Multipole expansion of the large-scale velocity field - Using the tensor window function

1989 ◽  
Vol 345 ◽  
pp. 627 ◽  
Author(s):  
Eniko Regos ◽  
Alexander S. Szalay
Keyword(s):  
Velocity Field ◽  
Large Scale ◽  
Multipole Expansion ◽  
Window Function

The entrainment interface

1972 ◽  
Vol 51 (1) ◽  
pp. 97-118 ◽  
Author(s):  
O. M. Phillips
Keyword(s):  
Velocity Field ◽  
Turbulent Flow ◽  
Surface Area ◽  
Large Scale ◽  
Positive Curvature ◽  
Lagrangian Description ◽  
Eulerian Description ◽  
Entrainment Process ◽  
Necessary And Sufficient ◽  
Small Disturbances

A theory is developed to describe the evolution of the entrainment interface in turbulent flow, in which the surface is convoluted by the large-scale eddies of the motion and at the same time advances relative to the fluid as a result of the micro-scale entrainment process. A pseudo-Lagrangian description of the process indicates that the interface is characterized by the appearance of ‘billows’ of negative curvature, over which surface area is, on average, being generated, separated by re-entrant wedges (lines of very large positive curvature) where surface area is consumed. An alternative Eulerian description allows calculation of the development of the interfacial configuration when the velocity field is prescribed. Several examples are considered in which the prescribed velocity field in the z direction is of the general form w = Wf(x – Ut), where the maximum value of the function f is unity. These indicate the importance of leading points on the surface which are such that small disturbances in the vicinity will move away from the point in all directions. The necessary and sufficient condition for the existence of one or more leading points on the surface is that U [les ] V, the speed of advance of an element of the surface relative to the fluid element at the same point. The existence of leading points is accompanied by the appearance of line discontinuities in the surface slope re-entrant wedges, In these circumstances, the overall speed of advance of the convoluted surface is found to be W + (V2 – U2)½, where W is the maximum outwards velocity in the region; this result is independent of the distribution f.When the speed U with which an ‘eddy’ moves relative to the outside fluid is greater than the speed of advance V of an element of the front, the interface develops neither leading points nor discontinuities in slope; the amplitude of the surface convolutions and the overall entrainment speed are both reduced greatly. In a turbulent flow, therefore, the large-scale motions influencing entrainment are primarily those that move slowly relative to the outside fluid (with relative speed less than V). The experimental results of Kovasznay, Kibens & Blackwelder (1970) are reviewed in the light of these conclusions. It appears that in their experiments the entrainment speed V is of the order fifteen times the Kolmogorov velocity, the large constant of proportionality being apparently the result of augmentation by micro-convolutions of the interface associated with small and meso-scale eddies of the turbulence.

Buoyancy effects on large-scale motions in convective atmospheric boundary layers: implications for modulation of near-wall processes

2018 ◽  
Vol 856 ◽  
pp. 135-168 ◽  
Author(s):  
S. T. Salesky ◽  
W. Anderson
Keyword(s):  
Boundary Layer ◽  
Velocity Field ◽  
Boundary Layers ◽  
Vertical Velocity ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Small Scale ◽  
Convective Conditions ◽  
Wide Range

A number of recent studies have demonstrated the existence of so-called large- and very-large-scale motions (LSM, VLSM) that occur in the logarithmic region of inertia-dominated wall-bounded turbulent flows. These regions exhibit significant streamwise coherence, and have been shown to modulate the amplitude and frequency of small-scale inner-layer fluctuations in smooth-wall turbulent boundary layers. In contrast, the extent to which analogous modulation occurs in inertia-dominated flows subjected to convective thermal stratification (low Richardson number) and Coriolis forcing (low Rossby number), has not been considered. And yet, these parameter values encompass a wide range of important environmental flows. In this article, we present evidence of amplitude modulation (AM) phenomena in the unstably stratified (i.e. convective) atmospheric boundary layer, and link changes in AM to changes in the topology of coherent structures with increasing instability. We perform a suite of large eddy simulations spanning weakly ($-z_{i}/L=3.1$) to highly convective ($-z_{i}/L=1082$) conditions (where$-z_{i}/L$is the bulk stability parameter formed from the boundary-layer depth$z_{i}$and the Obukhov length $L$) to investigate how AM is affected by buoyancy. Results demonstrate that as unstable stratification increases, the inclination angle of surface layer structures (as determined from the two-point correlation of streamwise velocity) increases from$\unicode[STIX]{x1D6FE}\approx 15^{\circ }$for weakly convective conditions to nearly vertical for highly convective conditions. As$-z_{i}/L$increases, LSMs in the streamwise velocity field transition from long, linear updrafts (or horizontal convective rolls) to open cellular patterns, analogous to turbulent Rayleigh–Bénard convection. These changes in the instantaneous velocity field are accompanied by a shift in the outer peak in the streamwise and vertical velocity spectra to smaller dimensionless wavelengths until the energy is concentrated at a single peak. The decoupling procedure proposed by Mathiset al.(J. Fluid Mech., vol. 628, 2009a, pp. 311–337) is used to investigate the extent to which amplitude modulation of small-scale turbulence occurs due to large-scale streamwise and vertical velocity fluctuations. As the spatial attributes of flow structures change from streamwise to vertically dominated, modulation by the large-scale streamwise velocity decreases monotonically. However, the modulating influence of the large-scale vertical velocity remains significant across the stability range considered. We report, finally, that amplitude modulation correlations are insensitive to the computational mesh resolution for flows forced by shear, buoyancy and Coriolis accelerations.

Spiral Galaxies, Elliptical Galaxies and the Large-Scale Velocity Field Within 3500 Km/s of the Local Group

1988 ◽  
pp. 177-180 ◽  
Author(s):  
David Burstein ◽  
Roger L. Davies ◽  
Alan Dressler ◽  
S. M. Faber ◽  
Donald Lynden-Bell ◽  
...  
Keyword(s):  
Velocity Field ◽  
Large Scale ◽  
Local Group ◽  
Spiral Galaxies ◽  
Elliptical Galaxies

scholarly journals Re-examination of Large Scale Structure & Cosmic Flows

2014 ◽  
Vol 11 (S308) ◽  
pp. 310-317
Author(s):  
Marc Davis ◽  
Adi Nusser
Keyword(s):  
Perturbation Theory ◽  
Velocity Field ◽  
Gravity Field ◽  
Inverse Method ◽  
Large Scale ◽  
Linear Perturbation ◽  
Data Set ◽  
Galaxy Distribution ◽  
Standard Values ◽  
Linear Perturbation Theory

AbstractComparison of galaxy flows with those predicted from the local galaxy distribution ended as an active field after two analyses came to vastly different conclusions 25 years ago, but that was due to faulty data. All the old results are therefore suspect. With new data collected in the last several years, the problem deserves another look. The goal is to explain the 640 km/s dipole anisotropy of the CMBR. For this we analyze the gravity field inferred from the enormous data set derived from the 2MASS collection of galaxies (Huchra et al. 2005), and compare it to the velocity field derived from the well calibrated SFI++ Tully-Fisher catalog (Springob et al. 2007). Using the “Inverse Method” to minimize Malmquist biases, within 10,000 km/s the gravity field is seen to predict the velocity field (Davis et al. 2011) to remarkable consistency. This is a beautiful demonstration of linear perturbation theory and is fully consistent with standard values of the cosmological variables.

scholarly journals Examination of large-scale structures in a turbulent plane mixing layer. Part 2. Dynamical systems model

2001 ◽  
Vol 441 ◽  
pp. 67-108 ◽  
Author(s):  
L. UKEILEY ◽  
L. CORDIER ◽  
R. MANCEAU ◽  
J. DELVILLE ◽  
M. GLAUSER ◽  
...  
Keyword(s):  
Dynamical System ◽  
Velocity Field ◽  
Large Scale ◽  
Stokes Equations ◽  
Temporal Dynamics ◽  
Mixing Layer ◽  
Basis Set ◽  
Large Scale Structures ◽  
Scale Structures ◽  
Low Order

The temporal dynamics of large-scale structures in a plane turbulent mixing layer are studied through the development of a low-order dynamical system of ordinary differential equations (ODEs). This model is derived by projecting Navier–Stokes equations onto an empirical basis set from the proper orthogonal decomposition (POD) using a Galerkin method. To obtain this low-dimensional set of equations, a truncation is performed that only includes the first POD mode for selected streamwise/spanwise (k1/k3) modes. The initial truncations are for k3 = 0; however, once these truncations are evaluated, non-zero spanwise wavenumbers are added. These truncated systems of equations are then examined in the pseudo-Fourier space in which they are solved and by reconstructing the velocity field. Two different methods for closing the mean streamwise velocity are evaluated that show the importance of introducing, into the low-order dynamical system, a term allowing feedback between the turbulent and mean flows. The results of the numerical simulations show a strongly periodic flow indicative of the spanwise vorticity. The simulated flow had the correct energy distributions in the cross-stream direction. These models also indicated that the events associated with the centre of the mixing layer lead the temporal dynamics. For truncations involving both spanwise and streamwise wavenumbers, the reconstructed velocity field exhibits the main spanwise and streamwise vortical structures known to exist in this flow. The streamwise aligned vorticity is shown to connect spanwise vortex tubes.

Bulk Motion of Galaxies and Hubble Flow Anisotropy on a Scale of 100 Mpc

2005 ◽  
Vol 201 ◽  
pp. 501-502
Author(s):  
S. L. Parnovsky ◽  
V. E. Karachentseva ◽  
Yu. N. Kudrya ◽  
I. D. Karachentsev
Keyword(s):  
Velocity Field ◽  
Large Scale ◽  
Spiral Galaxies ◽  
Dipole Component ◽  
Bulk Motion ◽  
Flow Anisotropy ◽  
Strong Dipole ◽  
Hubble Flow

We study a large-scale bulk motion of thin edge-on spiral galaxies from the RFGC catalogue using a multipole decomposition of velocity field. The quadrupole and octupole components are statistically significant. The first one corresponds to the Hubble flow anisotropy, the second one leads to decrease of modulus of dipole component due to the strong dipole-octupole interaction.

scholarly journals A slight excess of large-scale power from moments of the peculiar velocity field

2011 ◽  
Vol 414 (1) ◽  
pp. 621-626 ◽  
Author(s):  
E. Macaulay ◽  
H. Feldman ◽  
P. G. Ferreira ◽  
M. J. Hudson ◽  
R. Watkins
Keyword(s):  
Velocity Field ◽  
Large Scale ◽  
Peculiar Velocity ◽  
Slight Excess

The infrared measurement cascade: Connecting large scale meteorologically induced surface temperature perturbations to local spatial velocity structures

2020 ◽  
Author(s):  
Benjamin Schumacher ◽  
Marwan Katurji ◽  
Jiawei Zhang
Keyword(s):  
Boundary Layer ◽  
Velocity Field ◽  
Brightness Temperature ◽  
High Speed ◽  
Surface Brightness ◽  
Large Scale ◽  
Mean Velocity ◽  
Near Surface ◽  
Multi Scale ◽  
Infrared Cameras

<p>The evolution of micrometeorological measurements has been recently manifested by developments in methodological and analytical techniques using spatial surface brightness temperature captured by infrared cameras (Schumacher et al. 2019, Katurji and Zawar-Reza 2016). The Thermal Image Velocimetry (TIV) method can now produce accurate 2D advection-velocities using high speed (>20Hz) infrared imagery (Inagaki 2013, Schumacher 2019). However, to further develop TIV methods and achieve a novel micrometeorological measurement technique, all scales of motion within the boundary layer need to be captured.</p><p>Spatial observations of multi-frequency and multi-scale temperature perturbations are a result from the turbulent interaction of the overlying atmosphere and the surface. However, these surface signatures are connected to the larger scales of the atmospheric boundary layer (McNaughton 2002, Träumner 2015). When longer periods (a few hours to a few days) of spatial surface brightness temperatures are observed, the larger scale information needs to be accounted for to build a comprehensive understanding of surface-atmospheric spatial turbulent interactions. Additionally, the time-frequency decomposition of brightness temperature perturbations shows longer periods of 4-15 minutes superimposed over shorter periods of ~ 4–30 seconds. This suggests that that boundary layer dynamic scales (of longer periods) can influence brightness temperature perturbations on the local turbulent scale. An accurate TIV algorithm needs to account for all scales of motion when analysing the time-space variability of locally observed spatial brightness temperature patterns.</p><p>To analyse these propositions temporally high resolved geostationary satellite infrared data from the Himawari 8 satellite was compared to near-surface and high speed (20 Hz) measured air and brightness temperature using thermocouple measurements and infrared cameras. The satellite provides a temporal resolution of 10-minutes and a horizontal resolution of 2 by 2 km per pixel and therefore captures the atmospheric meso γ and micro α scale which signals are usually active for ~10 minutes to < 12 hours. Moreover, the Himawari 8 brightness temperature was used to create the near-surface mean velocity field using TIV. Afterwards, the velocity field was compared to the in-situ measured wind velocity over several days during January 2019.</p><p>The results show that the atmospheric forcing from the micro α scale to lower atmospheric scales has a major impact on the near-surface temperature over several minutes. A significant (p-value: 0.02) positive covariance between the Himawari 8 measurement and the local measured temperature 1.5 cm above the ground on a 10 minute average, specifically concerning cooling and heating patterns, has been found.</p><p>Further analysis demonstrates that the retrieved near-surface 2-D velocity field calculated from the Himawari 8 brightness temperature perturbations is correctly representing the mean velocity. This finding allows the classification of meso-scale atmospheric forcing and its direct connection to local scale turbulent 2-D velocity measurements. This extends the TIV algorithm by a multi-scale component which allows to address inter-scale boundary layer analysis from a new point of view. In respect to the current findings a new experiment will focus on the repeated induced local velocity patterns from large scale forcing which will be measured through the surface brightness temperature.</p>

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