Estimation of the Kolmogorov constant (C0) for the Lagrangian structure function, using a second‐order Lagrangian model of grid turbulence

1995 ◽  
Vol 7 (12) ◽  
pp. 3083-3090 ◽  
Author(s):  
Shuming Du ◽  
Brian L. Sawford ◽  
John D. Wilson ◽  
David J. Wilson
Keyword(s):  
Structure Function ◽  
Second Order ◽  
Lagrangian Model ◽  
Grid Turbulence ◽  
Kolmogorov Constant

A Turbulent Model for Gas-Particle Jets

2000 ◽  
Vol 122 (3) ◽  
pp. 505-509 ◽  
Author(s):  
J. Garcı´a ◽  
A. Crespo
Keyword(s):  
Mixing Layer ◽  
Stokes Number ◽  
Particle Dispersion ◽  
Lagrangian Model ◽  
Grid Turbulence ◽  
Mean Velocity ◽  
Dissipation Term ◽  
Particle Flows ◽  
Integral Scales ◽  
Kolmogorov Constant

This work is concerned with turbulent diffusion in gas-particle flows. The cases studied correspond to dilute flows and small Stokes number, this implies that the mean velocity of the particles is very similar to that of the fluid element. The classical k-ε method is used to model the gas-phase, modified with additional terms for the k and ε equations, that takes into account the effect of particles on the carrier phase. The additional dissipation term included in the equation for k is due to the slip between phases at an intermediate scale, far from both the Kolmogorov and the integral scales. This term has a proportionality constant equal to 3/2 of Kolmogorov constant, C0. In this paper, a value of 3.0 has been used for this constant as suggested by Du et al., 1995, “Estimation of the Kolmogorov Constant C0 for the Langarian Structure Using a Second-Order Lagrangian Model of Grid Turbulence,” Phys. Fluids 7, (12), pp. 3083–3090. The additional source term for the ε equation is taken as proportional to ε/k, as is usually done. In all experiments analyzed the particles increased the dissipation of turbulent kinetic energy. A comparison is made between the results obtained with the model proposed in this work and the experiments of Shuen et al., 1985, “Structure of Particle-Laden Jets: Measurements and Predictions,” AIAA Journal, 23, No. 3, and Hishida et al., 1992, “Experiments on Particle Dispersion in a Turbulent Mixing Layer,” ASME Journal of Fluids Engineering, 119, pp. 181–194. [S0098-2202(00)02103-9]

A Second Order Lagrangian Model for Irregular Ocean Waves

2005 ◽  
Vol 128 (3) ◽  
pp. 177-183 ◽  
Author(s):  
Sébastien Fouques ◽  
Harald E. Krogstad ◽  
Dag Myrhaug
Keyword(s):  
Specular Reflection ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Wave Theory ◽  
Ocean Waves ◽  
Second Order ◽  
Lagrangian Model ◽  
Lagrangian Description ◽  
Linear Wave ◽  
Irregular Solution

Synthetic aperture radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, slope, and mean curvature are studied.

Reynolds number dependence of the second-order turbulent pressure structure function

1999 ◽  
Vol 11 (1) ◽  
pp. 241-243 ◽  
Author(s):  
R. A. Antonia ◽  
D. K. Bisset ◽  
P. Orlandi ◽  
B. R. Pearson
Keyword(s):  
Reynolds Number ◽  
Structure Function ◽  
Second Order ◽  
Turbulent Pressure ◽  
Reynolds Number Dependence

A Second Order Lagrangian Model for Irregular Ocean Waves

2004 ◽  
Author(s):  
Se´bastien Fouques ◽  
Harald E. Krogstad ◽  
Dag Myrhaug
Keyword(s):  
Specular Reflection ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Wave Theory ◽  
Ocean Waves ◽  
Second Order ◽  
Lagrangian Model ◽  
Lagrangian Description ◽  
Linear Wave ◽  
Irregular Solution

Synthetic Aperture Radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, the slope and the mean curvature are studied.

An empirical expression for on the axis of a slightly heated turbulent round jet

2019 ◽  
Vol 867 ◽  
pp. 392-413 ◽  
Author(s):  
J. Lemay ◽  
L. Djenidi ◽  
R. A. Antonia ◽  
A. Benaïssa
Keyword(s):  
Structure Function ◽  
Dissipation Rate ◽  
Velocity Structure ◽  
Power Laws ◽  
Second Order ◽  
Temperature Structure ◽  
Analytical Expression ◽  
Round Jet ◽  
Mean Temperature ◽  
The Mean

Self-preservation analyses of the equations for the mean temperature and the second-order temperature structure function on the axis of a slightly heated turbulent round jet are exploited in an attempt to develop an analytical expression for$\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}$, the mean dissipation rate of$\overline{\unicode[STIX]{x1D703}^{2}}/2$, where$\overline{\unicode[STIX]{x1D703}^{2}}$is the temperature variance. The analytical approach follows that of Thiessetet al.(J. Fluid Mech., vol. 748, 2014, R2) who developed an expression for$\unicode[STIX]{x1D716}_{k}$, the mean turbulent kinetic energy dissipation rate, using the transport equation for$\overline{(\unicode[STIX]{x1D6FF}u)^{2}}$, the second-order velocity structure function. Experimental data show that complete self-preservation for all scales of motion is very well satisfied along the jet axis for streamwise distances larger than approximately 30 times the nozzle diameter. This validation of the analytical results is of particular interest as it provides justification and confidence in the analytical derivation of power laws representing the streamwise evolution of different physical quantities along the axis, such as:$\unicode[STIX]{x1D702}$,$\unicode[STIX]{x1D706}$,$\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}$,$R_{U}$,$R_{\unicode[STIX]{x1D6E9}}$(all representing characteristic length scales), the mean temperature excess$\unicode[STIX]{x1D6E9}_{0}$, the mixed velocity–temperature moments$\overline{u\unicode[STIX]{x1D703}^{2}}$,$\overline{v\unicode[STIX]{x1D703}^{2}}$and$\overline{\unicode[STIX]{x1D703}^{2}}$and$\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}$. Simple models are proposed for$\overline{u\unicode[STIX]{x1D703}^{2}}$and$\overline{v\unicode[STIX]{x1D703}^{2}}$in order to derive an analytical expression for$A_{\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}}$, the prefactor of the power law describing the streamwise evolution of$\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}$. Further, expressions are also derived for the turbulent Péclet number and the thermal-to-mechanical time scale ratio. These expressions involve global parameters that are most likely to be influenced by the initial and/or boundary conditions and are therefore expected to be flow dependent.

scholarly journals An improved Lagrangian model for the time evolution of nonlinear surface waves

2019 ◽  
Vol 876 ◽  
pp. 527-552 ◽  
Author(s):  
Charles-Antoine Guérin ◽  
Nicolas Desmars ◽  
Stéphan T. Grilli ◽  
Guillaume Ducrozet ◽  
Yves Perignon ◽  
...  
Keyword(s):  
Surface Waves ◽  
Time Evolution ◽  
Forecast Accuracy ◽  
Second Order ◽  
Stokes Drift ◽  
Irregular Waves ◽  
Lagrangian Model ◽  
Simple Method ◽  
Lagrangian Models ◽  
Wave Forecast

Accurate real-time simulations and forecasting of phase-revolved ocean surface waves require nonlinear effects, both geometrical and kinematic, to be accurately represented. For this purpose, wave models based on a Lagrangian steepness expansion have proved particularly efficient, as compared to those based on Eulerian expansions, as they feature higher-order nonlinearities at a reduced numerical cost. However, while they can accurately model the instantaneous nonlinear wave shape, Lagrangian models developed to date cannot accurately predict the time evolution of even simple periodic waves. Here, we propose a novel and simple method to perform a Lagrangian expansion of surface waves to second order in wave steepness, based on the dynamical system relating particle locations and the Eulerian velocity field. We show that a simple redefinition of reference particles allows us to correct the time evolution of surface waves, through a modified nonlinear dispersion relationship. The resulting expressions of free surface particle locations can then be made numerically efficient by only retaining the most significant contributions to second-order terms, i.e. Stokes drift and mean vertical level. This results in a hybrid model, referred to as the ‘improved choppy wave model’ (ICWM) (with respect to Nouguier et al.’s J. Geophys. Res., vol. 114, 2009, p. C09012), whose performance is numerically assessed for long-crested waves, both periodic and irregular. To do so, ICWM results are compared to those of models based on a high-order spectral method and classical second-order Lagrangian expansions. For irregular waves, two generic types of narrow- and broad-banded wave spectra are considered, for which ICWM is shown to significantly improve wave forecast accuracy as compared to other Lagrangian models; hence, ICWM is well suited to providing accurate and efficient short-term ocean wave forecast (e.g. over a few peak periods). This aspect will be the object of future work.

scholarly journals Corrections to the scaling of the second-order structure function in isotropic turbulence

2009 ◽  
Vol 26 (2) ◽  
pp. 151-157 ◽  
Author(s):  
Le Fang ◽  
Wouter J. T. Bos ◽  
Xiaozhou Zhou ◽  
Liang Shao ◽  
Jean-Pierre Bertoglio
Keyword(s):  
Structure Function ◽  
Isotropic Turbulence ◽  
Second Order ◽  
Order Structure

scholarly journals A semi-implicit, second-order-accurate numerical model for multiphase underexpanded volcanic jets

2013 ◽  
Vol 6 (6) ◽  
pp. 1905-1924 ◽  
Author(s):  
S. Carcano ◽  
L. Bonaventura ◽  
T. Esposti Ongaro ◽  
A. Neri
Keyword(s):  
Relaxation Time ◽  
Numerical Model ◽  
Numerical Simulations ◽  
Solid Phase ◽  
Maximum Velocity ◽  
Second Order ◽  
Three Dimensions ◽  
Lagrangian Model ◽  
Coarse Particles ◽  
Nonequilibrium Effects

Abstract. An improved version of the PDAC (Pyroclastic Dispersal Analysis Code, Esposti Ongaro et al., 2007) numerical model for the simulation of multiphase volcanic flows is presented and validated for the simulation of multiphase volcanic jets in supersonic regimes. The present version of PDAC includes second-order time- and space discretizations and fully multidimensional advection discretizations in order to reduce numerical diffusion and enhance the accuracy of the original model. The model is tested on the problem of jet decompression in both two and three dimensions. For homogeneous jets, numerical results are consistent with experimental results at the laboratory scale (Lewis and Carlson, 1964). For nonequilibrium gas–particle jets, we consider monodisperse and bidisperse mixtures, and we quantify nonequilibrium effects in terms of the ratio between the particle relaxation time and a characteristic jet timescale. For coarse particles and low particle load, numerical simulations well reproduce laboratory experiments and numerical simulations carried out with an Eulerian–Lagrangian model (Sommerfeld, 1993). At the volcanic scale, we consider steady-state conditions associated with the development of Vulcanian and sub-Plinian eruptions. For the finest particles produced in these regimes, we demonstrate that the solid phase is in mechanical and thermal equilibrium with the gas phase and that the jet decompression structure is well described by a pseudogas model (Ogden et al., 2008). Coarse particles, on the other hand, display significant nonequilibrium effects, which associated with their larger relaxation time. Deviations from the equilibrium regime, with maximum velocity and temperature differences on the order of 150 m s−1 and 80 K across shock waves, occur especially during the rapid acceleration phases, and are able to modify substantially the jet dynamics with respect to the homogeneous case.

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