MULTIRESOLUTION FEATURE ANALYSIS AND OTHER TECHNIQUES FOR UNDERSTANDING
AND MODELING TURBULENCE IN STABLE ATMOSPHERES

R. L. Street and F. L. Ludwig
Environmental Fluid Mechanics Laboratory,
Department of Civil and Environmental Engineering,
Stanford University

ABSTRACT

We will acquire data sets from earlier field campaigns. They will serve as test cases for modifying and refining our analysis techniques to prepare for the VTMX data. We will synthesize data from the many different platforms used during earlier field programs into three dimensional descriptions of ABL motions, using methods that have already been developed for combining surface and upper level wind observations into consistent three dimensional wind fields [1] and vector interpolation techniques that we have been evaluating. Once the data have been integrated into a convenient gridded form, we will apply multiresolution feature analysis (MFA) techniques to the observations. This analytical technique [2] identifies preferred local patterns of motion at several scales. It will be modified to identify the relationships between the active areas at the different scales, thereby helping to bridge the gap in scales between the strong local gradients and small sized features that characterize turbulent bursts in the stable ABL and the much coarser scales of large eddy simulations (LES) and mesoscale models.

The refined data synthesis and analysis techniques will then be used with the data from the VTMX. We expect that these new data will span a wide range of scales. Of particular interest will be observations from the newer instruments that provide the detailed observations required to achieve the full potential of MFA. Such instruments include the turbulent eddy profiler and radar systems to be operated by the University of Massachusetts, and Pennsylvania State University, and the volume imaging, scanning, high-resolution Raman water vapor-temperature lidar and aerosol elastic backscatter lidar that will be fielded by Los Alamos National Laboratory. We plan to synthesize data from these instruments with the observations at other scales that are planned for the VTMX.

We will look for the specific nature of the turbulent events in stable atmospheres, and how the intensity and location of active areas at different scales are related while we interpret our MFA results. If we are able to identify the relationship between the relatively small scale bursts of turbulence and the patterns of motion that can be found at larger scales, we will have the information necessary to introduce adaptive gridding strategies and advanced subgrid modeling into atmospheric simulation codes in ways that are consistent with the field observations, thereby confining the use of fine grids to those locations where needed most. The analysis should also show how energy is transferred between scales, and what processes successful subgrid scale models must be able to represent.

Models for the unresolved scales in large eddy simulations (LES) have been evolving rapidly. It appears pertinent now to evaluate models in three main categories. First, we will consider the two-component (mixed dynamic) model of Zang, et al. [3]. Second, we will examine so-called deconvolution models [4]. In particular, we will consider a non-eddy viscosity model [5], proposed by Shah and Ferziger that requires no adjustable constants, adds little to the computational cost, provides a simple means for generating the stress tensor for the unresolved motions, and produces results for shear flows in a channel that are better than those from the mixed models and the Smagorinsky model. We have developed a simplified version of the Shah-Ferziger non-eddy viscosity model. Finally, we will evaluate the Fourier-series expansion models [see Ref. 6]. We will employ these three subfilter-scale model variants and assess their efficacy in existing LES codes and in the context of the VTMX databases. We will not build new codes, but rather we will incorporate these ideas in existing atmospheric codes and assist collaborating researchers that choose to incorporate the ideas into their own models.

REFERENCES
  1. Ludwig et al., 1991, J. Appl. Meteorol., 30, 1490-1499.
  2. Ludwig and Street, 1995, J. Atmos. Sci., 52, 139-157.
  3. Zang, Street and Koseff, 1993, Phys. Fluids A, 5, 3186-3196.
  4. Stolz, S., and N. A. Adams, 1999, Physics of Fluids, 11(7), 1699-1701.
  5. Shah, K., and J. H. Ferziger, 1995, Ann. Res. Briefs, Ctr. Turb. Res. NASA-Stanford, 73-90.
  6. Domardzki, J. A., and E. Saiki, 1997, Phys. Fluids, 9(7), 2148-2164.

CONTACTS:

Robert L. Street, tel: (650) 723-4969, e-mail: street@ce.stanford.edu and Francis L. Ludwig, tel: (650) 725-5948, e-mail: fludwig@ce.stanford.edu

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