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ABL Parameterization


Sensor Networks


Large Eddy Simulations


Multiscale Atmospheric Simulations


Urban Micrometeorology and Energy Studies


Turbulence Structure


Large Eddy Simulation

BASICS

Apart from subsurface flows, most environmental and geophysical flows are turbulent. Turbulence can be conceptualized as consisting of the superposition of a mean motion and a range of chaotic motions at various scales (the turbulent eddies). This decomposition is due to Osborne Reynolds and has proven very useful in the study and modeling of turbulent flows. Nevertheless, the mean flow and the eddies are strongly coupled and their dynamics cannot be separated. Unfortunately, it turns out that modeling the coupled dynamics of the mean flow and all the turbulent scales is at present (and in the foreseeable future) simply impossible for most relevant environmental  and engineering flows, due to the huge computational resources this problem would require. The "classic" practical approach to modeling engineering and environmental turbulent flows is the Reynolds Averaged Navier-Stokes (RANS) technique which models only the dynamics of the mean flow and parameterizes the interaction (coupling) of this mean flow with all the scales of turbulence. A better alternative which has been gaining in popularity in the past 20 years is the large eddy-simulation (LES) technique. In LES, we model the mean flow and all the large eddies that we can afford (computationally) to capture, and we parameterize the remaining small eddies. Most of our numerical modeling work uses the large-eddy simulation technique which is emerging as a tool of choice for high Reynolds number turbulent flows in both geophysical and engineering systems.

In the atmosphere, turbulence is mostly present in the region near the earth surface, the so called atmospheric boundary layer (ABL). In that layer, turbulent motions span several orders of magnitude and turbulence is generated by mechanical shear and buoyancy. The scale of the smallest turbulent motions, known as the Kolmogorov scale, is on the order of 1 millimeter, while the largest scales are of the size of the turbulent boundary layer depth (0.5-2 km). Resolving all the spatial and temporal scales would hence require something on the order of 1024 floating point operation, far beyond what is possible today. This is where LES turns out to be quite useful tool

The underlying assumption justifying the application of LES to ABL modeling is that the largest eddies contain most of the energy and are responsible for most of the transport of momentum and scalars (heat, moisture, pollutant,...) . Nonetheless, the effect of the sub-grid scale structures cannot be discarded and appears as an additional term in the filtered Navier-Stokes equations:

This additional term , ∂τij/xj , is the divergence of subgrid-scale (SGS) stress tensor. We also make use of the mass conservation equations (the continuity equation) for incompressible fluids

and we couple the equations above to the resolved heat transport equation

in which another additional term , πj/xj , the divergence of SGS heat flux vector, also appears. These two new terms, the SGS stress tensor and the SGS heat flux vector are new unknowns introduced into the system of equations qhich now becomes unclosed (more unknowns that equations). Hence the turbulence closure problem, which results from strong nonlinear interactions between different scales, emerges. The molecular viscous term is usually neglected but the Coriolis forcing, and/or other forcing terms, are represented by the term Fi.

To close the system of equations, a model for the subgrid-scale stress is required. The results of large-eddy simulations are quite sensitive to this model especially in the vicinity of solid boundaries where the subgrid-scale fluxes are important and their physics are harder to model.

We have worked extensively on the development and testing of SGS models that are applicable, without any tuning, to the widest possible range of flows. The current model we use, the Lagrangian scale-dependent dynamic (LASD) model, has no ad-hoc or tunable coefficients at all. The figure below (left) shows the ability of different SGS models to reproduce the logarithmic velocity profile, expected in the atmospheric surface layer and depicted by the black line in the figure.  The LASD model clearly gives the best results.

  

 

 

APPLICATIONS

We are currently using our Large Eddy Simulation code to model flow over the Princeton Campus, and to study the effects of mesoscale variability and surface heterogeneity on stable ABLs. We are also starting a project to use the Weather Research and Forecasting (WRF) Model, to downscale mesoscale predictions over Central New Jersey and the New York Metropolitan Area to local scales, at sites where we have field measurement equipment. An example from an LES simulation of the flow over the campus of the Ecole Polytechnique Fédérale de Lausanne is shown below.

 

 

last update on: August 05, 2011 14:02,  contact webmaster

Contact Information

Elie Bou-Zeid
Department of Civil & Environmental Engineering
Princeton University, C326 EQuad
Princeton, NJ 08544, USA

phone  :  +1-609-258-5429
fax        :  +1-609-258-2799
email   :  
ebouzeid@princeton.edu
web      :  http://efm.princeton.edu/