An evaluation and parameterization of stably stratified turbulence: insights on the atmospheric boundary layer and implications for wind energy
Date
2014
Authors
Wilson, Jordan M., author
Venayagamoorthy, Subhas K., advisor
Birner, Thomas, committee member
Heyliger, Paul R., committee member
Moriarty, Patrick J., committee member
Journal Title
Journal ISSN
Volume Title
Abstract
This research focuses on the dynamics of turbulent mixing under stably stratified flow conditions. Velocity fluctuations and instabilities are suppressed by buoyancy forces limiting mixing as stability increases and turbulence decreases until the flow relaminarizes. Theories that ubiquitously assume turbulence collapse above a critical value of the gradient Richardson number (e.g. Ri > Ric) are common in meteorological and oceanographic communities. However, most theories were developed from results of small-scale laboratory and numerical experiments with energetic levels several orders of magnitude less than geophysical flows. Geophysical flows exhibit strong turbulence that enhances the transport of momentum and scalars. The mixing length for the turbulent momentum field, LM, serves as a key parameter in assessing large-scale, energy-containing motions. For a stably stratified turbulent shear flow, the shear production of turbulent kinetic energy, P, is here considered to be of greater relevance than the dissipation rate of turbulent kinetic energy, ε. Thus, the turbulent Reynolds number can be recast as Re ≡ k2/(ν P) where k is the turbulent kinetic energy, allowing for a new perspective on flow energetics. Using an ensemble data set of high quality direct numerical simulation (DNS) results, large-eddy simulation (LES) results, laboratory experiments, and observational field data of the stable atmospheric boundary layer (SABL), the dichotomy of data becomes apparent. High mixing rates persist to strong stability (e.g. Ri ≈ 10) in the SABL whereas numerical and laboratory results confirm turbulence collapse for Ri ~ O(1). While this behavior has been alluded to in literature, this direct comparison of data elucidates the disparity in universal theories of stably stratified turbulence. From this theoretical perspective, a Reynolds-averaged framework is employed to develop and evaluate parameterizations of turbulent mixing based on the competing forces of mean shear and buoyancy frequency, S and N, respectively. Length scale estimates for LM are given by LkS ≡ k1/2/S and LkN ≡ k1/2/N, where LkS provides an accurate estimate for eddy viscosity, νt, under neutral to strongly stable conditions for SABL data. The relative influence of shear and buoyancy are given by the ratio of the respective time scales, S-1 and N-1, with the pertinent time scale of the large-scale motions, TP ≡ k/P, through the parameters STP and NTP. LkS's range of applicability is further assessed in a STP-NTP parameter space. In developing these parameterizations, the stress-intensity ratio, c2, is evaluated using high-Re stably stratified data and is shown to exhibit a near constant value (c2 ≈ 0.25) for stably stratified geophysical turbulence. These findings provide a clear trajectory for numerical modeling of stably stratified geophysical shear turbulence without reliance on stability or damping functions, tuning parameters, or artificial parameterizations. An initial modeling study of moderate-Re channel and Ekman layer flows using the proposed parameterizations confirms this supposition. Finally, it is in this new light that large-scale implications of wind energy can now be considered. As a first step in this process, computational fluid dynamics (CFD) studies of wind turbine interactions are carried out under neutrally stratified conditions. Simulations clearly show that actuator line models provide efficacy in wake generation, interaction, and restoration and highlight model requirements for stably stratified conditions. Results suggest that standard horizontal spacings of 5-10 rotor diameters yield significant reductions in power output and increases turbulence intensity and fatigue loading.
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Subject
computational fluid dynamics
turbulent mixing
turbulence parameterization
stratified turbulence