeffrey ◽  
Eduard P. Kontar

Abstract Magnetohydrodynamic plasma turbulence is believed to play a vital role in the production of energetic electrons during solar flares, and the nonthermal broadening of spectral lines is a key sign of this turbulence. Here, we determine how flare turbulence evolves in time and space using spectral profiles of Fe xxiv, Fe xxiii, and Fe xvi, observed by the Hinode/EUV Imaging Spectrometer. Maps of nonthermal velocity are created for times covering the X-ray rise, peak, and decay. For the first time, the creation of kinetic energy density maps reveal where energy is available for energization, suggesting that similar levels of energy may be available to heat and/or accelerate electrons in large regions of the flare. We find that turbulence is distributed throughout the entire flare, often greatest in the coronal loop tops, and decaying at different rates at different locations. For hotter ions (Fe xxiv and Fe xxiii), the nonthermal velocity decreases as the flare evolves and during/after the X-ray peak shows a clear spatial variation decreasing linearly from the loop apex toward the ribbon. For the cooler ion (Fe xvi), the nonthermal velocity remains relativity constant throughout the flare, but steeply increases in one region corresponding to the southern ribbon, peaking just prior to the peak in hard X-rays before declining. The results suggest turbulence has a more complex temporal and spatial structure than previously assumed, while newly introduced turbulent kinetic energy maps show the availability of the energy and identify important spatial inhomogeneities in the macroscopic plasma motions leading to turbulence.


2021 ◽  
Vol 930 ◽  
Author(s):  
A. Tilgner

Bounds are derived for rotating Rayleigh–Bénard convection with free slip boundaries as a function of the Rayleigh, Taylor and Prandtl numbers ${\textit {Ra}}$ , ${\textit {Ta}}$ and ${\textit {Pr}}$ . At infinite ${\textit {Pr}}$ and ${\textit {Ta}} > 130$ , the Nusselt number ${\textit {Nu}}$ obeys ${\textit {Nu}} \leqslant \frac {7}{36} \left ({4}/{{\rm \pi} ^2} \right )^{1/3} {\textit {Ra}} {\textit {Ta}}^{-1/3}$ , whereas the kinetic energy density $E_{kin}$ obeys $E_{kin} \leqslant ({7}/{72 {\rm \pi}}) \left ({4}/{{\rm \pi} } \right )^{1/3} {\textit {Ra}}^2 {\textit {Ta}}^{-2/3}$ in the frame of reference in which the total momentum is zero, and $E_{kin} \leqslant ({1}/{2{\rm \pi} ^2})({{\textit {Ra}}^2}/{{\textit {Ta}}})({\textit {Nu}}-1)$ . These three bounds are derived from the momentum equation and the maximum principle for temperature and are extended to general ${\textit {Pr}}$ . The extension to finite ${\textit {Pr}}$ is based on the fact that the maximal velocity in rotating convection at infinite ${\textit {Pr}}$ is bound by $1.23 {\textit {Ra}} {\textit {Ta}}^{-1/3}$ .


2021 ◽  
Vol 2090 (1) ◽  
pp. 012123
Author(s):  
Bader H Aldossari ◽  
Mel Levy ◽  
Abdulaziz H Al-Aswad ◽  
Fahhad H Alharbi

Abstract An approach guided by physical consistency in determining the general forms of D-dimensional kinetic energy density functionals (KEDF) has been demonstrated previously, producing an expansion which contains the majority of the known one-point KEDF forms. It is known that any noninteracting KEDF shall necessarily have a homogeneity degree of 2 in coordinate scaling. This paper demonstrates that this condition is already satisfied in the general expansion despite not being conceived with the scaling as a constraint.


Author(s):  
David Henry

This article presents results concerning the excess kinetic and potential energies for exact nonlinear water waves. In particular, it is proven, for periodic travelling irrotational water waves, that the excess kinetic energy density is always negative, whereas the excess potential energy density is always positive, in the steady reference frame. A characterization of the total excess energy density as a weighted mean of the kinetic energy along the wave surface profile is also presented.


Author(s):  
Vittoria Urso

The development of novel Kinetic Energy (KE) functionals is an important topic in density functional theory (DFT). In particular, this happens by means of an analysis with newly developed benchmark sets. Here, I present a study of Laplacian-level kinetic energy functionals applied to metallic nanosystems. The nanoparticles are modeled using jellium sph eres of different sizes, background densities, and number of electrons. The ability of different functionals to reproduce the correct kinetic energy density and potential of various nanoparticles is investigated and analyzed in terms of semilocal descriptors. Most semilocal KE functionals are based on modifications of the second-order gradient expansion GE2 or GE4. I find that the Laplacian contribute is fundamental for the description of the energy and the potential of nanoparticles.


Atmosphere ◽  
2021 ◽  
Vol 12 (10) ◽  
pp. 1347
Author(s):  
Alexander Potekaev ◽  
Nikolay Krasnenko ◽  
Liudmila Shamanaeva

The diurnal hourly dynamics of the kinetic energy flux density vector, called the Umov vector, and the mean and turbulent components of the kinetic energy are estimated from minisodar measurements of wind vector components and their variances in the lower 200-meter layer of the atmosphere. During a 24-hour period of continuous minisodar observations, it was established that the mean kinetic energy density dominated in the surface atmospheric layer at altitudes below ~50 m. At altitudes from 50 to 100 m, the relative contributions of the mean and turbulent wind kinetic energy densities depended on the time of the day and the sounding altitude. At altitudes below 100 m, the contribution of the turbulent kinetic energy component is small, and the ratio of the turbulent to mean wind kinetic energy components was in the range 0.01–10. At altitudes above 100 m, the turbulent kinetic energy density sharply increased, and the ratio reached its maximum equal to 100–1000 at altitudes of 150–200 m. A particular importance of the direction and magnitude of the wind effect, that is, of the direction and magnitude of the Umov vector at different altitudes was established. The diurnal behavior of the Umov vector depended both on the time of the day and the sounding altitude. Three layers were clearly distinguished: a near-surface layer at altitudes of 5–15 m, an intermediate layer at altitudes from 15 m to 150 m, and the layer of enhanced turbulence above. The feasibility is illustrated of detecting times and altitudes of maximal and minimal wing kinetic energy flux densities, that is, time periods and altitude ranges most and least favorable for flights of unmanned aerial vehicles. The proposed novel method of determining the spatiotemporal dynamics of the Umov vector from minisodar measurements can also be used to estimate the effect of wind on high-rise buildings and the energy potential of wind turbines.


2021 ◽  
Vol 925 ◽  
Author(s):  
Amir Atoufi ◽  
K. Andrea Scott ◽  
Michael L. Waite

In this paper, the kinetic energy cascade in stably stratified open-channel flows is investigated. A mathematical framework to incorporate vertical scales into the conventional kinetic energy spectrum and its budget is introduced. This framework defines kinetic energy density in horizontal spectral and vertical scale space. The energy cascade is studied by analysing the evolution of kinetic energy density. It is shown that energetic streamwise scales ($\lambda _x$) become larger with increasing vertical scale. For the strongest stratification, for which the turbulence becomes intermittent, the energetic streamwise scales are suppressed, and energy density resides in $\lambda _x$ of the size of the domain. It is shown that, in an unstratified case, vertical scales of the size comparable to the height of the logarithmic layer connect viscous regions to the outer layer. By contrast, in stratified cases, such a connection is not observed. Moreover, it is shown that nonlinear transfer for streamwise scales is dominated by in-plane triad interactions and inter-plane transfer is more active in transferring energy density among small vertical scales of the size comparable to the height of viscous sublayer. The vertical scales of size comparable to the height of the viscous sublayer and buffer layer are the most active scales in the viscous term and the production term in the energy density budget, respectively.


Author(s):  
Subrata Jana ◽  
Sushant Kumar Behera ◽  
Szymon Śmiga ◽  
Lucian A. Constantin ◽  
Prasanjit Samal

Author(s):  
Hossein A. Kafiabad ◽  
Jacques Vanneste ◽  
William R. Young

AbstractAnticyclonic vortices focus and trap near-inertial waves so that near-inertial energy levels are elevated within the vortex core. Some aspects of this process, including the nonlinear modification of the vortex by the wave, are explained by the existence of trapped near-inertial eigenmodes. These vortex eigenmodes are easily excited by an initialwave with horizontal scale much larger than that of the vortex radius. We study this process using a wave-averaged model of near-inertial dynamics and compare its theoretical predictions with numerical solutions of the three-dimensional Boussinesq equations. In the linear approximation, the model predicts the eigenmode frequencies and spatial structures, and a near-inertial wave energy signature that is characterized by an approximately time-periodic, azimuthally invariant pattern. The wave-averaged model represents the nonlinear feedback of the waves on the vortex via a wave-induced contribution to the potential vorticity that is proportional to the Laplacian of the kinetic energy density of the waves. When this is taken into account, the modal frequency is predicted to increase linearly with the energy of the initial excitation. Both linear and nonlinear predictions agree convincingly with the Boussinesq results.


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