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Thesis (M.Sc.Eng.) PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / The study of wave-wave interactions in the ionosphere is important for designing communication systems, satellite systems, and spacecraft. Ionospheric research also informs laser and magnetic fusion plasma physics. This thesis focuses on two nonlinear wave-wave interactions in the ionosphere. The first interaction is a nonlinear mode conversion. Very Low Frequency (VLF) waves transmitted from the ground travel through the ionosphere as injected whistler waves. The whistler waves interact with naturally-occurring density fluctuations in the ionosphere and are mode converted into lower hybrid waves. The lower hybrid waves accelerate electrons along the geomagnetic field and the resulting beam mode Langmuir waves are detectable by radar. This type of mode conversion may combine additively with a four wave interaction with the same VLF wave as its source. Data collected at the Arecibo Observatory in Puerto Rico during the occurrence of spread F and sporadic E was analyzed. Plasma line enhancements may indicate the nonlinear mode conversion both separately from and in conjunction with the four wave interaction. The second nonlinear wave-wave interaction is the parametric decay instability (PDI) excited by High Frequency (HF) heater waves at the High Frequency Active Auroral Research Program facility in Gakona, Alaska. Resonant PDI cascades downwards, resulting in up-shifted ion line enhancements as detected by radar. This process has been detected in the presence of down-shifted ion line enhancements which may be caused by beating between PDI-produced Langmuir waves, or by naturally occurring ionospheric currents. / 2031-01-01

The exact mechanisms responsible for heating the solar atmosphere in regions such as the chromosphere (partially ionized) and the corona (fully ionized) remain quantitatively unknown. This thesis demonstrates that the ions can be heated by Alfven waves with low frequencies in fully and partially ionized low beta plasmas, which is contrary to the customary expectation. For the partially ionized case, we find the heating process to be less efficient than the scenario with no ion-neutral collisions, and that the heating efficiency depends on the ratio of ion-neutral collision frequency to the ion gyrofrequency. For Alfven waves propagating obliquely to the background magnetic field in fully ionized plasmas, we find the heating process to be more efficient than the situation with Alfven waves propagating along the background magnetic field. Furthermore, the simulation results show the parallel kinetic temperature can become even larger than the perpendicular component for the case of obliquely propagating Alfven waves.

Internal waves are prominent fluid phenomena in both the atmosphere and ocean. Because internal waves have the ability to transfer a large amount of energy, they contribute to the global distribution of energy. This causes internal waves to influence global climate patterns and critical ocean mixing. Therefore, studying internal waves provides additional insight in how to model geophysical phenomena that directly impact our lives. There is a myriad of fluid phenomena with which internal waves can interact, including other internal waves. Equipment and processes are developed to perform laboratory experiments analyzing the interaction of two colliding nonresonant internal waves. Nonresonant interactions have not been a major focus in previous research. The goal of this study is to visualize the flow field, compare qualitative results to Tabaei et al., and determine the energy partition to the second-harmonic for eight unique interaction configurations. When two non-resonant internal waves collide, harmonics are formed at the sum and difference of multiples of the colliding waves' frequencies. In order to create the wave-wave interaction, two identical wave generators were designed and manufactured. The interaction flow field is visualized using synthetic schlieren and the energy entering and leaving the interaction region is analyzed. It is found that the energy partitioned to the harmonics is much more dependent on the general direction the colliding waves approach each other than on the angle. Depending on the configurations, between 0.5 and 7 percent of the energy within the colliding waves is partitioned to the second-harmonics. Interactions in which the colliding waves have opposite signed vertical wavenumber partition much more energy to the harmonics. Most of the energy entering the interaction is dissipated by viscous forces or leaves the interaction within the colliding waves. For all eight configurations studied, 5 to 8 percent of the energy entering the interaction has an unknown fate.

The study of waves and instabilities in quantum plasmas is of fundamental importance for understanding collective interactions in superdense astrophysical objects, in high intense laser-plasma/solid-matter interactions, in microelectronic devices and metallic nanostructures. In dense quantum plasmas, there are new pressure laws associated with the Fermi-Dirac distribution functions and new quantum forces associated with the quantum Bohm potential and the Bohr magnetization involving electron ½ spin. These forces significantly alter the collective behavior of dense quantum plasmas. This thesis contains six papers, considering several novel collective modes and instabilities at quantum scales. In Paper I, we have used the quantum hydrodynamical (QHD) model for studying the one-dimensional dust-acoustic (DA) waves incorporating the Fermi pressure law and the quantum Bohm potential. The latter modifies the DA wave dispersion relation in a collisional plasma. In Paper II, we have calculated the electrostatic potential of a test charge in an unmagnetized electron-ion quantum plasma. It is found that the Debye-Hückel and oscillatory wake potentials strongly depend upon the Fermi energy at quantum scales. The results can be of interest for explaining the charged particle attraction and repulsion in degenerate quantum plasmas, such as those in semiconductor and microelectronic devices. Paper III presents the parametric study of nonlinear electrostatic waves in two-dimensional collisionless quantum dusty plasmas. A reductive perturbation method has been employed to the QHD equations together with the Poisson equation, obtaining the cylindrical Kadomtsev-Petviashvili (CKP) equations and their stationary localized solutions. We have numerically examined the quantum mechanical and geometrical effects on the profiles of nonplanar quantum dust-ion-acoustic (DIA) and DA solitary waves. The role of static as well as mobile (negatively or positively charged) dust particles on the low-frequency electrostatic waves has also been highlighted for metallic nanostructures. Paper IV introduces the nonlinear properties of the ion-sound waves in a dense electron-ion Fermi magnetoplasma. The computational analysis of the nonlinear system reveals that the Sagdeev-like potential and the ion-sound density excitations are significantly affected by the wave direction cosine and the Mach number at quantum scales. Paper V considers the nonlinear interactions of electrostatic upper-hybrid (UH), ion-cyclotron (IC), lower-hybrid (LH), and Alfvén waves in a quantum magnetoplasma. The nonlinear dispersion relations have been analyzed analytically to obtain the growth rates for both the decay and modulational instabilities involving the dispersive IC, LH, and Alfvén waves. In Paper VI, we have identified a new drift-like dissipative instability in a collisional quantum plasma. The modified unstable drift-like mode can cause cross-field anomalous ion-diffusion at quantum scales.

Les échanges de chaleur et de quantité de mouvement à l'interface-océan atmosphère jouent un rôle majeur dans la formation et la dynamique des masses d'air et d'eau. Malgré des décennies de recherche, nous avons encore besoin d'améliorer nos connaissances sur ces échanges, et plus spécifiquement nos connaissances sur les flux turbulents, qui sont des variables clés dans les modèles météorologiques et de climat. Dans ces modèles, les processus turbulents sont des processus sous-maille, non-résolus explicitement, ainsi les flux turbulents doivent être modélisés, au travers de paramétrisations, qui sont pour la plupart réalisées à partir de la théorie des similitudes de Monin-Obukhov [1954]. Cependant, d'une part, l'utilisation d'un modèle implique que les coefficients doivent être ajustés. D'autre part, le modèle lui-même peut demander des améliorations. Malheureusement, l'obtention d'estimations de flux avec une bonne précision est un gros défi, à cause des effets intrusifs de la plate-forme sur la mesure, de la précision limité des instruments et des capacités d'échantillonnages propres de chaque instrument.Notre étude porte sur l'estimation des flux turbulents en mer à partir de mesures réalisées avec la nouvelle plate-forme OCARINA (trimaran autonome) lors des campagnes STRASSE 2012 et AMOP 2014. Nous analysons les caractéristiques de la turbulence dans la couche limite de surface, nous estimons les flux turbulents par différentes méthodes, et nous comparons les valeurs des flux en fonction des conditions environnementales, en prenant en compte l'état de mer. / Exchanges of heat and momentum at the air-sea interface play a major role in the formation and the dynamics of water and air masses. In spite of decades of research, we still need to improve our knowledge of these exchanges, and more specifically our knowledge of turbulent fluxes, which are key variables in meteorological and climate models. In these models, sub-grid turbulent processes, thus turbulent fluxes also have to be modeled, which is mostly done with the Monin-Obukhov (1954, MOS hereafter) similarity theory. However, on the one hand, the use of a model implies that coefficients have to be adjusted. On the other hand, the model itself may require improvements. Unfortunately, obtaining flux estimates that have a good accuracy is a challenging effort, because of the intrusive effect of the platform, the limited accuracy the instruments, and because the instruments have their own sampling volume.Our study focuses on the estimation of turbulent fluxes at sea from measurements made with the new OCARINA platform (autonomous trimaran) during two campaigns : STRASSE 2012 and AMOP 2014. We analyze the characteristics of turbulence in the surface boundary layer, we estimate the turbulent fluxes by different methods, and compare the values of fluxes depending on environmental conditions, taking into account the sea state.

Electromagnetic waves can be used to transmit information over long distances and are therefore often employed for communication purposes. The electromagnetic waves are reflected off material objects on their paths and interact with the medium through which they propagate. For instance, the plasma in the ionosphere can refract and even reflect radio waves propagating through it. By increasing the power of radio waves injected into the ionosphere, the waves start to modify the plasma, resulting in the generation of a wide range of nonlinear processes, including turbulence, in particular near the reflection region. By systematically varying the injected radio waves in terms of frequency, power, polarisation, duty cycle, inclination, etc. the ionosphere can be used as an outdoor laboratory for investigating fundamental properties of the near-Earth space environment as well as of plasma turbulence. In such ionospheric modification experiments, it has been discovered that the irradiation of the ionosphere by powerful radio waves leads to the formation of plasma density structures and to the emission of secondary electromagnetic radiation, a phenomenon known as stimulated electromagnetic emission. These processes are highly repeatable and have enabled systematic investigations of the nonlinear properties of the ionospheric plasma. In this thesis we investigate features of the plasma density structures and the secondary electromagnetic radiation. In a theoretical study we analyse a certain aspect of the formation of the plasma structures. The transient dynamics of the secondary radiation is investigated experimentally in a series of papers, focussing on the initial stage as well as on the decay. In one of the papers we use the transient dynamics of the secondary radiation to reveal the intimate relation between certain features of the radiation and structures of certain scales. Further, we present measurements of unprecedentedly strong secondary radiation, attributed to stimulated Brillouin scattering, and report measurements of the secondary radiation using a novel technique imposed on the transmitted radio waves.

In the Thesis, two important theoretical problems arising in the theory of one-dimensional defocusing nonlinear Schrödinger (NLS) flows are investigated analytically and numerically: (i) the resonant generation of dispersive shock waves (DSWs) in one-dimensional NLS flow past a broad repulsive penetrable barrier; and (ii) the interaction of counter-propagating DSW and a simple rarefaction wave (RW), which is referred to as the DSW refraction problem. The first problem is motivated by the recent experimental observations of dark soliton radiation in a cigar-shaped BEC by sweeping through it a localised repulsive potential; the second problem represents a dispersive-hydrodynamic counterpart of the classical gas-dynamics problem of the shock wave refraction on a RW, and, apart from its theoretical significance could also find applications in superfluid dynamics. Both problems also naturally arise in nonlinear optics, where the NLS equation is a standard mathematical model and the `superfluid dynamics of light' can be used for an all-optical modelling of BEC flows. The main results of the Thesis are as follows: (i) In the problem of the transcritical flow of a BEC through a wide repulsive penetrable barrier an asymptotic analytical description of the arising wave pattern is developed using the combination of the localised ``hydraulic'' solution of the 1D Gross-Pitaevskii (GP) equation with repulsion (the defocusing NLS equation with an added external potential) and the appropriate exact solutions of the Whitham-NLS modulation equations describing the resolution of the upstream and downstream discontinuities through DSWs. We show that the downstream DSW effectively represents the train of dark solitons, which can be associated with the excitations observed experimentally by Engels and Atherton (2008). (ii) The refraction of a DSW due to its head-on collision with the centred RW is considered in the frameworks of two one-dimensional defocusing NLS models: the standard cubic NLS equation and the NLS equation with saturable nonlinearity, the latter being a standard model for the light propagation through photorefractive optical crystals. For the cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain key parameters of the DSW refraction. In both problems, we undertake a detailed analysis of the flow structure for different parametric regimes and calculate physical quantities characterising the output flows in terms of relevant input parameters. Our modulation theory analytical results are supported by direct numerical simulations of the corresponding full dispersive initial value problems (IVP).

Nonlinear wave-wave interactions and wave breaking contribute to nearshore wave energy dissipation. These factors can be analyzed by the principles of wave self-similarity. The equilibrium range can be shown in wind-driven wave spectra that exist in the form ( ) and However, the appropriate methods used to determine this loss of energy are controversial. This study examines an approach that reinvestigates the self-similarity principles. Wave spectra with lower peak periods are dominated by nonlinear wave-wave interactions which produce a scaling in shallow water. This thesis investigates the relative role of spectral similarity in different conditions in the nearshore region of the U.S. Army Corps of Engineers Field Research Facility in Duck, North Carolina. The results show young sea waves (wave spectra in which the propagation speed of waves at the spectral peak is much smaller than the wind speed) are dominated by nonlinear wave-wave interactions in the nearshore while older waves (wave spectra in which the propagation speed of waves at the spectral peak is equal to or greater than the wind speed) are dominated by wave breaking in deep water. Furthermore, nearshore wave models need to incorporate the self-similarity concept in deep and shallow water to better understand and quantify important aspects of wave physics in shallow water.

L'Océan Austral est une zone clef pour la circulation océanique tant à cause de l'intensité du courant circumpolaire antarctique qu'en tant que région de formation des masses d'eaux abyssales de l'océan global. Pour modéliser l'océan et prévoir les changements climatiques futurs, il est important de comprendre les processus de mélange diapycnal qui lient ces eaux abyssales aux couches supérieures. Dans l'Océan Austral, des courants profonds et intenses s'écoulent sur une topographie accidentée, ce qui génère des ondes internes de relief très énergétiques. Actuellement, la dissipation de l'énergie induite par ces ondes de relief est la candidate principale pour expliquer les forts taux de mélange observés à ces latitudes. L'objet du présent travail de thèse est de comprendre comment les ondes internes de relief sont dissipées et affectent la circulation et le mélange diapycnal dans l'océan abyssal. Nous examinons l'impact de ces ondes sur le mélange profond au moyen d'une combinaison d'expertise de terrain, de simulations non hydrostatiques bi-dimensionnelles et de calculs théoriques. Sur la gamme de paramètres étudiés, nous montrons, en présence des ondes de relief, une intensification du taux de dissipation d'énergie cinétique turbulente sur une profondeur de 1000 m au-dessus de la topographie, atteignant typiquement ~20 mW/m2. Nous montrons également comment les ondes participent à des interactions triadiques impliquant des oscillations inertielles qui sont amplifiées par intéractions résonantes contrôlées par les ondes de relief. Finalement, nous préparons de futures études tri-dimensionnelles en concevant un cadre numérique et en décrivant des outils théoriques adaptés à ce problème. Nos résultats préliminaires en trois dimensions montrent qui le confinement méridien de la topographie réduit significativement l'émissions d'ondes internes de relief. / The Southern Ocean plays a key role in global ocean circulation by connecting the major ocean basins with the intense Antarctic Circumpolar Current and as a formation region for abyssal water masses of the global ocean. Understanding the diapycnal mixing processes that link these abyssal waters to the overlying layers is essential both for ocean modelling and for predicting future climate change. In the Southern Ocean, deep reaching currents impinge on rough topography and create highly energetic internal lee waves. The dissipation of the energy of these internal lee waves is the main candidate for explaining the high mixing rates between waters of different densities observed at these latitudes. The purpose of this study is to understand the fate of the internal lee wave energy and how it affects the circulation and diapycnal mixing in the abyssal ocean. We first study the impact of internal lee waves on deep mixing with the combination of field expertise, two-dimensional non hydrostatic numerical simulations and theoretical developments. Over the range of parameters studied, an enhanced bottom turbulent kinetic energy dissipation is observed in the bottom 1000 m, typically reaching $sim$ 20 mW.m$^{-2}$. We further show that internal lee waves undergo non-dissipative wave-wave interactions that can be rationalized as resonant triad interactions between the bottom emitted internal lee waves, inertial oscillations and linear combinations of these two waves. We then build a three-dimensional model configuration and specific diagnostic methods that pave the way for future investigations in three dimensions. Preliminary results with the three-dimensional numerical configuration show that the meridional confinement of the topography notably reduces the emission of internal lee waves.