In this dissertation, the quantitative and qualitative aspects of modeling shallow water flow driven mainly by gravitational forces and dominated by shear stress, using an effective equation often referred to in the literature as the diffusive wave approximation of the shallow water equations (DSW) are presented. These flow conditions arise for example in overland flow and water flow in vegetated areas such as wetlands. The DSWequation arises in shallow water flow models when special assumptions are used to simplify the shallow water equations and contains as particular cases: the Porous Medium equation and the time evolution of the p-Laplacian. It has been successfully applied as a suitable model to simulate overland flow and water flow in vegetated areas such as wetlands; yet, no formal mathematical analysis has been carried out addressing, for example, conditions for which weak solutions may exist, and conditions for which a numerical scheme can be successful in approximating them. This thesis represents a first step in that direction. The outline of the thesis is as follows. First, a survey of relevant results coming from the studies of doubly nonlinear diffusion equations that can be applied to the DSWequation when topographic effects are ignored, is presented. Furthermore, an original proof of existence of weak solutions using constructive techniques that directly lead to the implementation of numerical algorithms to obtain approximate solutions is shown. Some regularity results about weak solutions are presented as well. Second, a numerical approach is proposed as a means to understand some properties of solutions to the DSW equation, when topographic effects are considered, and conditions for which the continuous and discontinuous Galerkin methods will succeed in approximating these weak solutions are established. / text

Ship-shaped hulls have often been found to be subject to excessive roll motions, and therefore, inhibit their use as a stable production platform. To solve the problem, bilge keels have been widely adopted as an effective and economic way to mitigate roll motions, and their effectiveness lies in their ability to damp out roll motions over a range of frequencies. In light of this, the present research focuses on roll motions of shipshaped hulls. A finite volume method based two-dimensional Navier-Stokes solver is developed and further extended into three dimensions. The present numerical scheme is implemented for modeling the flow around ship-shaped hulls in roll motions and for predicting the corresponding hydrodynamic loads. Also conducted are studies on the hydrodynamic performance of ship-shaped hull sections in prescribed roll motions and in transient decay motions. Systematic studies of the grid resolutions and the effects of free surface, hull geometries and amplitude of roll angle are performed. Predictions from the present method compare well to those of other methods, as well as to measurements from experiments. Non-linear effects, due to flow viscosity, were observed in small as well as in large roll amplitudes, particularly in the cases of hulls with sharp corners. The study also shows that it is inadequate to use a linear combination of added-mass and damping coefficients to represent the corresponding hydrodynamic loads. As a result, it also makes the calculation of the hull response in time domain inevitable. Finally, the capability of the present numerical scheme to apply to fully three-dimensional ship motion simulations is demonstrated. / text

This dissertation details the development of a block model for the movement of submarine slides with emphasis on possible hydroplaning. Unlike previous models, the block model simulated the mechanism of hydroplaning by monitoring the contact condition between the bottom surface of the slide mass and the underlying ground. The effect of hydroplaning on the movement of the slide mass is considered by changing the forces applied on the slide mass by the underlying ground according to the contact condition. The hydrodynamic stresses applied on the slide mass by the surrounding fluid are determined based on the numerical simulations of the flow around a sliding mass. The sliding process of the block is disretisized in a step-by-step manner using a Newmark scheme. A computer program is also written to implement the block model. The block model is validated by comparisons between the numerical results and data reported by Mohrig, et al (1999) for laboratory experiments on subaqueous slides. An illustrative study is also conducted using the block model for the movement of the sediment slabs during the Storegga Slide. The block model has successfully predicted the occurrence of hydroplaning and run-out distances of subaqueous slides. Numerical results with the block model supports the mechanism of hydroplaning for subaqueous slides with greater run-out distances than comparable subaerial slides.

Environmental flows (e.g. river and atmospheric flows) governed by the shallow water equations (SWE) are usually dominated by the advective mechanism over multiple time-scales. The combination of time dependency and nonlinear advection creates difficulties in the numerical solution of the SWE. A fully-implicit scheme is desirable because a relatively large time step may be used in a simulation. However, nonlinearity in a fully implicit method results in a system of nonlinear equations to be solved at each time step. To address this difficulty, a new method for implicit solution of unsteady nonlinear advection equations is developed in this research. This Time-Centered Split (TCS) method uses a nested application of the midpoint rule to computationally decouple advection terms in a temporally second-order accurate time-marching discretization. The method requires solution of only two sets of linear equations without an outer iteration, and is theoretically applicable to quadratically-nonlinear coupled equations for any number of variables. To explore its characteristics, the TCS algorithm is first applied to onedimensional problems and compared to the conventional nonlinear solution methods. The temporal accuracy and practical stability of the method is confirmed using these 1D examples. It is shown that TCS can computationally linearize unsteady nonlinear advection problems without either 1) outer iteration or 2) calculation of the Jacobian. A family of the TCS method is created in one general form by introducing weighting factors to different terms. We prove both analytically and by examples that the value of the weighting factors does not affect the order of accuracy of the scheme. In addition, the TCS method can not only computationally linearize but also decouple an equation system of coupled variables using special combinations of weighting factors. Hence, the TCS method provides flexibilities and efficiency in applications. / text

Hagfishes have both intrigued and confused biologists since Linnaeus first mistakenly classified one as an "intestinal worm." Modern hagfishes (Myxinidae) are elongate, marine fishes often described by what they lack: jaws, scales, paired fins, or a vertebral column. Accompanying this reduced morphology was a long-held view that hagfish are lazy animals that mostly lay about on the ocean floor, but more recent research has revealed them to be active hunters and scavengers in the benthic community. Routine swimming is a requisite part of these activities, yet knowledge of how these exceptionally flexible fishes swim is limited. Here, I use an integrative experimental approach to provide a more comprehensive, quantitative understanding of locomotory mechanisms in hagfishes. In Chapters 1 and 2, I use high-speed videography to quantify whole-body kinematics of steady and unsteady swimming in Eptatretus stoutii and Myxine glutinosa, representing the two main lineages within Myxinidae. Both species generally swim with high amplitude head movements and use tail beat frequency to control swim speed, but inter- and intra-specific variation in other undulatory wave variables suggests multiple mechanisms to modulate speed. Changes in the shape of the body wave characterize the observed unsteady swimming behaviors. During positive linear accelerations, hagfish transiently adopt a larger, longer body wave. During lateral maneuvers, hagfish approximate “sidewinding” behavior as anterior body regions interact with the substrate while posterior body regions propagate waves of lateral bending toward the tail tip. Chapter 3 integrates kinematics with hydrodynamics, using particle image velocimetry to visualize the flow field around swimming E. stoutii. The steady swimming wake consists of caudolateral fluid jets, which turn caudally during linear accelerations. Wake jets orient asymmetrically during lateral swimming, contributing both forward and lateral thrust over a complete tail beat. The hydrodynamic patterns observed reinforce kinematics-based hypotheses on how hagfishes enact their various swimming behaviors. In Chapter 4, I use simple robotically-controlled physical models to examine functional relationships between body flexural stiffness, shape, kinematics, hydrodynamics, and swimming performance. I relate model swim performance to characteristics of hagfish swimming, and describe lessons that passively undulating models impart for understanding locomotion by live elongate undulatory swimmers.

published_or_final_version / abstract / toc / Mechanical Engineering / Doctoral / Doctor of Philosophy

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In this thesis, the hydrodynamics of massive star interiors are explored. Our primary theoretical tool is multi-dimensional hydrodynamic simulation using realistic initial conditions calculated with the one-dimensional stellar evolution code, TYCHO. The convective shells accompanying oxygen and carbon burning are examined, including models with single as well as multiple, simultaneously burning shells. A convective core during hydrogen burning is also studied in order to test the generality of the flow characteristics. Two and three dimensional models are calculated. We analyze the properties of turbulent convection, the generation of internal waves in stably stratified layers, and the rate and character of compositional mixing at convective boundaries.

Core-collapse supernovae are some of the most energetic events in the Universe, they herald the birth of neutron stars and black holes, are a major site for nucleosynthesis, influence galactic hydrodynamics, and trigger further star formation. As such, it is important to understand the mechanism of explosion. Moreover, observations imply that asymmetries are, in the least, a feature of the mechanism, and theory suggests that multi-dimensional hydrodynamics may be crucial for successful explosions. In this dissertation, we present theoretical investigations into the multi-dimensional nature of the supernova mechanism. It had been suggested that nuclear reactions might excite non-radial g-modes (the ε-mechanism) in the cores of progenitors, leading to asymmetric explosions. We calculate the eigenmodes for a large suite of progenitors including excitation by nuclear reactions and damping by neutrino and acoustic losses. Without exception, we find unstable g-modes for each progenitor. However, the timescales for growth are at least an order of magnitude longer than the time until collapse. Thus, the ε-mechanism does not provide appreciable amplification of non-radial modes before the core undergoes collapse. Regardless, neutrino-driven convection, the standing accretion shock instability, and other instabilities during the explosion provide ample asymmetry. To adequately simulate these, we have developed a new hydrodynamics code, BETHE-hydro that uses the Arbitrary Lagrangian-Eulerian (ALE) approach, includes rotational terms, solves Poisson’s equation for gravity on arbitrary grids, and conserves energy and momentum in its basic implementation. By using time dependent arbitrary grids that can adapt to the numerical challenges of the problem, this code offers unique flexibility in simulating astrophysical phenomena. Finally, we use BETHE-hydro to investigate the conditions and criteria for supernova explosions by the neutrino mechanism. We find that a critical luminosity/ mass-accretion-rate condition distinguishes non-exploding from exploding models in hydrodynamic 1D and 2D simulations. Importantly, the critical luminosity for 2D simulations is found to be ∼70% of the critical luminosity for 1D simulations. We identify the specifics ofmulti-dimensional hydrodynamic simulations that enable explosions at lower neutrino luminosities in 2D and discuss how these results might foreshadow successful explosions by eventual 3D radiation-hydrodynamic simulations.

The fitness of any evolutionary unit can be understood in terms of its two basic components: fecundity and viability. The trade-offs between these fitness components drive the evolution of a variety of life-history traits in extant multicellular lineages. Here, I show evidence that the evolution of germ-soma separation and the emergence of individuality at a higher level during the unicellular-multicellular transition are also consequences of these trade-offs. The transition from unicellular to larger multicellular organisms has benefits, costs, and requirements. I argue that germ-soma separation evolved as a means to counteract the increasing costs and requirements of larger multicellular colonies. Volvocalean green algae are uniquely suited for studying this transition since they range from unicells to undifferentiated colonies, to multicellular individuals with complete germ-soma separation. In these flagellated organisms, the increase in cell specialization observed as colony size increases can be explained in terms of increased requirements for self-propulsion and to avoid sinking. The collective flagellar beating also serves to enhance molecular transport of nutrients and wastes. Standard hydrodynamic measurements and concepts are used to analyze motility (self-propulsion) and its consequences for different degrees of cell specialization in the Volvocales as colony size increases. This approach is used to calculate the physical hydrodynamic limits on motility to the spheroid colony design. To test the importance of collective flagellar beating on nutrient uptake, the effect of advective dynamics on the productivity of large colonies is quantified. I conclude first, that when colony size exceeds a threshold, a specialized and sterile soma must evolve, and the somatic to reproductive cell ratio must increase as colony size increases to keep colonies buoyant and motile. Second, larger colonies have higher motility capabilities with increased germ-soma specialization due to an enhancement of colony design. Third, advection has a significant effect on the productivity of large colonies. And fourth, there are clear trade-offs between investing in reproduction, increasing colony size (i.e. colony radius), and motility. This work shows that the evolution of cell specialization is the expected outcome of reducing the cost of reproduction in order to realize the benefits associated with increasing size.