Understanding the interaction of wind farms and turbulent atmospheric boundary layer in a large eddy simulation framework: from periodic to LIDAR based data driven cases

Description
This thesis focuses on an improved understanding of the dynamics at different length scales of wind farms in an atmospheric boundary layer (ABL) using a series of visualization studies and Fourier, wavelet based spectral analysis using high fidelity large eddy…

This thesis focuses on an improved understanding of the dynamics at different length scales of wind farms in an atmospheric boundary layer (ABL) using a series of visualization studies and Fourier, wavelet based spectral analysis using high fidelity large eddy simulation (LES). For this purpose, a robust LES based neutral ABL model at very high Reynolds number has been developed using a high order spectral element method which has been validated against the previous literature. This ABL methodology has been used as a building block to drive large wind turbine arrays or wind farms residing inside the boundary layer as documented in the subsequent work. Studies conducted in the thesis involving massive periodic wind farms with neutral ABL have indicated towards the presence of large scale coherent structures that contribute to the power generated by the wind turbines via downdraft mechanisms which are also responsible for the modulation of near wall dynamics. This key idea about the modulation of large scales have seen a lot of promise in the application of flow past vertically staggered wind farms with turbines at different scales. Eventually, studies involving wind farms have been progressively evolved in a framework of inflow-outflow where the turbulent inflow is being fed from the precursor ABL using a spectral interpolation technique. This methodology has been used to enhance the understanding related to the multiscale physics of wind farm ABL interaction, where phenomenon like the growth of the inner layer, and wake impingement effects in the subsequent rows of wind turbines are important owing to the streamwise heterogeneity of the flow. Finally, the presence of realistic geophysical effects in the turbulent inflow have been investigated that influence the flow past the wind turbine arrays. Some of the geophysical effects that have been considered include the presence of the Coriolis forces as well as the temporal variation of mean wind magnitude and direction that might occur due to mesoscale dynamics. This study has been compared against field experimental results which provides an important step towards understanding the capability of the mean data driven LES methodology in predicting realistic flow structures.
Date Created
2018
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Effective-diffusion for general nonautonomous systems

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Description
The tools developed for the use of investigating dynamical systems have provided critical understanding to a wide range of physical phenomena. Here these tools are used to gain further insight into scalar transport, and how it is affected by mixing.…

The tools developed for the use of investigating dynamical systems have provided critical understanding to a wide range of physical phenomena. Here these tools are used to gain further insight into scalar transport, and how it is affected by mixing. The aim of this research is to investigate the efficiency of several different partitioning methods which demarcate flow fields into dynamically distinct regions, and the correlation of finite-time statistics from the advection-diffusion equation to these regions.

For autonomous systems, invariant manifold theory can be used to separate the system into dynamically distinct regions. Despite there being no equivalent method for nonautonomous systems, a similar analysis can be done. Systems with general time dependencies must resort to using finite-time transport barriers for partitioning; these barriers are the edges of Lagrangian coherent structures (LCS), the analog to the stable and unstable manifolds of invariant manifold theory. Using the coherent structures of a flow to analyze the statistics of trapping, flight, and residence times, the signature of anomalous diffusion are obtained.

This research also investigates the use of linear models for approximating the elements of the covariance matrix of nonlinear flows, and then applying the covariance matrix approximation over coherent regions. The first and second-order moments can be used to fully describe an ensemble evolution in linear systems, however there is no direct method for nonlinear systems. The problem is only compounded by the fact that the moments for nonlinear flows typically don't have analytic representations, therefore direct numerical simulations would be needed to obtain the moments throughout the domain. To circumvent these many computations, the nonlinear system is approximated as many linear systems for which analytic expressions for the moments exist. The parameters introduced in the linear models are obtained locally from the nonlinear deformation tensor.
Date Created
2018
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Observation and Simulation of Wave Breaking in the Southern Hemispheric Stratosphere During VORCORE

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Description

An interesting occurrence of a Rossby wave breaking event observed during the VORCORE experiment is presented and explained. Twenty-seven balloons were launched inside the Antarctic polar vortex. Almost all of these balloons evolved in the stratosphere around 500K within the…

An interesting occurrence of a Rossby wave breaking event observed during the VORCORE experiment is presented and explained. Twenty-seven balloons were launched inside the Antarctic polar vortex. Almost all of these balloons evolved in the stratosphere around 500K within the vortex, except the one launched on 28 October 2005. In this case, the balloon was caught within a tongue of high potential vorticity (PV), and was ejected from the polar vortex. The evolution of this event is studied for the period between 19 and 25 November 2005. It is found that at the beginning of this period, the polar vortex experienced distortions due to the presence of Rossby waves. Then, these waves break and a tongue of high PV develops. On 25 November, the tongue became separated from the vortex and the balloon was ejected into the surf zone. Lagrangian simulations demonstrate that the air masses surrounding the balloon after its ejection were originating from the vortex edge. The wave breaking and the development of the tongue are confined within a region where a planetary Quasi-Stationary Wave 1 (QSW1) induces wind speeds with weaker values. The QSW1 causes asymmetry in the wind speed and the horizontal PV gradient along the edge of the polar vortex, resulting in a localized jet. Rossby waves with smaller scales propagating on top of this jet amplify as they enter the jet exit region and then break. The role of the QSW1 on the formation of the weak flow conditions that caused the non-linear wave breaking observed near the vortex edge is confirmed by three-dimensional numerical simulations using forcing with and without the contribution of the QSW1.

Date Created
2013-04-16
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A New Numerical Method Based on Leapfrog for Atmospheric and Ocean Modeling

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Description
A semi-implicit, fourth-order time-filtered leapfrog numerical scheme is investigated for accuracy and stability, and applied to several test cases, including one-dimensional advection and diffusion, the anelastic equations to simulate the Kelvin-Helmholtz instability, and the global shallow water spectral model to…

A semi-implicit, fourth-order time-filtered leapfrog numerical scheme is investigated for accuracy and stability, and applied to several test cases, including one-dimensional advection and diffusion, the anelastic equations to simulate the Kelvin-Helmholtz instability, and the global shallow water spectral model to simulate the nonlinear evolution of twin tropical cyclones. The leapfrog scheme leads to computational modes in the solutions to highly nonlinear systems, and time-filters are often used to damp these modes. The proposed filter damps the computational modes without appreciably degrading the physical mode. Its performance in these metrics is superior to the second-order time-filtered leapfrog scheme developed by Robert and Asselin.
Date Created
2016-05
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Application of Individual Based Models in Modeding Brain Tumor

Description
Cancer modeling has brought a lot of attention in recent years. It had been proven to be a difficult task to model the behavior of cancer cells, since little about the "rules" a cell follows has been known. Existing models…

Cancer modeling has brought a lot of attention in recent years. It had been proven to be a difficult task to model the behavior of cancer cells, since little about the "rules" a cell follows has been known. Existing models for cancer cells can be generalized into two categories: macroscopic models which studies the tumor structure as a whole, and microscopic models which focus on the behavior of individual cells. Both modeling strategies strive the same goal of creating a model that can be validated with experimental data, and is reliable for predicting tumor growth. In order to achieve this goal, models must be developed based on certain rules that tumor structures follow. This paper will introduce how such rules can be implemented in a mathematical model, with the example of individual based modeling.
Date Created
2016-12
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A Numerical and Analytical Study of Wave Reflection and Transmission across the Tropopause

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Description
A numerical study of wave-induced momentum transport across the tropopause in the presence of a stably stratified thin inversion layer is presented and discussed. This layer consists of a sharp increase in static stability within the tropopause. The wave propagation…

A numerical study of wave-induced momentum transport across the tropopause in the presence of a stably stratified thin inversion layer is presented and discussed. This layer consists of a sharp increase in static stability within the tropopause. The wave propagation is modeled by numerically solving the Taylor-Goldstein equation, which governs the dynamics of internal waves in stably stratified shear flows. The waves are forced by a flow over a bell shaped mountain placed at the lower boundary of the domain. A perfectly radiating condition based on the group velocity of mountain waves is imposed at the top to avoid artificial wave reflection. A validation for the numerical method through comparisons with the corresponding analytical solutions will be provided. Then, the method is applied to more realistic profiles of the stability to study the impact of these profiles on wave propagation through the tropopause.
Date Created
2017-05
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Lagrangian Skeletons in Hurricane Katrina

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Description
This thesis shows analyses of mixing and transport patterns associated with Hurricane Katrina as it hit the United States in August of 2005. Specifically, by applying atmospheric velocity information from the Weather Research and Forecasting System, finite-time Lyapunov exponents have…

This thesis shows analyses of mixing and transport patterns associated with Hurricane Katrina as it hit the United States in August of 2005. Specifically, by applying atmospheric velocity information from the Weather Research and Forecasting System, finite-time Lyapunov exponents have been computed and the Lagrangian Coherent Structures have been identified. The chaotic dynamics of material transport induced by the hurricane are results from these structures within the flow. Boundaries of the coherent structures are highlighted by the FTLE field. Individual particle transport within the hurricane is affected by the location of these boundaries. In addition to idealized fluid particles, we also studied inertial particles which have finite size and inertia. Basing on established Maxey-Riley equations of the dynamics of particles of finite size, we obtain a reduced equation governing the position process. Using methods derived from computer graphics, we identify maximizers of the FTLE field. Following and applying these ideas, we analyze the dynamics of inertial particle transport within Hurricane Katrina, through comparison of trajectories of dierent sized particles and by pinpointing the location of the Lagrangian Coherent Structures.
Date Created
2012-12
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Lagrangian Transport of Inertial Particles in Hurricane Katrina

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Description
Using weather data from the Weather Research and Forecasting model (WRF), we analyze the transport of inertial particles in Hurricane Katrina in order to identify coherent patterns of motion. For our analysis, we choose a Lagrangian approach instead of an…

Using weather data from the Weather Research and Forecasting model (WRF), we analyze the transport of inertial particles in Hurricane Katrina in order to identify coherent patterns of motion. For our analysis, we choose a Lagrangian approach instead of an Eulerian approach because the Lagrangian approach is objective and frame-independent, and gives results which are better defined. In particular, we locate Lagrangian Coherent Structures (LCS), which are smooth sets of fluid particles which are locally most hyperbolic (either attracting or repelling). We implement a variational method for locating LCS and compare the results to previous computation of LCS using Finite-Time Lyapunov Exponents (FTLE) to identify regions of high stretching in the fluid flow.
Date Created
2013-05
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Visualizing Lagrangian Coherent Structures from Realistic Flow Data

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Description
The goal of this project was to examine the separatricies that define regions of distinct flow behaviors in realistic time-dependent dynamical systems. In particular, we adapted previously available methods for computing the Finite-Time Lyapunov Exponent (FTLE) to a set of…

The goal of this project was to examine the separatricies that define regions of distinct flow behaviors in realistic time-dependent dynamical systems. In particular, we adapted previously available methods for computing the Finite-Time Lyapunov Exponent (FTLE) to a set of measured wind velocity data in order to visualize the separatricies as ridges of the FTLE field in a section of the atmosphere. This visualization required a number of alterations to the original methods, including interpolation techniques and two different adaptive refinement schemes for producing more detailed results. Overall, there were two computations performed with the wind velocity data: once along a single spherical surface, on which the separatricies could be visualized as material lines, and then along a three-dimensional section of the atmosphere, for which the separatricies were material surfaces. The resulting figures provide an image of the Antarctic polar vortex from the wind velocity data, which is consistent with other data gathered on the same date.
Date Created
2014-05
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Regional-Scale Transport of Air Pollutants: Impacts of Southern California Emissions on Phoenix Ground-Level Ozone Concentrations

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Description

In this study, WRF-Chem is utilized at high resolution (1.333 km grid spacing for the innermost domain) to investigate impacts of southern California anthropogenic emissions (SoCal) on Phoenix ground-level ozone concentrations ([O3]) for a pair of recent exceedance episodes. First,…

In this study, WRF-Chem is utilized at high resolution (1.333 km grid spacing for the innermost domain) to investigate impacts of southern California anthropogenic emissions (SoCal) on Phoenix ground-level ozone concentrations ([O3]) for a pair of recent exceedance episodes. First, WRF-Chem control simulations, based on the US Environmental Protection Agency (EPA) 2005 National Emissions Inventories (NEI05), are conducted to evaluate model performance. Compared with surface observations of hourly ozone, CO, NOX, and wind fields, the control simulations reproduce observed variability well. Simulated [O3] are comparable with the previous studies in this region. Next, the relative contribution of SoCal and Arizona local anthropogenic emissions (AZ) to ozone exceedances within the Phoenix metropolitan area is investigated via a trio of sensitivity simulations: (1) SoCal emissions are excluded, with all other emissions as in Control; (2) AZ emissions are excluded with all other emissions as in Control; and (3) SoCal and AZ emissions are excluded (i.e., all anthropogenic emissions are eliminated) to account only for Biogenic emissions and lateral boundary inflow (BILB). Based on the USEPA NEI05, results for the selected events indicate the impacts of AZ emissions are dominant on daily maximum 8 h average (DMA8) [O3] in Phoenix. SoCal contributions to DMA8 [O3] for the Phoenix metropolitan area range from a few ppbv to over 30 ppbv (10–30 % relative to Control experiments). [O3] from SoCal and AZ emissions exhibit the expected diurnal characteristics that are determined by physical and photochemical processes, while BILB contributions to DMA8 [O3] in Phoenix also play a key role.

Date Created
2015-08-21
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