Turbulence, anisotropic

More advanced models, for example the algebraic stress model (ASM) and the Reynolds stress model (RSM), are not based on the eddy-viscosity concept and can thus account for anisotropic turbulence thereby giving still better predictions of flows. In addition to the transport equations, however, the algebraic equations for the Reynolds stress tensor also have to be solved. These models are therefore computationally far more complex than simple closure models (Kuipers and van Swaaij, 1997). 

Venneker et al. (2002) used as many as 20 bubble size classes in the bubble size range from 0.25 to some 20 mm. Just like GHOST , their in-house code named DA WN builds upon a liquid-only velocity field obtained with FLUENT, now with an anisotropic Reynolds Stress Model (RSM) for the turbulent momentum transport. To allow for the drastic increase in computational burden associated with using 20 population balance equations, the 3-D FLUENT flow field is averaged azimuthally into a 2-D flow field (Venneker, 1999, used a less elegant simplification )... 

Unlike the turbulence dissipation rate tensor, which is isotropic at high Reynolds number, the joint scalar dissipation rate tensor is usually highly anisotropic. Indeed, when r< = T, it is often the case for inert scalars that eap = eaa = , so that the joint scalar dissipation rate tensor is singular. 

In natural systems (lakes, oceans, atmosphere) turbulent diffusion is usually anisotropic (i.e., much larger in the horizontal than vertical direction). There are two main reasons for that observation (1) the extension of natural systems in the horizontal is usually much larger than in the vertical. Thus, the turbulent structures (often called eddies) that correspond to the mean free paths of random motions often look like pancakes that is, they are flat along the vertical axis and mainly extended along the horizontal axes. (2) Often the atmosphere or the water body in a lake or ocean is density stratified (i.e., the density increases with depth). This compresses the eddies even further in the vertical. Gravitational forces keep the water parcels from moving too far away from the depth where they are neutrally buoyant, that is, where they have the same density as their environment. Thus, the anisotropic shape of the eddies results in turbulent diffusivities which differ in size along different spatial directions. 

Why is turbulent diffusion in oceans and lakes usually anisotropic Explain the term anisotropy both in mathematical and normal language. 

The Kolmogorov relationships are not valid in immediate proximity of the wall, as the turbulence is strongly anisotropic in this region. For a first assessment of the order of size of the turbulence measurements, the point of maximum dissipation is chosen. 

The finite volume methods have been used to discretised the partial differential equations of the model using the Simple method for pressure-velocity coupling and the second order upwind scheme to interpolate the variables on the surface of the control volume. The segregated solution algorithm was selected. The Reynolds stress turbulence model was used in this model due to the anisotropic nature of the turbulence in cyclones. Standard fluent wall functions were applied and high order discretisation schemes were also used. 

Leonard [97] defined the complementary tensor, Ckk + Rkk), and suggested that this term can be added to the filtered pressure, p+ Ckk + Rkk)-In this way the complementary tensor requires no modeling. Analogous to the average turbulent kinetic energy quantity, one can also define a sub-grid scale kinetic energy variable, ksos = Cu + Ru). Hence, the anisotropic SGS... 

Zaichik, L., Oesterle, B. Aupchenkov, V. 2004 On the probability density function model for the transport of particles in anisotropic turbulent flow. Physics of Eluids 16 (6), 1956-1964. 

As indicated, the flux may be expressed either in units of molecules/m2 s or in units of kg/m2 s. Here, p and n are the density and number density of air, respectively, and K is called the eddy diffusion coefficient. This quantity must be treated as a tensor because atmospheric diffusion is highly anisotropic due to gravitational constraints on the vertical motion and large-scale variations in the turbulence field. Eddy diffusivity is a property of the flowing medium and not specific to the tracer. Contrary to molecular diffusion, the gradient is applied to the mixing ratio and not to number density, and the eddy diffusion coefficient is independent of the type of trace substance considered. In fact, aerosol particles and trace gases are expected to disperse with similar velocities. 

Nearly isotropic turbulence exists when there is no velocity gradient, as at the centerline of a pipe or beyond the outer edge of a boundary layer. Nearly isotropic turbulence is also found downstream of a grid placed in the flow. Turbulent flow near a boundary is anisotropic, but the anisotropy occurs mainly with the larger... 

REYNOLDS STRESSES. It has long been known that shear forces much larger than those occurring in laminar flow exist in turbulent flow wherever there is a velocity gradient across a shear plane. The mechanism of turbulent shear depends upon the deviating velocities in anisotropic turbulence. Turbulent shear stresses are called Reynolds stresses. They are measured by the correlation coefficients of the type defined in Eq. (3.15). 

In turbulent flow, as in laminar flow, the velocity gradient is zero at the centerline. It is known that the eddies in the turbulent core are large but of low intensity, and those in the transition zone are small but intense. Most of the kinetic-energy content of the eddies lies in the buffer zone and the outer portion of the turbulent core. At the centerline the turbulence is isotropic. In all other areas of the turbulent-flow regime, turbulence is anisotropic otherwise, there would be no shear. 

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