Effects of anisotropy on the geometry of tracer particle trajectories in turbulent flows
Yasmin HengsterMartin LellepJulian WeigelMatthew BrossJohannes BosbachDaniel SchanzAndreas SchröderFlorian HuhnMatteo NovaraDaniel Garaboa PazChristian J. KählerMoritz Linkmann
1
Citation
56
Reference
10
Related Paper
Citation Trend
Abstract:
Using curvature and torsion to describe Lagrangian trajectories gives a full description of these as well as an insight into small and large time scales as temporal derivatives up to order 3 are involved. One might expect that the statistics of these observables depend on the geometry of the flow. Therefore, we calculated curvature and torsion probability density functions (PDFs) of experimental Lagrangian trajectories processed using the Shake-the-Box algorithm of turbulent von Kármán flow, Rayleigh–Bénard convection and a zero-pressure-gradient turbulent boundary layer over a flat plate. The results for the von Kármán flow compare well with experimental results for the curvature PDF and results obtained by numerical simulations of homogeneous and isotropic turbulence for the torsion PDF. Results for Rayleigh–Bénard convection agree with those measured for von Kármán flow, while results for the logarithmic layer within the boundary layer differ slightly. We provide a potential explanation for the latter. To detect and quantify the effect of anisotropy either resulting from a mean flow or large-scale coherent motions on the geometry or tracer particle trajectories, we introduce the curvature vector. We connect its statistics with those of velocity fluctuations and demonstrate that strong large-scale motion in a given spatial direction results in meandering rather than helical trajectories.A variational principle approach to study the anisotropic self-focusing of ultrarelativistic laser beams in the undercritical plasma is performed in this paper. The presence of the anisotropic self-focusing laser intensity profile is viewed as a result of unstabilization of the isotropic profile. The isotropic laser profile is solved and then its stability relative to the anisotropic one is discussed. Numerical results show that parameters of the isotropic profile are important for its possibility of anisotropic unstabilization.
Cite
Citations (0)
Cite
Citations (1)
Cite
Citations (2)
In inhomogeneous isotropic regions, S-waves can be modeled using the ray method for isotropic media. In inhomogeneous strongly anisotropic regions, the independently propagating qS1- and qS2-waves can similarly be modeled using the ray method for anisotropic media. The latter method does not work properly in inhomogenous weakly anisotropic regions, however, where the split qS-waves couple. The zeroth‐order approximation of the quasi‐isotropic (QI) approach was designed for just such inhomogeneous weakly anisotropic media, for which neither the ray method for isotropic nor anisotropic media applies. We test the ranges of validity of these three methods using two simple synthetic models. Our results show that the QI approach more than spans the gap between the ray methods: it can be used in isotropic regions (where it reduces to the ray method for isotropic media), in regions of weak anisotropy (where the ray method for anisotropic media does not work properly), and even in regions of moderately strong anisotropy (in which the qS-waves decouple and thus could be modeled using the ray method for anisotropic media). A modeling program that switches between these three methods as necessary should be valid for arbitrary‐strength anisotropy.
Shear waves
Cite
Citations (33)
Linearization
USable
Cite
Citations (2)
Summary To solve an anisotropic flow problem, the problem is transformed into an equivalent isotropic problem. It is expected that an anisotropic solution can be readily obtained from the equivalent isotropic solution. However, sometimes that is not the case. Using the drawdown equation of a fully penetrated vertical well test and the drawdown and buildup equations for a probe test, this paper discusses when it is both possible and impossible to directly obtain an anisotropic solution from an isotropic solution. Because of the fact that transformation causes the changes in flow geometry and the shape of the wellbore or probe, the equivalent isotropic solution must be modified to obtain the anisotropic solution. Finally, a case of how horizontal well productivity was incorrectly derived in a published paper --caused by the misuse of the concept of anisotropy--is presented. The full manuscript of SPE 114504, Discussion of Permeability Anisotropy Effect, is available as a supplement to this article.
Drawdown (hydrology)
Cite
Citations (2)
Homogeneous isotropic turbulence
Cite
Citations (50)
Susceptibility measurements have been done on a random mixture of two anisotropic antiferromagnets with different orientations of easy axes, FeCl 2 ·2H 2 O and CoCl 2 ·2H 2 O. An isotropic state in which the anisotropy in the susceptibility becomes zero is found in the intermediate concentration region. A preliminary specific heat measurement suggests that the isotropic state lies within an ordered phase of the random mixture. The present experiment is discussed in connection with the existing theory.
Zero (linguistics)
Cite
Citations (13)
Cite
Citations (0)
Using matricant method elastic moduli of occasionally heterogeneous isotropic and anisotropic elastic media were received. Anisotropic behaviour and conditions for change in anisotropy of media associated with averaging of one-dimensional periodic structures was determined.
Cite
Citations (0)