The cause of HI velocity dispersions in the interstellar medium (ISM) of galaxies is often attributed to star formation, but recent evidence has shown these two quantities are not connected in regions of low star formation. This lack of connection is most apparent in dwarf galaxies and the outer disks of spiral galaxies. However, unique data sets have recently been collected that can help address this discrepancy. The ACS Nearby Survey Treasury Project (ANGST) has measured time-resolved star formation histories (SFHs) in ~70 nearby galaxies. The followup Very Large Array-ANGST survey (VLA-ANGST) provides complementary HI observations of a subset of ANGST galaxies. In this thesis, I explore the connection between star formation and HI kinematics in a number of nearby dwarf galaxies. I first present the Very Large Array-ACS Nearby Galaxy Survey Treasury Project (ANGST). VLA-ANGST was designed to provide high spatial and velocity resolution observations of the HI component of the interstellar medium (ISM) in ANGST galaxies. I describe the data calibration and imaging procedures, and then present the publicly-available data products. The observations from this survey and from The HI Nearby Galaxy Survey (THINGS) comprise the majority of data in my thesis. Using VLA-ANGST and THINGS data, I present a method to measure the average HI kinematics in a number of nearby dwarf galaxies by co-adding individual line-of-sight profiles. These "superprofiles" are composed of a central narrow peak (6-10 km/s) with higher velocity wings to either side. When scaled to the same half-width half-maximum, the shapes of the superprofiles are very similar. I interpret the central peak as representative of the average turbulent motion; the wings are then due to HI moving faster than expected compared to the average kinematics. I then compare the superprofile parameters to physical properties such as mass surface density and star formation intensity. The average velocity dispersion correlate most strongly with HI surface density, and do not show correlations with star formation intensity unless higher mass galaxies were included. The properties of the wings are more connected with star formation. By applying energy arguments, I determine that star formation can provide enough energy to drive the HI kinematics over 10 Myr timescales, while a gravitational instability cannot. I then extend this analysis to spatially-resolved scales in these galaxies, and generated superprofiles in regions determined by radius or by star formation intensity. These superprofiles provide a more direct comparison between HI kinematics and local ISM properties compared to the analysis on global scales. The spatially-resolved superprofiles indicate that star formation does not uniquely determine the HI velocity dispersion, but it does appear to provide a lower floor below which velocity dispersions cannot fall. I also find that the coupling efficiency between star formation and HI kinematics decreases with increasing star formation surface density, which may indicate that star formation energy couples more consistently to other phases of the ISM. I finally explore the timescale over which HI responds to star formation using a combination of VLA-ANGST, THINGS, and ANGST data. Using time-resolved SFHs from ANGST, I measure the average star formation rate as a function of time and compared it to present-day HI kinematics. I find that the HI kinematics are most strongly correlated with star formation that occurred 30-40 Myr ago, which supports the idea that supernova explosions are one driver of HI kinematics even in low star formation systems.

This timely volume presents a series of review articles covering every aspect of interstellar turbulence--from accretion disks, molecular clouds, atomic and ionized media, through to spiral galaxies - based on a major international conference held in Mexico City.With advances in observational techniques and the development of more efficient computer codes and faster computers, research in this area has made spectacular progress in recent years. This book provides a comprehensive overview of the most important developments in observing and modelling turbulent flows in the cosmos. It provides graduate student and researchers with a state-of-the-art summary of observational, theoretical and computational research in interstellar turbulence.

Magnetohydrodynamic (MHD) turbulence is a critical component of the current paradigms of star formation, dynamo theory, particle transport, magnetic reconnection and evolution of the interstellar medium (ISM). In order to gain understanding of how MHD turbulence regulates processes in the ISM of galaxies a confluence of numerics, observations, and theory should be used. In this thesis I detail progress that I have made on the connections between theoretical, numerical, and observational understanding of MHD turbulence as it applies to the neutral, ionized, and molecular interstellar medium. In particular, I discuss the development of several new techniques for studies of turbulence to be applied to observations in order to obtain information about the turbulence cascade and the compressibility and magnetization of the fluid. These techniques are first tested on numerical simulations by means of synthetic observations. For most of the numerical tests in this thesis I make use of three-dimensional 512x512x512 compressible MHD isothermal simulations performed for different sonic and Alfvenic Mach numbers. The post processing of these simulations for tests of the turbulence diagnostics include the transformation to column density maps and position-position-velocity (PVV) cubes and can include radiative transfer, telescope beam smoothing, cloud boundaries, and noise. Throughout this thesis I explore the use of new techniques such as the bispectrum, genus statistic, probability distribution function (PDF), hierarchical structure trees (dendrograms), and extend the knowledge of the 2D power spectrum as applied to observations. I discus the application of these techniques to 21-cm data (tracing the warm and cold neutral medium), linear polarization gradients (tracing the warm ionized medium) and emission from carbon monoxide and its isotopes (tracing the molecular medium). This thesis represents a bridge between numerics and observations towards the effort to understand Galactic and extragalactic turbulence and it is just the beginning (i.e. further studies are being conducted that could not be included here). The use of multiple techniques can provide a more accurate indication of the turbulence parameters of interest. The results presented here are based on works I have previously published as first author papers.