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Register a new userLearning the structure of wind: A data-driven nonlocal turbulence model for the atmospheric boundary layer
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We develop a novel data-driven approach to modeling the atmospheric boundary layer. This approach leads to a nonlocal, anisotropic synthetic turbulence model which we refer to as the deep rapid distortion (DRD) model. Our approach relies on an operator regression problem which characterizes the best fitting candidate in a general family of nonlocal covariance kernels parameterized in part by a neural network. This family of covariance kernels is expressed in Fourier space and is obtained from approximate solutions to the Navier--Stokes equations at very high Reynolds numbers. Each member of the family incorporates important physical properties such as mass conservation and a realistic energy cascade. The DRD model can be calibrated with noisy data from field experiments. After calibration, the model can be used to generate synthetic turbulent velocity fields. To this end, we provide a new numerical method based on domain decomposition which delivers scalable, memory-efficient turbulence generation with the DRD model as well as others. We demonstrate the robustness of our approach with both filtered and noisy data coming from the 1968 Air Force Cambridge Research Laboratory Kansas experiments. Using this data, we witness exceptional accuracy with the DRD model, especially when compared to the International Electrotechnical Commission standard.
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The fluid dynamics video considers an array of two NREL 5-MW turbines separated by seven rotor diameters in a neutral atmospheric boundary layer (ABL). The neutral atmospheric boundary-layer flow data were obtained from a precursor ABL simulation using a Large-Eddy Simulation (LES) framework within OpenFOAM. The mean wind speed at hub height is 8m/s, and the surface roughness is 0.2m. The actuator line method (ALM) is used to model the wind turbine blades by means of body forces added to the momentum equation. The fluid dynamics video shows the root and tip vortices emanating from the blades from various viewpoints. The vortices become unstable and break down into large-scale turbulent structures. As the wakes of the wind turbines advect further downstream, smaller-scale turbulence is generated. It is apparent that vortices generated by the blades of the downstream wind turbine break down faster due to increased turbulence levels generated by the wake of the upstream wind turbine.
Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori-Zwanzig (MZ) formalism provides a mathematically formal procedure for constructing reduced-order representations of high-dimensional dynamical systems, where the effect due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. Turbulence models based on MZ formalism have been scarce due to the limited knowledge of the MZ operators, which originates from the difficulty in deriving MZ kernels for complex nonlinear dynamical systems. In this work, we apply a recently developed data-driven learning algorithm, which is based on Koopmans description of dynamical systems and Moris linear projection operator, on a set of fully-resolved isotropic turbulence datasets to extract the Mori-Zwanzig operators. With data augmentation using known turbulence symmetries, the extracted Markov term, memory kernel, and orthogonal dynamics are statistically converged and the Generalized Fluctuation-Dissipation Relation can be verified. The properties of the memory kernel and orthogonal dynamics, and their dependence on the choices of observables are investigated to address the modeling assumptions that are commonly used in MZ-based models. A series of numerical experiments are then constructed using the extracted kernels to evaluate the memory effects on predictions. Results show that the prediction errors are strongly affected by the choice of observables and can be further reduced by including the past history of the observables in the memory kernel.
In this work we compare the spectral properties of the daily medium temperature fluctuations with the experimental results of the Chicago Group, in which the local temperature fluctuations were measured in a helium cell. The results suggest that the dynamics of the daily temperature fluctuations is determined by the oft turbulent state of the atmospheric boundary layer, which state is significantly different from low dimensional chaos.
It is commonly accepted that the breakup criteria of drops or bubbles in turbulence is governed by surface tension and inertia. However, also {it{buoyancy}} can play an important role at breakup. In order to better understand this role, here we numerically study Rayleigh-Benard convection for two immiscible fluid layers, in order to identify the effects of buoyancy on interface breakup. We explore the parameter space spanned by the Weber number $5leq We leq 5000$ (the ratio of inertia to surface tension) and the density ratio between the two fluids $0.001 leq Lambda leq 1$, at fixed Rayleigh number $Ra=10^8$ and Prandtl number $Pr=1$. At low $We$, the interface undulates due to plumes. When $We$ is larger than a critical value, the interface eventually breaks up. Depending on $Lambda$, two breakup types are observed: The first type occurs at small $Lambda ll 1$ (e.g. air-water systems) when local filament thicknesses exceed the Hinze length scale. The second, strikingly different, type occurs at large $Lambda$ with roughly $0.5 < Lambda le 1$ (e.g. oil-water systems): The layers undergo a periodic overturning caused by buoyancy overwhelming surface tension. For both types the breakup criteria can be derived from force balance arguments and show good agreement with the numerical results.
The turbulent boundary layer over a flat plate is computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations as a test bed for a synthetic turbulence generator (STG) inflow boundary condition. The inlet momentum thickness Reynolds number is approximately 1,000. The study provides validation of the ability of the STG to develop accurate turbulence in 5 to 7 boundary layer thicknesses downstream of the boundary condition. Also tested was the effect of changes in the stabilization scheme on the development of the boundary layer. Moreover, the grid resolution required for both the development region and the downstream flow is investigated when using a stabilized finite element method.
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