Browsing by Subject "Internal waves"
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Item The fluid dynamics of flagellar swimming by microorganisms and harmonic generation by reflecting internal, ocean-like waves(2011-12) Rodenborn, Bruce Edward; Swinney, H. L., 1939-This dissertation includes two fluid dynamics studies that involve fluid flows on vastly different scales, and therefore vastly different physics. The first study is of bacterial swimming using a flagellum for propulsive motion. Because bacteria are only about 10 [micrometers] in length, they swim in a very low Reynolds number (10⁻⁴) world, which is described by the linear set of governing equations known as the Stokes equations, that are a simplified version of the Navier-Stokes equations. The second study is of harmonic generation from nonlinear effects in internal, ocean-like wave beams that reflect from boundaries in a density stratified fluid. Internal wave reflection is an important oceanic process and may help sustain ocean circulation and affect global weather patterns. Such ocean processes have typical Reynold's numbers of 10¹⁰ or more and are only described by the full, nonlinear Navier-Stokes equations. In the low Reynolds number study, I examine theories by Gray et al.(1956) and Lighthill (1975) that describe swimming microorganisms using a helical flagellum for propulsive motion. I determine the resistance matrix, which can fully describe the dynamics of a flagellum, for flagella with different geometries, defined by: filament radius a, helical radius R, helical pitch [lambda], and axial length L. I use laboratory experiments and numerical simulations conducted in collaboration with Dr. Hepeng Zhang. The experiments, conducted with assistance from a fellow graduate student Chih-Hung Chen, use macroscopic scale models of bacterial flagella in a bath of highly viscous silicone oil. Numerical simulations use the Regularized Stokeslet method, which approximates the Stokeslet representation of an immersed body in a low Reynolds number flow. My study covers a biologically relevant parameter regime: 1/10R < a < 1/25R, R < [lambda] < 20R, and 2R< L <40R. I determine the three elements of the resistance matrix by measuring propulsive force and torque generated by a rotating, non-translating flagellum, and the drag force on a translating, non-rotating flagellum. I investigate the dependences of the resistance matrix elements on both the flagellum's axial length and its wavelength. The experimental and numerical results are in excellent agreement, but they compare poorly with the predictions of resistive force theory. The theory's neglect of hydrodynamic interactions is the source of the discrepancies in both the length dependence and wavelength dependence studies. I show that the experimental and simulation data scale as L/ln(L/r), a scaling analytically derived from slender body theory by my other collaborator Dr. Bin Liu. This logarithmic scaling is new and missing from the widely used resistive force theory. Dr. Zhang's work also includes a new parameterized version of resistive force theory. The second part of the dissertation is a study of harmonic generation by internal waves reflected from boundaries. I conduct laboratory experiments and two-dimensional numerical simulations of the Navier-Stokes equations to determine the value of the topographic slope that gives the most intense generation of second harmonic waves in the reflection process. The results from my experiments and simulations agree well but differ markedly from theoretical predictions by Thorpe (1987) and by Tabaei et al. (2005), except for nearly inviscid, weakly nonlinear flow. However, even for weakly nonlinear flow (where the dimensionless Dauxois-Young amplitude parameter value is only 0.01), I find that the ratio of the reflected wavenumber to the incoming wavenumber is very different from the prediction of weakly nonlinear theory. Further, I observe that for incident beams with a wide range of angles, frequencies, and intensities, the second harmonic beam produced in reflection has a maximum intensity when its width is the same as the width of the incident beam. This observation yields a prediction for the angle corresponding to the maximum in second harmonic intensity that is in excellent accord with my results from experiments and numerical simulations.Item Hydrostatic and non-hydrostatic internal wave models(2004) Wadzuk, Bridget Marie; Hodges, Ben R.Item Internal gravity waves generated by tidal flow over topography(2012-12) Dettner, Amadeus Konstantin; Swinney, H. L., 1939-The majority of internal gravity wave energy in the ocean is produced by tidal flow over bottom topography. Regions of critical topography, where the topographic slope is equal to the slope of the internal gravity waves, is often believed to contribute most significantly to the radiated internal gravity wave power. Here, we present 2D computational studies of internal gravity wave generation by tidal flow over several types of topographic ridges. We vary the criticality parameter [epsilon], which is the ratio of the topographic slope to the wave beam slope, by independently changing the tidal frequency, stratification and topographic slope, which allows to study subcritical ([epsilon] < 1), critical ([epsilon] = 1), and supercritical ([epsilon] > 1) topography. This parameter variation allows us to explore a large range of criticality parameter, namely 0.1< [epsilon] < 10, as well as beam slope S, 0.05< S < 10. As in prior work [Zhang et al., Phys. Rev. Lett. (2008)], we observe resonant boundary currents for [epsilon] = 1. However, we find that the normalized radiated power monotonically increases with internal wave beam slope. We show that an appropriate normalization condition leads to a universal scaling of the radiated power that is proportional to the inverse of the beam slope 1/S and the tidal intensity I[subscript tide], except near [epsilon] = 1 where the behavior undergoes a transition. We characterize this transition and the overall scaling with the criticality parameter f([epsilon]), which is weak compared to the scalings mentioned before and only varies by a factor of two over the entire range of criticality parameter that we explored. Our results therefore suggest that estimates of the ocean energy budget must account for the strong scaling with the local beam slope, which dominates the conversion of tidal motions to internal wave energy. Thus we argue that detailed characterization of the stratification in the ocean is more important for global ocean models than high-resolution bathymetry to determine the criticality parameter.Item Internal wave generation in the presence of turning depths : laboratory models of the deep ocean(2012-12) Drake, Matthew C.; Swinney, H. L., 1939-; Hegelich, Bjorn MIn the ocean, internal gravity waves are generated by tidal flow over sea floor topography. An internal gravity wave is only able to freely propagate if the buoyancy frequency is greater than the driving frequency, where the buoyancy frequency is proportional to the square root of the density gradient. A turning depth is defined as a height below which the buoyancy frequency is less than the driving frequency. King et al. showed that turning depths for internal waves generated by lunar tidal flow exist in the ocean, at varying heights from the sea floor [11]. The present study is the first to examine the generation and propagation of internal waves by tidal flow over topography that lies below a turning depth. I use laboratory experiments and numerical simulations to examine the effect of these turning depths on energy flux of the internal waves generated by tidal flow over topography. I find excellent agreement between numerical and laboratory work, and I show that the internal wave energy is strongly damped by the presence of a turning depth above the topography. Further, this has strong implications for ocean energy budget calculations.Item Laboratory and numerical studies of internal wave generation and propagation in the ocean(2010-08) King, Benjamin Thomas; Swinney, H. L., 1939-Internal waves are generated in the ocean by oscillating tidal flow over bottom topography such as ridges, seamounts, and continental slopes. They are similar to the more familiar surface waves, but not being constrained to move on the surface, propagate throughout the bulk of the world oceans. Internal waves transmit energy over thousands of kilometers, ultimately breaking and releasing their energy into turbulence and mixing. Where these internal waves are generated, as well as where and how they break and cause mixing, has important effects on the general circulation of the ocean, which is in turn a major component in earth's climate. As a first step in a more thorough understanding of the evolution of internal waves in the ocean, it is important to characterize their generation. The two-dimensional generation problem has been studied for four decades, with ample experimental, numerical, and theoretical results. Most of this past work has also been done using linear, inviscid approximations. However, wave generation in the ocean is three-dimensional (3D), and in many locations, nonlinear and viscous effects can be significant. Recent advances in experimental and numerical techniques are only now making the fully nonlinear, 3D generation process accessible. We utilize these new techniques to perform both laboratory experiments and numerical simulations on internal wave generation in 3D. We find that a significant component of the internal wave field generated by tidal flow over 3D topography is radiated in the direction perpendicular to the tidal forcing direction. This could lead to substantial improvements of global internal wave generation models. In addition, we have developed a new method for statistical analysis of ocean data sets, and have found large regions in the deep ocean where internal waves may not propagate. This will also have important effects on the way researchers study the propagation of internal waves, which, when propagating downward, were previously thought to always reflect from the sea floor.Item Models for internal waves in two-fluid systems(2001-05) Kalisch, Henrik W.; Bona, J. L.Item Nonlinear interaction of internal wave beams upon reflection at a sloping boundary(2007-08) Kiefer, Daniel; Swinney, H.L., 1939-Internal gravity waves are supported by any fluid of varying density in height and propagate obliquely through the fluid with an angle determined by the wave frequency and the density gradient of the fluid stratification. Internal waves are suspected to play a key role in the dynamics of the ocean. Despite their great oceanographic importance, the dynamics of the internal waves are widely unknown. When an internal wave reflects from a sloping boundary, the nonlinear interaction of incoming and reflected beams gives rise to additional higher harmonic waves. Quantitative laboratory experiments were conducted on the nonlinear internal wave beam reflection. Strong internal wave beams were generated in a linearly stratified fluid and reflected by a sloping boundary. Second harmonic beams generated at the interaction region of incoming and reflected beam were clearly observed for different slope angles. The existence of a resonant slope orientation at which the second harmonic generation became strongest was precisely determined in the measurements. The resonant angle was always found to be smaller than the angle of the incoming beam and also depended on the beam profile. The observed sensitive dependence on the beam profile was unexpected and warrants further study.