scholarly journals The dimensionless dissipation rate and the Kolmogorov (1941) hypothesis of local stationarity in freely decaying isotropic turbulence

2018 ◽  
Vol 59 (7) ◽  
pp. 073103 ◽  
Author(s):  
W. D. McComb ◽  
R. B. Fairhurst
Keyword(s):  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Local Stationarity

Dissipation rate estimation from PIV in zero-mean isotropic turbulence

2008 ◽  
Vol 46 (3) ◽  
pp. 499-515 ◽  
Author(s):  
J. de Jong ◽  
L. Cao ◽  
S. H. Woodward ◽  
J. P. L. C. Salazar ◽  
L. R. Collins ◽  
...  
Keyword(s):  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Rate Estimation

On the interaction of Taylor length scale size droplets and isotropic turbulence

2016 ◽  
Vol 806 ◽  
pp. 356-412 ◽  
Author(s):  
Michael S. Dodd ◽  
Antonino Ferrante
Keyword(s):  
Surface Tension ◽  
Surface Area ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Droplet Surface ◽  
Rate Of Change ◽  
Length Scale ◽  
Fluid Viscosity ◽  
Carrier Fluid ◽  
Two Fluid

Droplets in turbulent flows behave differently from solid particles, e.g. droplets deform, break up, coalesce and have internal fluid circulation. Our objective is to gain a fundamental understanding of the physical mechanisms of droplet–turbulence interaction. We performed direct numerical simulations (DNS) of 3130 finite-size, non-evaporating droplets of diameter approximately equal to the Taylor length scale and with 5 % droplet volume fraction in decaying isotropic turbulence at initial Taylor-scale Reynolds number $\mathit{Re}_{\unicode[STIX]{x1D706}}=83$. In the droplet-laden cases, we varied one of the following three parameters: the droplet Weber number based on the r.m.s. velocity of turbulence ($0.1\leqslant \mathit{We}_{rms}\leqslant 5$), the droplet- to carrier-fluid density ratio ($1\leqslant \unicode[STIX]{x1D70C}_{d}/\unicode[STIX]{x1D70C}_{c}\leqslant 100$) or the droplet- to carrier-fluid viscosity ratio ($1\leqslant \unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x1D707}_{c}\leqslant 100$). In this work, we derive the turbulence kinetic energy (TKE) equations for the two-fluid, carrier-fluid and droplet-fluid flow. These equations allow us to explain the pathways for TKE exchange between the carrier turbulent flow and the flow inside the droplet. We also explain the role of the interfacial surface energy in the two-fluid TKE equation through the power of the surface tension. Furthermore, we derive the relationship between the power of surface tension and the rate of change of total droplet surface area. This link allows us to explain how droplet deformation, breakup and coalescence play roles in the temporal evolution of TKE. Our DNS results show that increasing $\mathit{We}_{rms}$, $\unicode[STIX]{x1D70C}_{d}/\unicode[STIX]{x1D70C}_{c}$ and $\unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x1D707}_{c}$ increases the decay rate of the two-fluid TKE. The droplets enhance the dissipation rate of TKE by enhancing the local velocity gradients near the droplet interface. The power of the surface tension is a source or sink of the two-fluid TKE depending on the sign of the rate of change of the total droplet surface area. Thus, we show that, through the power of the surface tension, droplet coalescence is a source of TKE and breakup is a sink of TKE. For short times, the power of the surface tension is less than $\pm 5\,\%$ of the dissipation rate. For later times, the power of the surface tension is always a source of TKE, and its magnitude can be up to 50 % of the dissipation rate.

Compressibility effects on the growth and structure of homogeneous turbulent shear flow

1993 ◽  
Vol 256 ◽  
pp. 443-485 ◽  
Author(s):  
G. A. Blaisdell ◽  
N. N. Mansour ◽  
W. C. Reynolds
Keyword(s):  
Growth Rate ◽  
Shear Flow ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Compressible Turbulence ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Homogeneous Shear ◽  
Homogeneous Shear Flow ◽  
Compressibility Effects

Compressibility effects within decaying isotropic turbulence and homogeneous turbulent shear flow have been studied using direct numerical simulation. The objective of this work is to increase our understanding of compressible turbulence and to aid the development of turbulence models for compressible flows. The numerical simulations of compressible isotropic turbulence show that compressibility effects are highly dependent on the initial conditions. The shear flow simulations, on the other hand, show that measures of compressibility evolve to become independent of their initial values and are parameterized by the root mean square Mach number. The growth rate of the turbulence in compressible homogeneous shear flow is reduced compared to that in the incompressible case. The reduced growth rate is the result of an increase in the dissipation rate and energy transfer to internal energy by the pressure–dilatation correlation. Examination of the structure of compressible homogeneous shear flow reveals the presence of eddy shocklets, which are important for the increased dissipation rate of compressible turbulence.

Scalar dissipation rate and dissipative anomaly in isotropic turbulence

2005 ◽  
Vol 532 ◽  
pp. 199-216 ◽  
Author(s):  
D. A. DONZIS ◽  
K. R. SREENIVASAN ◽  
P. K. YEUNG
Keyword(s):  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate

Time-dependent, non-monotonic mixing in stratified turbulent shear flows: implications for oceanographic estimates of buoyancy flux

2013 ◽  
Vol 736 ◽  
pp. 570-593 ◽  
Author(s):  
A. Mashayek ◽  
C. P. Caulfield ◽  
W. R. Peltier
Keyword(s):  
Reynolds Number ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Buoyancy Flux ◽  
Shear Instability ◽  
Turbulent Shear ◽  
Mixing Efficiency ◽  
Small Scale ◽  
Stratified Turbulence ◽  
Flow Evolution

AbstractWe employ direct numerical simulation to investigate the efficiency of diapycnal mixing by shear-induced turbulence in stably stratified free shear layers for flows with bulk Richardson numbers in the range $0. 12\leq R{i}_{0} \leq 0. 2$ and Reynolds number $Re= 6000$. We show that mixing efficiency depends non-monotonically upon $R{i}_{0} $, peaking in the range 0.14–0.16, which coincides closely with the range in which both the buoyancy flux and the dissipation rate are maximum. By detailed analyses of the energetics of flow evolution and the underlying dynamics, we show that the existence of high mixing efficiency in the range $0. 14\lt R{i}_{0} \lt 0. 16$ is due to the emergence of a large number of small-scale instabilities which do not exist at lower Richardson numbers and are stabilized at high Richardson numbers. As discussed in Mashayek & Peltier (J. Fluid Mech., vol. 725, 2013, pp. 216–261), the existence of such a well-populated ‘zoo’ of secondary instabilities at intermediate Richardson numbers and the subsequent high mixing efficiency is realized only if the Reynolds number is higher than a critical value which is generally higher than that achievable in laboratory settings, as well as that which was achieved in the majority of previous numerical studies of shear-induced stratified turbulence. We furthermore show that the primary assumptions upon which the widely employed Osborn (J. Phys. Oceanogr. vol. 10, 1980, pp. 83–89) formula is based, as well as its counterparts and derivatives, which relate buoyancy flux to dissipation rate through a (constant) flux coefficient ($\Gamma $), fail at higher Richardson numbers provided that the Reynolds number is sufficiently high. Specifically, we show that the assumptions of fully developed, stationary, and isotropic turbulence all break down at high Richardson numbers. We show that the breakdown of these assumptions occurs most prominently at Richardson numbers above that corresponding to the maximum mixing efficiency, a fact that highlights the importance of the non-monotonicity of the dependence of mixing efficiency upon Richardson number, which we establish to be characteristic of stratified shear-induced turbulence. At high $R{i}_{0} $, the lifecycle of the turbulence is composed of a rapidly growing phase followed by a phase of rapid decay. Throughout the lifecycle, there is considerable exchange of energy between the small-scale turbulence and larger coherent structures which survive the various stages of flow evolution. Since shear instability is one of the most prominent mechanisms for turbulent dissipation of energy at scales below hundreds of metres and at various depths of the ocean, our results have important implications for the inference of turbulent diffusivities on the basis of microstructure measurements in the oceanic environment.

scholarly journals Local dissipation scales and energy dissipation-rate moments in channel flow

2012 ◽  
Vol 701 ◽  
pp. 419-429 ◽  
Author(s):  
P. E. Hamlington ◽  
D. Krasnov ◽  
T. Boeck ◽  
J. Schumacher
Keyword(s):  
Energy Dissipation ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Energy Dissipation Rate ◽  
Wall Region ◽  
Dissipation Scale ◽  
High Order Statistics

AbstractLocal dissipation-scale distributions and high-order statistics of the energy dissipation rate are examined in turbulent channel flow using very high-resolution direct numerical simulations at Reynolds numbers ${\mathit{Re}}_{\tau } = 180$, $381$ and $590$. For sufficiently large ${\mathit{Re}}_{\tau } $, the dissipation-scale distributions and energy dissipation moments in the channel bulk flow agree with those in homogeneous isotropic turbulence, including only a weak Reynolds-number dependence of both the finest and largest scales. Systematic, but ${\mathit{Re}}_{\tau } $-independent, variations in the distributions and moments arise as the wall is approached for ${y}^{+ } \lesssim 100$. In the range $100\lt {y}^{+ } \lt 200$, there are substantial differences in the moments between the lowest and the two larger values of ${\mathit{Re}}_{\tau } $. This is most likely caused by coherent vortices from the near-wall region, which fill the whole channel for low ${\mathit{Re}}_{\tau } $.

scholarly journals Lagrangian cascade in three-dimensional homogeneous and isotropic turbulence

2014 ◽  
Vol 741 ◽  
Author(s):  
Yongxiang Huang ◽  
François G. Schmitt
Keyword(s):  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Energy Dissipation Rate ◽  
Inertial Range ◽  
Order Moment ◽  
Scaling Exponent ◽  
Tracer Particles ◽  
Homogeneous And Isotropic Turbulence ◽  
Multiplicative Cascade

AbstractIn this work, the scaling statistics of the dissipation along Lagrangian trajectories are investigated by using fluid tracer particles obtained from a high-resolution direct numerical simulation with $\mathit{Re}_{\lambda }=400$. Both the energy dissipation rate $\epsilon $ and the local time-averaged $\epsilon _{\tau }$ agree rather well with the lognormal distribution hypothesis. Several statistics are then examined. It is found that the autocorrelation function $\rho (\tau )$ of $\ln (\epsilon (t))$ and variance $\sigma ^2(\tau )$ of $\ln (\epsilon _{\tau }(t))$ obey a log-law with scaling exponent $\beta '=\beta =0.30$ compatible with the intermittency parameter $\mu =0.30$. The $q{\rm th}$-order moment of $\epsilon _{\tau }$ has a clear power law on the inertial range $10<\tau /\tau _{\eta }<100$. The measured scaling exponent $K_L(q)$ agrees remarkably with $q-\zeta _L(2q)$ where $\zeta _L(2q)$ is the scaling exponent estimated using the Hilbert methodology. All of these results suggest that the dissipation along Lagrangian trajectories could be modelled by a multiplicative cascade.

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