A long-standing question in planet formation is the origin of planetesimals, the kilometre-sized precursors to protoplanets. Asteroids and distant Kuiper Belt objects are believed to be remnant planetesimals from the beginnings of our Solar system. A leading mechanism for explaining the formation of these bodies directly from centimetre-sized dust pebbles is the streaming instability (SI). Using high resolution numerical simulations of protoplanetary discs, we probe the behavior of the non-linear SI and planetesimal formation in previously unexplored configurations. Small variations in initial state of the disc can lead to different macroscopic outcomes such as the total mass converted to planetesimals, or the distribution of planetesimal masses. These properties can vary considerably within large simulations, or across smaller simulations re-run with different initial perturbations. However, there is a similar spread in outcomes between multiple smaller simulations and between smaller sub-regions in larger simulations. In small simulations, filaments preferentially form rings while in larger simulations they are truncated. Larger domains permit dynamics on length scales inaccessible to the smaller domains. However, the overall mass concentrated in filaments across various length scales is consistent in all simulations. Small simulations in our suite struggle to resolve dynamics at the natural filament separation length scale, which restricts the possible filament configurations in these simulations. We also model discs with multiple grain species, sampling a size distribution predicted from theories of grain coagulation and fragmentation. The smallest grains do not participate in the formation of planetesimals or filaments, even while they co-exist with dust that readily forms such dense features. For both single-grain and multiple-grain models, we show that the clumping of dust into dense features results in saturated thermal emission, requiring an observational mass correction factor that can be as large as 20-80\%. Finally, we present preliminary work showing that the critical dust-to-gas mass ratio required to trigger the SI can vary between 3D and 2D simulations. / Thesis / Doctor of Philosophy (PhD)

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In this study, a new and efficient numerical algorithm is developed to solve both the two-dimensional and three-dimensional compressible hydrodynamic stability problem. A parametric study of free shear flows with two or more supersonic streams is performed. Flows examined included shear layers, jets/wakes, and various geometrical combinations of these flows. The effect of Mach number on the stability characteristics of the flow is studied and found to confirm the work of other researchers who found that increasing the relative (or convective) Mach number increases the stability of the flow. For 2-D mean flows, the most amplified disturbance is shown to be axial for M<1.2 and fully three-dimensional for M> 1.2. Disturbances for three-dimensional mean flows are found here to be axial in the presence of side walls. The variation of the eigenfunctions and flow field disturbances as a function of Mach number and the flow geometry was also studied. Comparisons of the stability code results are also made to several turbulent mixing experiments. The stability code correctly predicts which parameters will accelerate mixing. New correlations of the effects of some important parameters on stability are developed. / Ph. D.

Yes / The present study investigates the turbulent hydrodynamics in an open channel flow with an emergent and sparse vegetation patch placed in the middle of the channel. The dimensions of the rigid vegetation patch are 81 cm long and 24 cm wide and it is prepared by a 7× 10 array of uniform acrylic cylinders by maintaining 9 cm and 4 cm spacing between centers of two consecutive cylinders along streamwise and lateral directions respectively. From the leading edge of the patch, the observed nature of time averaged flow velocities along streamwise, lateral and vertical directions is not consistent up to half length of the patch; however the velocity profiles develop a uniform behavior after that length. In the interior of the patch, the magnitude of vertical normal stress is small in comparison to the magnitudes of streamwise and lateral normal stresses. The magnitude of Reynolds shear stress profiles decreases with increasing downstream length from the leading edge of the vegetation patch and the trend continues even in the wake region downstream of the trailing edge. The increased magnitude of turbulent kinetic energy profiles is noticed from leading edge up to a certain length inside the patch; however its value decreases with further increasing downstream distance. A new mathematical model is proposed to predict time averaged streamwise velocity inside the sparse vegetation patch and the proposed model shows good agreement with the experimental data. / Debasish Pal received financial assistance from SRIC Project of IIT Kharagpur (Project code: FVP)

Inlet transitions with sub-critical flow from trapezoidal to rectangular sections are studied. The water depths range from 5 to 10 feet and the bottom widths range from 5 to 12.5 feet. Graphs were constructed to design these types of transitions. The behavior of a given transition with different discharges is also studied. It was found that more efficiency is gained when a given transition is used with a discharge greater than the design discharge, than when the transition is used with a discharge less than the design discharge. / Master of Science

The straight line calm water performance of stepped planing hulls has been studied experimentally, by prediction method, and numerically. A model test was conducted to provide a systematic understanding of the effects that displacement and step location have on the performance of a stepped planing hull. Ten different step configurations were tested at three different displacements and over a range of four different speeds in calm water. Seven of these configurations were tested at two different Longitudinal Center of Gravity (LCG) locations. Of all the configurations tested, the stepped hull configurations showed reduced resistance compared to the unstepped hull. The configurations with the largest step height aft showed the least amount of resistance over the speed range tested. Increasing displacement and shifting LCG had similar effects on craft performance for both stepped and unstepped hulls. The current stepped hull prediction method was expanded to include a three dimension wave profile and the ability for the stagnation line to cross the step. Using previous model test data and existing two dimension wave profile equations, a single equation was developed to predict the three dimension wave profile aft of a step. Formulations were added to Savitsky's planing prediction method to include very high speed craft and chines dry conditions. Lastly, two simulations were performed using two computational fluid dynamics numerical tools, OpenFOAM, and NFA. The results of these simulations were compared to the experimental test results to assess each code's relative strengths and weaknesses for use in detail design of stepped planing craft. / Ph. D.

This work deals with the linear two-dimensional free vibrations of an inflated cylindrical membrane. An air-inflated membrane is considered first. Vibration frequencies and modes are determined for various cases. The lowest mode shape is anti-symmetric. In the rest of the work, the membrane is inflated with water. In some cases there is a reservoir of water on one side of the membrane. The membrane equation of motion is solved using a finite difference method, and the hydrodynamic pressures on the membrane, caused by the motion of the internal and external water domains, are treated by the boundary element method. The effects of the membrane parameters, internal and external water head, and density of the membrane on the lowest four frequencies are illustrated. For the membrane without the outside water, the first two natural frequencies agree well with experimental values. The existence of the upstream head has a significant influence on the frequencies, and the mode shapes are shown to be tilted toward the downstream side of the membrane. / Ph. D.

A procedure to generate an approximate bifurcation diagram for a single-degree-of-freedom system in a selected parameter space is developed. The procedure is based on the application of Floquet analysis to determine the stability of second-order perturbation approximations of the solutions of the system in the neighborhoods of specific resonances. As a control parameter is varied, a combination of elementary concepts of bifurcation theory and the proposed method are used to detect the first bifurcation from the periodic solutions and hence infer the qualitative changes that the system experiences. Codimension-one bifurcations are investigated in a two-dimensional parameter space composed of the amplitude and frequency of the excitation. The behavior of a softening Duffing oscillator is analyzed under external and parametric excitation. The dynamics of a ship rolling in waves is also considered and three types of excitations are treated: external, parametric, and a combination of both. Analog- and digital-computer simulations are used to verify the accuracy of the analytical predictions. It is found that the predictions based on the first bifurcation of the analytical solution give a good estimate of the actual behavior of the system. The stability regions of the solutions near each of the resonances display a self-similar structure in the parameter space. The physical implications of these bifurcation patterns are important for the prediction of the capsizing of ships. The dangerous regions of the parameter space where capsizing might occur are identified for a given system. Capsizing is found to occur via two distinct scenarios: one evolving from a large oscillation through a disappearance of a chaotic attractor (crises) and a second, potentially more dangerous, developing from a small oscillation through a sudden tangent instability. These scenarios agree with previous experimental studies. / Ph. D.

published_or_final_version / abstract / toc / Civil Engineering / Master / Master of Philosophy