scholarly journals Inertial range skewness of the longitudinal velocity derivative in locally isotropic turbulence

2018 ◽  
Vol 3 (11) ◽  
Author(s):  
S. Sukoriansky ◽  
E. Kit ◽  
E. Zemach ◽  
S. Midya ◽  
H. J. S. Fernando
Keyword(s):  
Isotropic Turbulence ◽  
Longitudinal Velocity ◽  
Inertial Range ◽  
Velocity Derivative

scholarly journals A Lagrangian direct-interaction approximation for homogeneous isotropic turbulence

1997 ◽  
Vol 345 ◽  
pp. 307-345 ◽  
Author(s):  
SHIGEO KIDA ◽  
SUSUMU GOTO
Keyword(s):  
Energy Spectrum ◽  
Differential Equations ◽  
Isotropic Turbulence ◽  
Longitudinal Velocity ◽  
Direct Interaction ◽  
Homogeneous Isotropic Turbulence ◽  
Velocity Correlation ◽  
Stationary Turbulence ◽  
Direct Interaction Approximation ◽  
Velocity Derivative

A set of integro-differential equations in the Lagrangian renormalized approximation (Kaneda 1981) is rederived by applying a perturbation method developed by Kraichnan (1959), which is based upon an extraction of direct interactions among Fourier modes of a velocity field and was applied to the Eulerian velocity correlation and response functions, to the Lagrangian ones for homogeneous isotropic turbulence. The resultant set of integro-differential equations for these functions has no adjustable free parameters. The shape of the energy spectrum function is determined numerically in the universal range for stationary turbulence, and in the whole wavenumber range in a similarly evolving form for the freely decaying case. The energy spectrum in the universal range takes the same shape in both cases, which also agrees excellently with many measurements of various kinds of real turbulence as well as numerical results obtained by Gotoh et al. (1988) for a decaying case as an initial value problem. The skewness factor of the longitudinal velocity derivative is calculated to be −0.66 for stationary turbulence. The wavenumber dependence of the eddy viscosity is also determined.

scholarly journals Closure model for homogeneous isotropic turbulence in the Lagrangian specification of the flow field

2018 ◽  
Vol 841 ◽  
pp. 521-551
Author(s):  
Makoto Okamura
Keyword(s):  
Flow Field ◽  
Isotropic Turbulence ◽  
Longitudinal Velocity ◽  
Navier Stokes ◽  
Homogeneous Isotropic Turbulence ◽  
Closure Model ◽  
Navier Stokes Equation ◽  
Closed Set ◽  
Proposed Model ◽  
Velocity Derivative

This paper proposes a new two-point closure model that is compatible with the Kolmogorov$-5/3$power law for homogeneous isotropic turbulence in an incompressible fluid using the Lagrangian specification of the flow field. A closed set of three equations was derived from the Navier–Stokes equation with no adjustable free parameters. The Kolmogorov constant and the skewness of the longitudinal velocity derivative were evaluated to be 1.779 and$-0.49$, respectively, using the proposed model. The bottleneck effect was also reproduced in the near-dissipation range.

scholarly journals Refinement of a Previous Hypothesis of the Lyapunov Analysis of Isotropic Turbulence

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Nicola de Divitiis
Keyword(s):  
Structure Function ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Longitudinal Velocity ◽  
Navier Stokes ◽  
Lyapunov Analysis ◽  
Velocity Difference ◽  
Navier Stokes Equations ◽  
Previous Hypothesis ◽  
Kolmogorov Theory

The purpose of this paper is to improve a hypothesis of the previous work of N. de Divitiis (2011) dealing with the finite-scale Lyapunov analysis of isotropic turbulence. There, the analytical expression of the structure function of the longitudinal velocity differenceΔuris derived through a statistical analysis of the Fourier transformed Navier-Stokes equations and by means of considerations regarding the scales of the velocity fluctuations, which arise from the Kolmogorov theory. Due to these latter considerations, this Lyapunov analysis seems to need some of the results of the Kolmogorov theory. This work proposes a more rigorous demonstration which leads to the same structure function, without using the Kolmogorov scale. This proof assumes that pair and triple longitudinal correlations are sufficient to determine the statistics ofΔurand adopts a reasonable canonical decomposition of the velocity difference in terms of proper stochastic variables which are adequate to describe the mechanism of kinetic energy cascade.

Scale-dependent alignment, tumbling and stretching of slender rods in isotropic turbulence

2018 ◽  
Vol 860 ◽  
pp. 465-486 ◽  
Author(s):  
Nimish Pujara ◽  
Greg A. Voth ◽  
Evan A. Variano
Keyword(s):  
Isotropic Turbulence ◽  
Fluid Velocity ◽  
Inertial Range ◽  
Small Scale ◽  
Strain Rate Tensor ◽  
Scaling Exponents ◽  
Slender Body Theory ◽  
Velocity Statistics ◽  
Rigid Rods ◽  
Dissipation Range

We examine the dynamics of slender, rigid rods in direct numerical simulation of isotropic turbulence. The focus is on the statistics of three quantities and how they vary as rod length increases from the dissipation range to the inertial range. These quantities are (i) the steady-state rod alignment with respect to the perceived velocity gradients in the surrounding flow, (ii) the rate of rod reorientation (tumbling) and (iii) the rate at which the rod end points move apart (stretching). Under the approximations of slender-body theory, the rod inertia is neglected and rods are modelled as passive particles in the flow that do not affect the fluid velocity field. We find that the average rod alignment changes qualitatively as rod length increases from the dissipation range to the inertial range. While rods in the dissipation range align most strongly with fluid vorticity, rods in the inertial range align most strongly with the most extensional eigenvector of the perceived strain-rate tensor. For rods in the inertial range, we find that the variance of rod stretching and the variance of rod tumbling both scale as $l^{-4/3}$, where $l$ is the rod length. However, when rod dynamics are compared to two-point fluid velocity statistics (structure functions), we see non-monotonic behaviour in the variance of rod tumbling due to the influence of small-scale fluid motions. Additionally, we find that the skewness of rod stretching does not show scale invariance in the inertial range, in contrast to the skewness of longitudinal fluid velocity increments as predicted by Kolmogorov’s $4/5$ law. Finally, we examine the power-law scaling exponents of higher-order moments of rod tumbling and rod stretching for rods with lengths in the inertial range and find that they show anomalous scaling. We compare these scaling exponents to predictions from Kolmogorov’s refined similarity hypotheses.

scholarly journals Reynolds number effect on the velocity derivative flatness factor

2018 ◽  
Vol 856 ◽  
pp. 426-443 ◽  
Author(s):  
M. Meldi ◽  
L. Djenidi ◽  
R. Antonia
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Nauk Sssr ◽  
Quantitative Agreement ◽  
Homogeneous Isotropic Turbulence ◽  
Simulation Data ◽  
Akad Nauk Sssr ◽  
Analytic Expression ◽  
Velocity Derivative ◽  
Flatness Factor

This paper investigates the effect of a finite Reynolds number (FRN) on the flatness factor ($F$) of the velocity derivative in decaying homogeneous isotropic turbulence by applying the eddy damped quasi-normal Markovian (EDQNM) method to calculate all terms in an analytic expression for $F$ (Djenidi et al., Phys. Fluids, vol. 29 (5), 2017b, 051702). These terms and hence $F$ become constant when the Taylor microscale Reynolds number, $Re_{\unicode[STIX]{x1D706}}$ exceeds approximately $10^{4}$. For smaller values of $Re_{\unicode[STIX]{x1D706}}$, $F$, like the skewness $-S$, increases with $Re_{\unicode[STIX]{x1D706}}$; this behaviour is in quantitative agreement with experimental and direct numerical simulation data. These results indicate that one must first ensure that $Re_{\unicode[STIX]{x1D706}}$ is large enough for the FRN effect to be negligibly small before the hypotheses of Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941a, pp. 301–305; Dokl. Akad. Nauk SSSR, vol. 32, 1941b, pp. 16–18; J. Fluid Mech., vol. 13, 1962, pp. 82–85) can be assessed unambiguously. An obvious implication is that results from experiments and direct numerical simulations for which $Re_{\unicode[STIX]{x1D706}}$ is well below $10^{4}$ may not be immune from the FRN effect. Another implication is that a power-law increase of $F$ with respect to $Re_{\unicode[STIX]{x1D706}}$, as suggested by the Kolmogorov 1962 theory, is not tenable when $Re_{\unicode[STIX]{x1D706}}$ is large enough.

On the dynamics of turbulence near a free surface

2017 ◽  
Vol 821 ◽  
pp. 248-265 ◽  
Author(s):  
Oscar Flores ◽  
James J. Riley ◽  
Alexander R. Horner-Devine
Keyword(s):  
Free Surface ◽  
Vertical Velocity ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Field Measurements ◽  
Inertial Range ◽  
Stratified Flows ◽  
Range Type ◽  
Spectral Behaviour ◽  
Vertical Shearing

We report on direct numerical simulations to examine the spectral behaviour of turbulence close to and at a flat, stress-free surface. We find, consistent with field measurements near such a free surface, that an inertial-range type of behaviour is obtained for the horizontal components of the velocity at and near the stress-free surface, at horizontal wavelengths for which the vertical velocity is much smaller than the horizontal components. At approximately an integral length scale from the stress-free surface, the flow has adjusted back to more classical isotropic turbulence. The behaviour of the turbulence near the stress-free surface is similar to that observed recently for strongly stratified flows, and we argue that the causes of that behaviour are the same in both flows: the suppression of the large-scale vertical velocity and the allowance of strong vertical shearing of the horizontal velocity leading to a downscale transfer of energy and to the development of the$-5/3$spectra for the horizontal velocities.

Turbulence structure behind the shock in canonical shock–vortical turbulence interaction

2014 ◽  
Vol 756 ◽  
Author(s):  
Jaiyoung Ryu ◽  
Daniel Livescu
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Isotropic Turbulence ◽  
Interaction Analysis ◽  
Longitudinal Velocity ◽  
Wave Structure ◽  
Turbulence Structure ◽  
Turbulent Structures ◽  
Linear Interaction ◽  
Third Invariant

AbstractThe interaction between vortical isotropic turbulence (IT) and a normal shock wave is studied using direct numerical simulation (DNS) and linear interaction analysis (LIA). In previous studies, agreement between the simulation results and the LIA predictions has been limited and, thus, the significance of LIA has been underestimated. In this paper, we present high-resolution simulations which accurately solve all flow scales (including the shock-wave structure) and extensively cover the parameter space (the shock Mach number, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}M_s$, ranges from 1.1 to 2.2 and the Taylor Reynolds number, ${\mathit{Re}}_{\lambda }$, ranges from 10 to 45). The results show, for the first time, that the turbulence quantities from DNS converge to the LIA solutions as the turbulent Mach number, $M_t$, becomes small, even at low upstream Reynolds numbers. The classical LIA formulae are extended to compute the complete post-shock flow fields using an IT database. The solutions, consistent with the DNS results, show that the shock wave significantly changes the topology of the turbulent structures, with a symmetrization of the third invariant of the velocity gradient tensor and ($M_s$-mediated) of the probability density function (PDF) of the longitudinal velocity derivatives, and an $M_s$-dependent increase in the correlation between strain and rotation.

scholarly journals The theory of axisymmetric turbulence

1946 ◽  
Vol 186 (1007) ◽  
pp. 480-502 ◽  
Keyword(s):  
Viscous Dissipation ◽  
Invariant Theory ◽  
Isotropic Turbulence ◽  
Longitudinal Velocity ◽  
Practical Interest ◽  
Mean Flow ◽  
Velocity Correlation ◽  
Rates Of Change ◽  
The Mean ◽  
Velocity Pressure

This paper discusses a type of turbulence in a uniform stream which is next to isotropic turbulence in order of simplicity. Instead of spherical symmetry, or isotropy, axially symmetical turbulence possesses symmetry about an axis which in practice is usually the direction of mean flow. The analysis is developed with the aid of invariant theory, as suggested by a previous paper by Robertson. The form of the fundamental velocity correlation is obtained, and scales of axisymmetric turbulence are defined. The results of greatest practical interest concern the time rates of change of the mean squares of the lateral and longitudinal velocity components. The rates of change involve two terms, the first representing viscous dissipation, and the second representing a transfer of energy from one component to the other due to the finite correlation between the velocity and pressure at neighbouring points. The effect of the velocity-pressure correlation is to bring the two velocity components towards equality, while the effect of the viscous dissipation will only be towards equality if an inequality between the curvatures at the origin of two particular velocity correlation coefficient curves, both of which are measurable, is obeyed. The rates of change of the mean squares of the vorticity components are also obtained.

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