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In this work the effect of elasticity on turbulent drag reduction due to polymers is investigated using a hybrid Direct Numerical Simulation (D.N.S) and Langevin dynamics approach. Simulations are run at a friction Reynolds number of Reτ = 560 for 960.000 dumbbells with Deborah numbers of De = 0, De = 1, and De = 10. The conclusions are that it is possible to simulate a drag reduced flow using hybrid D.N.S. with Langevin dynamics, that polymers, like other occurrences of drag reduction, reduce drag through streak stabilization, and that the essential property of polymers and fibers in having a drag reducing effect is their ability to exert a torque on the solvent when they orientate in the boundary layer of the turbulent flow.

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The framework for the Hall magnetohydrodynamic (MHD) model for plasma physics is built up from kinetic theory and used to analytically solve problems of interest in the field. The Hall MHD model describes fast magnetic reconnection processes in space and laboratory plasmas. Specifically, the magnetic reconnection process at an X-type neutral point, where current sheets form and store enormous amounts of magnetic energy which is later released as magnetic storms when the sheets break up, is investigated. The phenomena of magnetic flux pile-up driving the merging of antiparallel magnetic fields at an ion stagnation-point flow in a thin current sheet, called the Parker problem, also receives rigorous mathematical analysis.

Much progress has been made in understanding of plasmas through the use of the MHD equations and newer models such as Hall MHD and electron MHD. As with most equations of fluid behavior, these equations are nonlinear, and no general solutions can be found. The use of invariant structures allows limited predictions of fluid behavior without requiring a full solution of the underlying equations. The use of gauge transformation can allow the creation of new invariants, while differential geometry offers useful tools for constructing additional invariants from those that are already known. Using these techniques, new geometric, integral and topological invariants are constructed for Hall and electron MHD models. Both compressible and incompressible models are considered, where applicable. An application of topological invariants to magnetic reconnection is provided. Finally, a particular geometric invariant, which can be interpreted as the fluid impulse density, is studied in greater detail, its nature and invariance in plasma models is demonstrated, and its behavior is predicted in particular geometries under different models.

The simulation of the atmospheric turbulence has wide applications in science and engineering. There are a variety of modelling techniques for synthesizing a wind speed time series available today. To decide which model to use one has to know the characteristics of the simulation technique. In this dissertation, alternative approaches for synthetically generating a wind speed time series are discussed. These approaches include: (1) the use of independent values from a specific probability distribution; (2) the use of an algorithm based on the statistical behavior of a one step Markov chain; (3) the use of an algorithm based on the behavior of a transition probability matrix that describes the next wind speed value statistically as a function of the current wind speed value and the previous wind speed value; (4) the use of Box-Jenkins model; (5) the use of the Shinozuka algorithm; (6) the use of an embedded Markov chain; and (7) the use of the fractal concept. The ability of each approach to capture the statistical properties of the desired wind speed time series is discussed. Wind speed collected at Windsor, Massachusetts and at Altamont, California are used as target wind speed values. Each model will be used to generate a synthetic wind speed for each site to compare with the real wind speed. The performance of each model will be decided on by the statistical similarity of the synthetic wind speed to the real wind speed. The criteria of the statistical similarity include the mean and the variance of the wind speed values, the probability distribution of the wind speed values, the power spectrum of the wind speed values and the autocorrelation function of the wind speed values. One of the applications of the wind speed simulation is to fill in a missing segment of a wind speed time series. In this context the missing segment of the wind speed at Cuttyhunk island is simulated and filled in for the study of a wind/diesel energy conversion system.

Plasma waves are key drivers of the highly variable electron dynamics in Earth’s outer radiation belts. In particular, whistler mode chorus waves, which are commonly observed with intense wave amplitudes, are known to be a key driver of rapid electron acceleration and precipitation observed by many recent satellite (e.g., Arase, ELFIN, THEMIS, and Van Allen Probes) and balloon missions (BARREL). However, quantitative understanding of how electron acceleration and precipitation is modified due to the nonlinear interactions with chorus waves is limited. This dissertation systematically evaluates the nonlinear effects of chorus waves in the full electron pitch angle-energy space using test particle simulations, quasilinear models, and satellite observations. More specifically, the dependences of these nonlinear effects on the chorus wave amplitude modulation (waveform structures), as well as wave amplitude and frequency bandwidth (spectrum structures), are quantified over a wide range of wave parameters. The results show that realistic chorus wave structures tend to limit the nonlinear effects on energetic electrons. The system can be described by a diffusion model similar to quasilinear theory, but nonlinear effects alter the diffusion coefficients from quasilinear ones. Using an intriguing event observed by the Van Allen Probes, I further demonstrate that nonlinear phase trapping by the upper-band chorus waves can efficiently accelerate electrons to form the distinct butterfly pitch angle distribution within 30 seconds. The effects of nonlinear interaction (Landau trapping) on electron precipitation are also evaluated during a bursty electron precipitation event observed by the ELFIN CubeSats, in association with very oblique chorus waves observed by THEMIS near the equatorial plane. The test particle simulation results provide the first direct evidence of rapid (~5 s) electron precipitation driven by high-order resonances due to chorus waves. Overall, this dissertation provides a full quantification of nonlinear effects and their dependences on various electron and chorus wave parameters. The findings in this dissertation are crucial to our fundamental understanding of wave-particle interactions, particularly on short timescales in the Earth’s radiation belts and in other space plasma environments, such as solar wind and other planets, as well as astrophysical and laboratory plasmas.

Analytical as well as fundamental measurements were performed with an inductively coupled plasma (ICP) using the novel technique of cavity ringdown spectroscopy. A newly designed ICP torch was presented. Limits of detection were measured for elemental mercury, both in an ICP as well as in a cold mercury chemical generator. The efficiency of the technique was compared with laser-induced fluorescence (LIF) in the ICP. Isotopically resolved spectra of uranium were collected with this technique and results were compared to previous studies using LIF. Gas temperature and electron density estimations were done by lineshape measurements on lead atoms in the ICP. Abel inversion technique was used to extract absolute atom densities and ringdown proved to be an excellent candidate for trace detection when coupled with an atomization source. Spectra of hydroxyl radical coming from dissociation of water molecules in air were recorded and OH density was estimated. The plasma was found to be in local thermal equilibrium by comparing simulated and measured OH emission spectra. Future developments of cavity ringdown with ICP using continuous-wave lasers are discussed.

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No description available.