ﻻ يوجد ملخص باللغة العربية
Velocity gradient is the basis of many vortex recognition methods, such as Q criterion, $Delta$ criterion, $lambda_{2}$ criterion, $lambda_{ci}$ criterion and $Omega$ criterion, etc.. Except the $lambda_{ci}$ criterion, all these criterions recognize vortices by designing various invariants, based on the Helmholtz decomposition that decomposes velocity gradient into strain rate and spin. In recent years, the intuition of no vortex in straight flows has promoted people to analyze the vortex state directly from the velocity gradient, in which vortex can be distinguished from the situation that the velocity gradient has couple complex eigenvalues. A specious viewpoint to adopt the simple shear as an independent flow mode was emphasized by many authors, among them, Kolar proposed the triple decomposition of motion by extracting a so-called effective pure shearing motion; Li et al. introduced the so-called quaternion decomposition of velocity gradient and proposed the concept of eigen rotation; Liu et al. further mined the characteristic information of velocity gradient and put forward an effective algorithm of Liutex, and then developed the vortex recognition method. However, there is another explanation for the increasingly clear representation of velocity gradient, that is the local streamline pattern based on critical-point theory. In this paper, the tensorial expressions of the right/left real Schur forms of velocity gradient are clarified from the characteristic problem of velocity gradient. The relations between the involved parameters are derived and numerically verified. Comparing with the geometrical features of local streamline pattern, we confirm that the parameters in the right eigen-representation based on the right real Schur form of velocity gradient have good meanings to reveal the local streamline pattern. Some illustrative examples from the DNS data are presented.
We present results for the equilibrium statistics and dynamic evolution of moderately large ($n = {mathcal{O}}(10^2 - 10^3)$) numbers of interacting point vortices on the unit sphere under the constraint of zero mean angular momentum. We consider a b
We present velocity spectra measured in three cryogenic liquid 4He steady flows: grid and wake flows in a pressurized wind tunnel capable of achieving mean velocities up to 5 m/s at temperatures above and below the superfluid transition, down to 1.7
The Tayler instability is a kink-type flow instability which occurs when the electrical current through a conducting fluid exceeds a certain critical value. Originally studied in the astrophysical context, the instability was recently shown to be als
We use direct numerical simulations to calculate the joint probability density function of the relative distance $R$ and relative radial velocity component $V_R$ for a pair of heavy inertial particles suspended in homogeneous and isotropic turbulent
We explore the velocity fluctuations in a fluid due to a dilute suspension of randomly-distributed vortex rings at moderate Reynolds number, for instance those generated by a large colony of jellyfish. Unlike previous analysis of velocity fluctuation