Browsing by Subject "Hydrodynamics"

Animals experience hydrodynamic forces (lift, drag, and side) and moments (pitching, yawing, and rolling) as a result of motion in an aqueous medium. Under selective pressure, most cetaceans, including porpoises, dolphins, and whales, developed a streamlined body shape and modified limbs, which delay the separation of flow, create lower drag when they swim, and therefore decrease their locomotor cost. In order to calculate the locomotor cost and propulsive efficiency of cetaceans, accurate estimates of drag on marine animals are required. However, extra momentum imparted into the fluid from lift and side forces as well as pitching, rolling, and yawing moments (here, the parasitic loads) results in extra drag force on the animal. Therefore, in addition to streaming and delaying flow separation, animals must also minimize excess fluid momentum resulting from parasitic loads. Given the endangered status of the North Atlantic right whale (Eubalaena glacialis; hereafter NARW), analyzing the hydrodynamic characteristics of the NARWs was the focus of this work. Additionally, previous studies showed that body shape of NARWs changes with life stages, reproduction status, nutritive conditions or prey abundance, and the effects of entanglement in fishing gear. Therefore, in this study, computational fluid dynamics (CFD) analysis was performed on multiple 10 m three-dimensional NARW models with different body shapes (e.g., normal condition, emaciated, and pregnant) to measure baseline measurements of flow regimes and hydrodynamic loads on the animal. Swimming speeds covering known right whale speed range (0.125 m/s to 8 m/s) were simulated in most scenarios. In addition to the hydrodynamic effects of different body shapes, drag was also considered a function of parasitic loads. The NARW models were embedded with bone segments that allowed one to manipulate the body pose of the model via adjusting the flippers or the spine of the animal before measuring hydrodynamic drag. By doing so, momentum from parasitic loads was expected to be eliminated. CFD simulations revealed that drag on NARWs is dictated by its irregular outline and that the drag coefficient (0.0071-0.0059; or dimensionless drag) of on NARWs is approximately twice that of many previous estimates for large cetaceans. It was also found that pregnant NARW model encounters the lowest drag coefficient due to delayed flow separation resulting from enlarged abdomen, whereas the emaciated NARW model experiences the highest drag coefficient possibly due to the concavity at the post-nuchal region. These results suggested that drag on NARWs and their thrust power requirements were indeed affected by its body shape but the differences between the three NARW models tested were small. Lastly, minimum drag, which corresponds to the elimination of the parasitic loads, can be obtained by adjusting the pose of the animal. Thus, minimum drag occurs at the neutral trim pose. For the static, normo-nourished NARW model, simulations revealed that by changing the angle of attack of the flippers by 4.03° (relative to the free-stream flow) and pitching the spine downward by 5° while maintaining fluke angle, the drag was lowered by approximately 11% across the flow speeds tested. This drag reduction was relative to the drag study conducted on the same animal model but without body pose adjustments. Together the studies included in the present work explored and highlighted the capability of numerical methods in investigating the hydrodynamics and energetics of cetaceans. Future studies should address how computer solutions can be used to solve problems from a wider aspect. For instance, extra parasitic loads caused by attached gear as well as possible injuries due to the encounter with fishing gear should also be considered while evaluating the energy budget of the North Atlantic right whales.

Coral reef habitats are well-known for biodiversity, yet are declining worldwide due to multiple stressors from local to global scales. Scleractinian corals, as foundation species, contribute to building the three-dimensional reef structure, yet this structure can be degraded through natural or anthropogenic disturbances. Conservation actions such as restoration depend on an understanding of the spatial distributions of potential habitat. In this dissertation, I address how abiotic environmental limitations shape coral species habitat niches and relate to recovery from disturbances. To accomplish this, I first describe local limitations on reef recovery after physical disturbances and then scale up to regional models of environmental niche constraints on coral species and communities.

First, I compare divergent recovery trajectories at two proximal reefs disturbed by ship groundings that created abrupt and clearly delineated areas of altered substrate. Despite similar initial physical disturbances, there were marked differences between the grounding sites with higher coral recruitment and survival on disturbed pavement than rubble bottom, reference reef, or restoration structures. I hypothesized that subsequent episodic disturbances from rubble mobilization could be a mechanism driving divergent recovery patterns. To estimate whether local hydrodynamic conditions were sufficient to mobilize rubble, I used a combination of long-term monitoring, hydrodynamic modeling, and rubble transport mechanics to hindcast the potential for substrate mobility. Long-term model simulations of hydrodynamic forcing at the study sites show multiple events where bottom-orbital velocities exceeded thresholds required to mobilize rubble via sliding or overturning. The data and analyses indicate that the wave energy mobilizes rubble substrate multiple times annually and suggests a physical limitation on survival of coral recruits relative to those on pavement substrate. The combination of multiple hydrodynamic disturbances and unstable substrate limits coral recovery and contributes to prolonged habitat loss.

I next scaled up to a seascape approach to model how environmental limitations on individual species impact the coral community response. I used a joint species distribution modeling approach with new and spatially extensive coral monitoring data from Puerto Rico and the U.S. Virgin Islands. Using a multivariate spatial modeling approach, I explained relationships between species and environments and predicted species abundances (and associated uncertainties) into new, unsurveyed geographic areas in the U.S. Caribbean region. Joint model results showed how coral populations and communities are structured by geomorphological and climate factors. Species abundances and sizes showed correlations between species niches relative to depth, slope, wave energy near the seafloor, and thermal stress. Using inverse prediction, I showed how a scenario of increased wave energy or increased temperature ranges may shift habitats for individual species and impact overall species richness.

I then focused specifically on four of the major reef-building coral species that are currently listed as Threatened under the Endangered Species Act: Acropora cervicornis, Orbicella annularis, O. faveolata, and O. franksi. I modeled environmental limitations on species distributions in terms of occurrence, abundance, and size in Puerto Rico and the U.S. Virgin Islands. I used Bayesian Generalized Linear Models to predict species occurrence and abundance. I then compared results to the generalized joint attribute models that included abundance and size. Specific model applications were dependent on data availability. All species responded in different ways to environmental predictors, yet all showed environmental limitations from depth, wave energy near the seafloor, and thermal regimes.

In summary, in this dissertation I modeled limitations on coral habitat by abiotic variables and, in particular, wave energy. I applied multiple spatial quantitative approaches from local scales to seascape scales. Information about disturbance frequency and wave energy constraints on habitat recovery are applicable to support habitat restoration efforts. Predicted spatial distributions from community and species modeling approaches will support species-based and site-based restoration, conservation, and management efforts.

Dynamical models based on relativistic fluid dynamics provide a powerful tool to extract the properties of the strongly-coupled quark-gluon plasma (QGP) produced in the first ${\sim}10^{-23}$ seconds of an ultrarelativistic nuclear collision. The largest source of uncertainty in these model-to-data extractions is the choice of theoretical initial conditions used to model the distribution of energy or entropy at the hydrodynamic starting time.

Descriptions of the QGP initial conditions are generally improved through iterative cycles of testing and refinement. Individual models are compared to experimental data; the worst models are discarded and best models retained. Consequently, successful traits (assumptions) are passed on to subsequent generations of the theoretical landscape. This so-called bottom-up approach correspondingly describes a form of theoretical trial and error, where each trial proposes a first principles solution to the problem at hand.

A natural complement to this strategy is to employ a top-down or data driven approach which is able to reverse engineer properties of the initial conditions from the constraints imposed by the experimental data. In this dissertation, I motivate and develop a parametric model for initial energy and entropy deposition in ultrarelativistic nuclear collisions which is based on a family of functions known as the generalized means. The ansatz closely mimics the variability of first-principle calculations and hence serves as a reasonable parametric form for exploring QGP energy and entropy deposition assuming imperfect knowledge of the complex physical processes which lead to its creation.

With the parametric model in hand, I explore broad implications of the proposed ansatz using recently adapted Bayesian methods to simultaneously constrain properties of the initial conditions and QGP medium using experimental data from the Large Hadron Collider. These analyses show that the QGP initial conditions are highly constrained by available measurements and provide evidence of a unified hydrodynamic description of small and large nuclear collision systems.

The intent of the work discussed in this dissertation is to apply the engineering methods of theory/modeling, numerics/computation, and experimentation to a diverse assemblage of projects. Several projects are discussed: probabilistic modeling of decompression sickness, comparative hydrodynamics of cetacean flippers, optimization of CT/MRI protocols, evaluation of modified catheters, rudder cavitation, and modeling of mass transfer in amphibian cone outer segments.

The first project discussed is the probabilistic modeling of decompression sickness (DCS). This project involved developing a system for evaluating the success of decompression models in predicting DCS probability from empirical data. Model parameters were estimated using maximum likelihood techniques, and exact integrals of risk functions and tissue kinetics transition times were derived. Agreement with previously published results was excellent including maximum likelihood values within one log-likelihood unit of previous results and improvements by re-optimization, mean predicted DCS incidents within 1.4% of observed DCS, and time of DCS occurrence prediction. Alternative optimization and homogeneous parallel processing techniques yielded faster model optimization times. The next portion of this project involved investigating the nature and utility of marginal decompression sickness (DCS) events in fitting probabilistic decompression models to experimental dive trial data. Three null models were developed and compared to a known decompression model that was optimized on dive trial data containing only marginal DCS and no-DCS events. It was found that although marginal DCS events are related to exposure to decompression, empirical dive data containing marginal and full DCS outcomes are not combinable under a single DCS model; therefore, marginal DCS should be counted as no-DCS events when optimizing probabilistic DCS models with binomial likelihood functions. The final portion of this project involved the exploration of a multinomial DCS model. Two separate models based on the exponential-exponential/linear-exponential framework were developed: a trinomial model, which is able to predict the probabilities of mild, serious and no-DCS simultaneously, and a tetranomial model, which is able to predict the probabilities of mild, serious, marginal and no-DCS simultaneously. The trinomial DCS model was found to be qualitatively better than the tetranomial model, for reasons found earlier concerning the utility of marginal DCS events in DCS modeling.

The next project discussed is comparative hydrodynamics of cetacean flippers. Cetacean flippers may be viewed as being analogous to modern engineered hydrofoils, which have hydrodynamic properties such as lift coefficient, drag coefficient and associated efficiency. The hydrodynamics of cetacean flippers have not previously been rigorously examined and thus their performance properties are unknown. By conducting water tunnel testing using scale models of cetacean flippers derived via computed tomography (CT) scans, as well as computational fluid dynamic (CFD) simulations, a baseline work is presented to describe the hydrodynamic properties of several cetacean flippers. It was found that flippers of similar planform shape had similar hydrodynamic performance properties. Furthermore, one group of flippers of planform shape similar to modern swept wings was found to have lift coefficients that increased with angle of attack nonlinearly, which was caused by the onset of vortex-dominated lift. Drag coefficient versus angle of attack curves were found to be less dependent on planform shape. Larger cetacean flippers were found to have degraded performance at a Re of 250,000 compared to flippers of smaller odontocetes, while performance of larger and smaller cetacean flippers was similar at a swim speed of 2 m/s. Idealization of the planforms of cetacean flippers was found to capture the relevant hydrodynamic effects of the real flippers, although unintended consequences such as the lift curve slope changing from linear to nonlinear were sometimes observed. A numerical study of an idealized model of the humpback whale flipper showed that the leading-edge tubercles delay stall compared to a baseline (no tubercle) flipper because larger portions of the flow remaining attached at higher angles of attack.

The third project discussed is optimization of CT/MRI protocols. In order to optimize contrast material administration protocols for Computed Tomography (CT) and Magnetic Resonance Imaging (MRI), a custom-built physiologic flow phantom was constructed to model flow in the human body. This flow phantom was used to evaluate the effect of varying volumes, rates, and types of contrast material, use of a saline chase, and cardiac output on aortic enhancement characteristics. For CT, reducing the volume of contrast material decreased duration peak enhancement and reduced the maximum value of peak enhancement. Increasing the rate of contrast media administration increased peak enhancement and decreased duration of peak enhancement. Use of a saline chase resulted in an increase in peak enhancement. Peak aortic enhancement increased when reduced cardiac output was simulated. For MRI, when the same volume of contrast material was injected at the same rate, the type of contrast material used has a significant effect on the greatest peak signal intensity and duration peak signal intensity. A higher injection rate of saline chaser is more advantageous than a larger volume of saline chaser to increase the peak aortic signal intensity using low contrast material doses. Furthermore, for higher volumes of contrast material, the effect of increasing the volume of saline chaser makes almost no difference while increasing the rate of injection makes a significant difference. When a saline chaser with a high injection rate is used, the dose of the contrast material may be reduced by 25-50% and more than 86% of the non-reduced dose peak aortic enhancement will be attained.

The next project discussed is evaluation of modified angiocatheters. In this study, a standard peripheral end hole angiocatheter was compared to those modified with side holes or side slits by using experimental techniques to qualitatively compare the contrast material exit jets, and by using numeric techniques to provide flow visualization and quantitative comparisons. A Schlieren imaging system was used to visualize the angiocatheter exit jet fluid dynamics at two different flow rates, and a commercial computational fluid dynamics (CFD) package was used to calculate numeric results for various catheter orientations and vessel diameters. Experimental images showed that modifying standard peripheral intravenous angiocatheters with side holes or side slits qualitatively changed the overall flow field and caused the exiting jet to become less well-defined. Numeric calculations showed that the addition of side holes or slits resulted in a 9-30% reduction of the velocity of contrast material exiting the end hole of the angiocatheter. With the catheter tip directed obliquely to the wall, the maximum wall shear stress was always highest for the unmodified catheter and always lowest for the 4 side slit catheter. Modified angiocatheters may have the potential to reduce extravasation events in patients by reducing vessel wall shear stress.

The next project discussed involves studying the effect of leading-edge tubercles on cavitation characteristics for marine rudders. Three different rudders were constructed and tested in a water tunnel: baseline, 3-tubercle leading edge, and 5-tubercle leading edge. In the linear (non-stall) regime, tubercled rudders performed equally to the smooth rudder. Hydrodynamic stall occurred at smaller angles of attack for the tubercled rudders than for the smooth rudder. When stall did occur, it was more gradual for the tubercled rudders, whereas the smooth rudder demonstrated a more dramatic loss of lift. At lower Re, the tubercled rudders also maintained a higher value of lift post-stall than the smooth rudder. Cavitation onset for the tubercled rudders occurred at lower angles of attack and higher values of cavitation number than for the smooth rudder, but cavities on the tubercled rudders were localized in the slots as opposed to the smooth rudder where the cavity spread across the entire leading edge.

In the final project discussed, modeling of mass transfer in amphibian cone outer segments, a detailed derivation of a simplified (continuum, one-dimensional) mathematical model for the radio-labeled opsin density profile in the amphibian cone outer segment is presented. This model relies on only one free parameter, which was the mass transfer coefficient between the plasmalemma and disc region. The descriptive equations were nondimensionalized, and scale analysis showed that advective effects could be neglected as a first approximation for early times so that a simplified system could be obtained. Through numeric computation the solution behavior was found to have three distinct stages. The first stage was marked by diffusion in the plasmalemma and no mass transfer in the disc region. The second stage first involved the plasmalemma reaching a metastable state whereas the disc region density increased, then involved both the plasmalemma and disc regions increasing in density with their distributions being qualitatively the same. The final stage involved a slow relaxation to the steady-state solution.

Locomotion in any environment requires the use of energy to overcome the physical

forces inherent in the environment. Most large marine vertebrates have evolved

streamlined fusiform body shapes to minimize the resistive force of drag when in

a neutral position, but nearly all behaviors result in some increase in that force.

Too much energy devoted to locomotion may reduce the available surplus necessary

for population-level factors such as reproduction. The population of North Atlantic

right whales has not recovered following legal protection due to decreased fecundity,

including an increase in the intercalf interval, an increase in the years to first calf and

an increase in the number of nulliparous females in the population. This reproductive

impairment appears to be related to deficiencies in storing enough energy to meet the

costs of reproduction. The goal of this study was to determine whether increases in

moving between prey patches at the cost of decreased foraging opportunities could

shift these whales into a situation of negative energy gain. The first step is to

understand the locomotor costs for this species for the key behaviors of traveling and

foraging.

This study investigated the cost of locomotion in right whales by recording the

submerged diving behaviors of free-ranging individuals in both their foraging habitat

in the Bay of Fundy and their calving grounds in the South Atlantic Bight with a

suction-cupped archival tag. The data from the tags were used to quantify the oc-

currence of different behaviors and their associated swimming behaviors and explore

three behavioral strategies that reduce locomotor costs. First, the influence that

changes in blubber thickness has on the buoyancy of these whales was investigated

by comparing the descent and ascent glide durations of individual whales with differ-

ent blubber thicknesses. Next, the depth of surface dives made by animals of different

sizes was related to the depth where additional wave drag is generated. Finally, the

use of intermittent locomotion during foraging was investigated to understand how

much energy is saved by using this gait. The final piece in this study was to deter-

mine the drag related to traveling and foraging behaviors from glides recorded by

the tags and from two different numerical simulations of flow around whales. One, a

custom developed algorithm for multiphase flow, was used to determine the relative

drag, while a second commercial package was used to determine the absolute mag-

nitude of the drag force on the simplest model, the traveling animal. The resulting

drag estimates were then used in a series of theoretical models that estimated the

energetic profit remaining after shifts in the occurrence of traveling and searching

behaviors.

The diving behavior of right whales can be classified into three stereotyped be-

haviors that are characterized by differences in the time spent in different parts of the

water column. The time budgets and swimming movements during these behaviors

matched those in other species, enabling the dive shapes to be classified as foraging,

searching and traveling behaviors. Right whales with thicker blubber layers were

found to perform longer ascent glides and shorter descent glides than those with

thinner blubber layers, consistent with the hypothesis that positive buoyancy does

influence their vertical diving behavior. During horizontal traveling, whales made

shallow dives to depths that were slightly deeper than those that would cause ad-

ditional costs due to wave drag. These dives appear to allow whales to both avoid

the costs of diving as well as the costs of swimming near the surface. Next, whales

were found to glide for 12% of the bottom phases of their foraging dives, and the

use of `stroke-glide' swimming did not prolong foraging duration from that used by

continuous swimmers. Drag coefficients estimated from these glides had an average

of 0.014 during foraging dives and 0.0052 during traveling, values which fall in the

range of those reported for other marine mammals. One numerical simulation deter-

mined drag forces to be comparable, while the other drastically underestimated the

drag of all behaviors. Finally, alterations to the behavioral budgets of these animals

demonstrated their cost of locomotion constitutes a small portion (8-12%) of the

total energy consumed and only extreme increases in traveling time could result in a

negative energy balance. In summary, these results show that locomotor costs are no

more expensive in this species than those of other cetaceans and that when removed

from all the other stressors on this population, these whales are not on an energetic

`knife edge'.

In shallow water systems like coral reefs, bottom friction is often a significant part of the overall momentum balance. The frictional effects of the bottom on the flow are in part determined by the structure of the topography, which varies over orders of magnitude in spatial scale. Predicting spatial and temporal patterns of water motion depends on adequately capturing the relevant properties of the topography. However, representing and quantifying the complex, heterogeneous structure of coral reefs using measures of roughness or geometry remains a challenge.

Many roughness metrics have been proposed to relate seafloor structure to biological and physical processes. In Chapter 1, we assess the properties captured by one-dimensional roughness metrics previously proposed for the seafloor, as well as metrics developed to characterize other types of rough surfaces. We consider three classes of metrics: properties of the bottom elevation distribution (e.g., standard deviation), length scale ratios (e.g., rugosity), and metrics that describe how topography varies with spatial scale (e.g., Hölder exponents). We evaluate these metrics using idealized topography and natural seafloor topography of a reef lagoon system from airborne lidar measurements. The analyses illustrate that common metrics of bathymetric roughness (e.g., rugosity) can have the same value for topographies that are geometrically very different, thus limiting their utility. Application of the wavelet leaders technique to the reef dataset demonstrates that the topography has a power law scaling behavior, but it is multifractal so a distribution of Hölder exponents is needed to describe its scaling behavior. Using principal component analysis, we identify three dominant modes of topographic variability, or ways metrics covary, among and within reef zones. While individual roughness metrics that capture specific topography properties relevant to a given process may be suitable for some studies, for many applications, adequately parameterizing bathymetric roughness will require a set of metrics.

For reefs where the roughness layer takes up a large fraction of the water column, parameterizations of bottom friction require a representation of three-dimensional canopy geometry. In Chapter 2, we assess the implications of using obstacle- and surface-based representations to estimate geometric properties of coral colonies needed to parameterize drag. We collected high-resolution topography data using a scanning multi-beam sonar that resolved individual coral colonies within a set of 100 m2 reef patches primarily composed of mounding Porites corals. The topography measurements yielded 1-cm resolution gridded surfaces consisting of a single elevation value for each position in a regular horizontal grid. These surfaces were analyzed by (1) defining discrete obstacles and quantifying their properties (dimensions, shapes), and (2) computing properties of the elevation field (rms elevations, rms slopes, spectra). We then computed the roughness density (i.e., frontal area per unit plan area) using both analysis approaches. The obstacle and surface-based estimates of roughness density did not agree, largely because small-scale topographic variations contributed significantly to total frontal area. These results challenge the common conceptualization of shallow-water canopies as obstacle arrays, which may not capture significant contributions of high-wavenumber roughness to total frontal area. In contrast, the full range of roughness length scales present in natural reefs is captured by the continuous surface representation. Parameterizations of drag could potentially be improved by considering the distribution of frontal area across length scales.

Collectively, the results presented in Chapters 1 and 2 show that coral reef topography is both multiscale and multifractal. However, there is a limited understanding of the effects of the structural complexity on water motion around individual and groups of corals. In Chapter 3, we present detailed hydrodynamic measurements from the same shallow reef sites for which we quantified reef geometry (Chapter 2). Using these measurements, we compare spatial and temporal variations in flow patterns across three sites: (1) a high relief site with waves; (2) a low relief site with waves; and (3) a high relief site without waves. Our observations suggest that the flow is likely unidirectional and current dominated over much of the backreef. These measurements also show that flow variations at different frequencies have different spatial patterns. At low frequencies, flow variations follow the spatial pattern of wakes. The lack of coherent structure in wave band variations can be explained by the distribution of orbital excursion length to colony diameter (Keulegan-Carpenter number), which is typically less than 2π, thus wakes do not form behind elements. Variations at high frequencies were up to two times larger in the canopy than upstream. In the future, these observations could be compared to computational models of flow at the sites, which would allow us to better understand mechanisms controlling frequency-dependent spatial patterns, as well as the importance of colony and patch-scale processes for reef and regional scale circulation.