اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدVelocity fluctuations in a dilute suspension of viscous vortex rings
87
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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 fluctuations associated with gravitational sedimentation or suspensions of microswimmers, here the vortices have a finite lifetime and are constantly being produced. We find that the net velocity distribution is similar to that of a single vortex, except for the smallest velocities which involve contributions from many distant vortices; the result is a truncated $5/3$-stable distribution with variance (and mean energy) linear in the vortex volume fraction $phi$. The distribution has an inner core with a width scaling as $phi^{3/5}$, then long tails with power law $|u|^{-8/3}$, and finally a fixed cutoff (independent of $phi$) above which the probability density scales as $|u|^{-5}$, where $u$ is a component of the velocity. We argue that this distribution is robust in the sense that the distribution of any velocity fluctuations caused by random forces localized in space and time has the same properties, except possibly for a different scaling after the cutoff.
قيم البحث
اقرأ أيضاً
We consider extensional flows of a dense layer of spheres in a viscous fluid and employ force and torque balances to determine the trajectory of particle pairs that contribute to the stress. In doing this, we use Stokesian dynamics simulations to gui
de the choice of the near-contacting pairs that follow such a trajectory. We specify the boundary conditions on the representative trajectory, and determine the distribution of particles along it and how the stress depends on the microstructure and strain rate. We test the resulting predictions using the numerical simulations. Also, we show that the relation between the tensors of stress and strain rate involves the second and fourth moments of the particle distribution function.
To study subregions of a turbulence velocity field, a long record of velocity data of grid turbulence is divided into smaller segments. For each segment, we calculate statistics such as the mean rate of energy dissipation and the mean energy at each
scale. Their values significantly fluctuate, in lognormal distributions at least as a good approximation. Each segment is not under equilibrium between the mean rate of energy dissipation and the mean rate of energy transfer that determines the mean energy. These two rates still correlate among segments when their length exceeds the correlation length. Also between the mean rate of energy dissipation and the mean total energy, there is a correlation characterized by the Reynolds number for the whole record, implying that the large-scale flow affects each of the segments.
A phenomenological theory of the fluctuations of velocity occurring in a fully developed homogeneous and isotropic turbulent flow is presented. The focus is made on the fluctuations of the spatial (Eulerian) and temporal (Lagrangian) velocity increme
nts. The universal nature of the intermittency phenomenon as observed in experimental measurements and numerical simulations is shown to be fully taken into account by the multiscale picture proposed by the multifractal formalism, and its extensions to the dissipative scales and to the Lagrangian framework. The article is devoted to the presentation of these arguments and to their comparisons against empirical data. In particular, explicit predictions of the statistics, such as probability density functions and high order moments, of the velocity gradients and acceleration are derived. In the Eulerian framework, at a given Reynolds number, they are shown to depend on a single parameter function called the singularity spectrum and to a universal constant governing the transition between the inertial and dissipative ranges. The Lagrangian singularity spectrum compares well with its Eulerian counterpart by a transformation based on incompressibility, homogeneity and isotropy and the remaining constant is shown to be difficult to estimate on empirical data. It is finally underlined the limitations of the increment to quantify accurately the singular nature of Lagrangian velocity. This is confirmed using higher order increments unbiased by the presence of linear trends, as they are observed on velocity along a trajectory.
Spark plasma discharges induce vortex rings and a hot gas kernel. We develop a model to describe the late stage of the spark induced flow and the role of the vortex rings in the entrainment of cold ambient gas and the cooling of the hot gas kernel. T
he model is tested in a plasma-induced flow, using density and velocity measurements obtained from simultaneous stereoscopic particle image velocimetry (S-PIV) and background oriented schlieren (BOS). We show that the spatial distribution of the hot kernel follows the motion of the vortex rings, whose radial expansion increases with the electrical energy deposited during the spark discharge. The vortex ring cooling model establishes that entrainment in the convective cooling regime is induced by the vortex rings and governs the cooling of the hot gas kernel, and the rate of cooling increases with the electrical energy deposited during the spark discharge.
For several flows of laboratory turbulence, we obtain long records of velocity data. These records are divided into numerous segments. In each segment, we calculate the mean rate of energy dissipation, the mean energy at each scale, and the mean tota
l energy. Their values fluctuate significantly among the segments. The fluctuations are lognormal, if the segment length lies within the range of large scales where the velocity correlations are weak but not yet absent. Since the lognormality is observed regardless of the Reynolds number and the configuration for turbulence production, it is expected to be universal. The likely origin is some multiplicative stochastic process related to interactions among scales through the energy transfer.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
