Pressure statistics in self-similar freely decaying isotropic turbulence

2013 ◽  
Vol 717 ◽  
Author(s):  
Marcello Meldi ◽  
Pierre Sagaut
Keyword(s):  
Reynolds Number ◽  
Scaling Laws ◽  
Isotropic Turbulence ◽  
Threshold Value ◽  
Time Decay ◽  
Self Similar ◽  
High Reynolds ◽  
Almost All ◽  
Time Decay Rate ◽  
Large Eddies

AbstractThe time evolution of pressure statistics in freely decaying homogeneous isotropic turbulence (HIT) is investigated via eddy-damped quasi-normal Markovian (EDQNM) computations. The present results show that the time decay rate of pressure-based statistical quantities, such as pressure variance and pressure gradient variance, are sensitive to the breakdown of permanence of large eddies. New formulae for the associated time-decay exponents are proposed, which extend previous relations proposed in Lesieur, Ossia & Metais (Phys. Fluids, vol. 11, 1999, p. 1535). Particular attention is paid to finite-Reynolds-number (FRN) effects on the pressure spectrum and pressure statistics. The results also suggest that $R{e}_{\lambda } = O(1{0}^{4} )$ must be considered to observe a one-decade inertial range in the pressure spectrum with Kolmogorov $- 7/ 3$ scaling. This threshold value is larger than almost all existing direct numerical simulation (DNS) and experimental data, justifying the discussion about other possible scaling laws. The $- 5/ 3$ slope reported in some DNS data is also recovered by the EDQNM model, but it is observed to be a low-Reynolds-number effect. Another important result is that FRN effects yield a departure from asymptotic theoretical behaviours which appear similar to some effects attributed to intermittency by most authors. This is exemplified by the ratio between pressure-based and velocity-based Taylor microscales. Therefore, high-Reynolds-number DNS or experiments such that $R{e}_{\lambda } = O(1{0}^{4} )$ would be required in order to remove FRN effects and to analyse pure intermittency effects.

Spectral modelling of high Reynolds number unstably stratified homogeneous turbulence

2015 ◽  
Vol 765 ◽  
pp. 17-44 ◽  
Author(s):  
A. Burlot ◽  
B.-J. Gréa ◽  
F. S. Godeferd ◽  
C. Cambon ◽  
J. Griffond
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Isotropic Turbulence ◽  
Spectral Energy Distribution ◽  
Homogeneous Turbulence ◽  
Spectral Energy ◽  
Characteristic Relaxation Time ◽  
Background Density ◽  
Self Similar ◽  
High Reynolds

AbstractWe study unconfined homogeneous turbulence with a destabilizing background density gradient in the Boussinesq approximation. Starting from initial isotropic turbulence, the buoyancy force induces a transient phase toward a self-similar regime accompanied by a rapid growth of kinetic energy and Reynolds number, along with the development of anisotropic structures in the flow in the direction of gravity. We model this with a two-point statistical approach using an axisymmetric eddy-damped quasi-normal Markovian (EDQNM) closure that includes buoyancy production. The model is able to match direct numerical simulations (DNS) in a parametric study showing the effect of initial Froude number and mixing intensity on the development of the flow. We further improve the model by including the stratification timescale in the characteristic relaxation time for triple correlations in the closure. It permits the computation of the long-term evolution of unstably stratified turbulence at high Reynolds number. This agrees with recent theoretical predictions concerning the self-similar dynamics and brings new insight into the spectral energy distribution and anisotropy of the flow.

Axisymmetric, constantly supplied gravity currents at high Reynolds number

2011 ◽  
Vol 675 ◽  
pp. 540-551 ◽  
Author(s):  
ANJA C. SLIM ◽  
HERBERT E. HUPPERT
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Threshold Value ◽  
Gravity Currents ◽  
Water Model ◽  
Closure Condition ◽  
Area Source ◽  
Radial Extent ◽  
Long Time ◽  
High Reynolds

We consider theoretically the long-time evolution of axisymmetric, high Reynolds number, Boussinesq gravity currents supplied by a constant, small-area source of mass and radial momentum in a deep, quiescent ambient. We describe the gravity currents using a shallow-water model with a Froude number closure condition to incorporate ambient form drag at the front and present numerical and asymptotic solutions. The predicted profile consists of an expanding, radially decaying, steady interior that connects via a shock to a deeper, self-similar frontal boundary layer. Controlled by the balance of interior momentum flux and frontal buoyancy across the shock, the front advances as (g′sQ/r1/4s)4/154/5, where g′s is the reduced gravity of the source fluid, Q is the total volume flux, rs is the source radius and is time. A radial momentum source has no effect on this solution below a non-zero threshold value. Above this value, the (virtual) radius over which the flow becomes critical can be used to collapse the solution onto the subthreshold one. We also use a simple parameterization to incorporate the effect of interfacial entrainment, and show that the profile can be substantially modified, although the buoyancy profile and radial extent are less significantly impacted. Our predicted profiles and extents are in reasonable agreement with existing experiments.

scholarly journals Circulation in High Reynolds Number Isotropic Turbulence is a Bifractal

2019 ◽  
Vol 9 (4) ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P. K. Yeung
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Isotropic Turbulence ◽  
High Reynolds

Clusters of sedimenting high-Reynolds-number particles

2009 ◽  
Vol 625 ◽  
pp. 371-385 ◽  
Author(s):  
W. BRENT DANIEL ◽  
ROBERT E. ECKE ◽  
G. SUBRAMANIAN ◽  
DONALD L. KOCH
Keyword(s):  
Reynolds Number ◽  
Mass Conservation ◽  
Characteristic Size ◽  
Quadratic Growth ◽  
Growth Exponent ◽  
Theoretical Predictions ◽  
Large Tank ◽  
Long Time ◽  
Self Similar ◽  
High Reynolds

We report experiments wherein groups of particles were allowed to sediment in an otherwise quiescent fluid contained in a large tank. The Reynolds number of the particles, defined as Re = aU/ν, ranged from 93 to 425; here, a is the radius of the spherical particle, U its settling velocity and ν the kinematic viscosity of the fluid. The characteristic size of a cluster, in a plane transverse to gravity, was measured by a ‘cluster variance’(〈r2t〉); the latter is defined as the mean square of the transverse coordinates of all constituent particles, averaged over a series of runs. The cluster variance, when plotted as a function of time, exhibited two regimes. There was a quadratic growth in the variance at short times(〈r2t〉 ∝ t2), while for long times, the cluster variance exhibited a slower sublinear growth with 〈r2t〉 ∝ t0.67. A theory, based on isotropic repulsive hydrodynamic interactions between particles, predicts the cluster variance to grow as t2/3 in the limit of long times. The theoretical framework was originally proposed to describe the long-time self-similar evolution of dilute clusters in the limit Re ≪ 1 Subramanian & Koch (J. Fluid Mech., vol. 603, 2008, p. 63), when the probability of wake-mediated interactions between particles remains asymptotically small; the latter requirement is satisfied for homogeneous spherical clusters larger than a critical radius, and is evidently satisfied for planar clusters oriented transversely to gravity. The isotropy of the interactions therefore stems from the isotropy, at large distances, of the disturbance velocity field produced by a single sedimenting particle outside its wake(which contains the compensating inflow to satisfy mass conservation). Herein, the theory is extended to large Re using an empirical correlation for the drag on a sedimenting particle. This allows one to predict, as a function of Re, the numerical prefactors in the expressions for the cluster variance of both spherical and planar clusters; the predictions for the growth exponent remain unchanged. The agreement between the theoretical and experimental growth exponents supports the hypothesis of a self-similar expansion at long times. The prefactor determined from the experimental observations is found to lie between the theoretical predictions for planar and spherical clusters.

scholarly journals Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

2013 ◽  
Vol 734 ◽  
pp. 275-316 ◽  
Author(s):  
Rashad Moarref ◽  
Ati S. Sharma ◽  
Joel A. Tropp ◽  
Beverley J. McKeon
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Low Rank ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Self Similar ◽  
The Mean ◽  
High Reynolds

AbstractWe study the Reynolds-number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier–Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. Using the accepted scalings of the mean velocity in wall-bounded turbulent flows, we establish that the resolvent operator admits three classes of wave parameters that induce universal behaviour with Reynolds number in the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. In addition, it is shown that a necessary condition for geometrically self-similar resolvent modes is the presence of a logarithmic turbulent mean velocity. Under the practical assumption that the mean velocity consists of a logarithmic region, we identify the scalings that constitute hierarchies of self-similar modes that are parameterized by the critical wall-normal location where the speed of the mode equals the local turbulent mean velocity. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (${Re}_{\tau } \approx 1{0}^{3} {\unicode{x2013}} 1{0}^{10} $). Results from this low-rank model of the Navier–Stokes equations compare favourably with experimental results in the literature.

Benchmarking of VIV Suppression Systems

2008 ◽  
Author(s):  
Kenneth J. Schaudt ◽  
Christopher Wajnikonis ◽  
Don Spencer ◽  
Jie Xu ◽  
Steve Leverette ◽  
...  
Keyword(s):  
Reynolds Number ◽  
The Body ◽  
Test Results ◽  
In Situ Tests ◽  
Image Velocimetry ◽  
High Reynolds ◽  
Viv Suppression ◽  
Almost All ◽  
Flow Splitter

A new form of Vortex-Induced Vibration (VIV) suppression device, the AIMS Dual-fin Flow Splitter (ADFS), has been developed, tested and benchmarked against bare-pipe, 5d and 15d pitch strakes and conventional teardrop fairings. Testing included high-mode number in-situ tests as well as low Reynolds number (<300,000) and high Reynolds number (<1.9 million) forced and free tank tests. Finally, wind tunnel tests and in-water Particle Image Velocimetry (PIV) were used to test the hypothesis that the dual-fin flow splitter replaces the oscillating wake of a blunt body with a stable, attached circulation behind the body and between the fins. Such a replacement was hypothesized to result in reduced drag, and the elimination of almost all VIV. The paper will describe the testing program and results, and present the incorporation of the test results into riser models.

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