Observations of the stratorotational instability in rotating concentric cylinders

We study the stability of density stratified flow between co-rotating vertical cylinders with rotation rates $\Omega_o < \Omega_i$ and radius ratio $r_i/r_o=0.877$, where subscripts $o$ and $i$ refer to the outer and inner cylinders. Just as in stellar and planetary accretion disks, the flow has rotation, anticyclonic shear, and a stabilizing density gradient parallel to the rotation axis. The primary instability of the laminar state leads not to axisymmetric Taylor vortex flow but to the non-axisymmetric {\it stratorotational instability} (SRI), so named by Shalybkov and R\"udiger (2005). The present work extends the range of Reynolds numbers and buoyancy frequencies ($N=\sqrt{(-g/\rho)(\partial \rho/\partial z)}$) examined in the previous experiments by Boubnov and Hopfinger (1997) and Le Bars and Le Gal (2007). Our observations reveal that the axial wavelength of the SRI instability increases nearly linearly with Froude number, $Fr= \Omega_i/N$. For small outer cylinder Reynolds number, the SRI occurs for inner inner Reynolds number larger than for the axisymmetric Taylor vortex flow (i.e., the SRI is more stable). For somewhat larger outer Reynolds numbers the SRI occurs for smaller inner Reynolds numbers than Taylor vortex flow and even below the Rayleigh stability line for an inviscid fluid. Shalybkov and R\"udiger (2005) proposed that the laminar state of a stably stratified rotating shear flow should be stable for $\Omega_o/ \Omega_i > r_i/r_o$, but we find that this stability criterion is violated for $N$ sufficiently large; however, the destabilizing effect of the density stratification diminishes as the Reynolds number increases. At large Reynolds number the primary instability leads not to the SRI but to a previously unreported nonperiodic state that mixes the fluid

No Simple Matter: Advice on Leading Students to a Deeper Understanding of the Three States of Matter

The following is an activity that utilizes the learning cycle to actively engage students in constructing a deep understanding of the states of matter. Students initially explore properties of solids, liquids, and gases through concrete experiences with familiar materials. Science jargon is appropriately delayed until after students have accurately interpreted their experiences. During the application phase students employ their knowledge of the states of matter to investigate the characteristics of an unusual substance to try to identify its state of matter. Key nature of science ideas are explicitly addressed throughout the activity. This article promotes National Science Education Standards A, B, and G, and Iowa Teaching Standards 1, 2, 3, 4, 5, and 6

Examination of the Importance of Auditory-Visual: Integration, Visual-Auditory Integration, Auditory Memory, and Visual Memory to Oral Reading

Elementary Educatio

Using Experimentally Calibrated Regularized Stokeslets to Assess Bacterial Flagellar Motility Near a Surface

The presence of a nearby boundary is likely to be important in the life cycle and evolution of motile flagellate bacteria. This has led many authors to employ numerical simulations to model near-surface bacterial motion and compute hydrodynamic boundary effects. A common choice has been the method of images for regularized Stokeslets (MIRS); however, the method requires discretization sizes and regularization parameters that are not specified by any theory. To determine appropriate regularization parameters for given discretization choices in MIRS, we conducted dynamically similar macroscopic experiments and fit the simulations to the data. In the experiments, we measured the torque on cylinders and helices of different wavelengths as they rotated in a viscous fluid at various distances to a boundary. We found that differences between experiments and optimized simulations were less than 5% when using surface discretizations for cylinders and centerline discretizations for helices. Having determined optimal regularization parameters, we used MIRS to simulate an idealized free-swimming bacterium constructed of a cylindrical cell body and a helical flagellum moving near a boundary. We assessed the swimming performance of many bacterial morphologies by computing swimming speed, motor rotation rate, Purcell’s propulsive efficiency, energy cost per swimming distance, and a new metabolic energy cost defined to be the energy cost per body mass per swimming distance. All five measures predicted that the optimal flagellar wavelength is eight times the helical radius independently of body size and surface proximity. Although the measures disagreed on the optimal body size, they all predicted that body size is an important factor in the energy cost of bacterial motility near and far from a surface

Living Mercy: Reflecting on the Vocation and Values of Salve Regina University

With this collection of essays, we honor the vocation and spirit of mercy that has enlivened and guided Salve Regina University for the last 75 years. Inspired by the accomplishments of the past and looking forward to the call of the future, these essays provide a starting point for University-wide conversations to support Salve Regina in discerning how it will move into the increasingly complex challenges of the future. Salve\u27s tradition of mercy is rooted in the example of Catherine McAuley, who founded the Sisters of Mercy in 19th-century Dublin, Ireland. It is a model of faith expressed through action and maintains that each person is called to and capable of contributing to the common good by responding to the needs of the day, to respond to the suffering and injustice of each era.Attending to this spirit of mercy that continues to guide our University, this project considers how the six core values of Salve’s Strategic Compass – purpose-driven education, respect and dignity for all, mercy community, integrity, faith and spirituality, and compassionate service and solidarity – relate to our shared mercy, Catholic heritage, and the mercy vocational paradigm. Exploring how to re-root and re-frame these values, we approached the project as a vocationally oriented narrative. This type of narrative focuses on the call and vocation, as well as the patterns of meaning that shape the unique identity of an institution in its founding and how the institution has evolved and changed in response to the claims and context of social and historic dynamics. Thus, these six essays are harmonized by a three-fold critical-creative structure that attends to the dynamic experience of the call and spirit of mercy modeled in the founding of the University, how we presently live this call, and envision the challenges and possibilities that lie on the horizon. We employed the perspectives of Foundations, Living Presence, and Horizons to frame an analogical exploration of the unique character, actions and ideals that have inspired and sustained the vocation and mission of Salve Regina University, and may be creatively transferred to shaping the horizon for future generations of students.Celebrating the 75th anniversary of the founding of Salve Regina University, we invite readers to reflect on this collection of essays and then to join the conversations that are to follow as we continue to discern the path forward as Salve takes its next steps into the future.https://digitalcommons.salve.edu/fac_staff_ebooks/1006/thumbnail.jp

The fluid dynamics of flagellar swimming by microorganisms and harmonic generation by reflecting internal, ocean-like waves

textThis 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.Physic