Adrienne L. Traxler

TURBULENT MIXING AND LAYER FORMATION IN DOUBLE-DIFFUSIVE CONVECTION: THREE-DIMENSIONAL NUMERICAL SIMULATIONS AND THEORY

Double-diffusive convection, often referred to as semi-convection in astrophysics, occurs in thermally and compositionally stratified systems which are stable according to the Ledoux-criterion but unstable according to the Schwarzchild criterion. This process has been given relatively little attention so far, and its properties remain poorly constrained. In this paper, we present and analyze a set of three-dimensional simulations of this phenomenon in a Cartesian domain under the Boussinesq approximation. We find that in some cases the double-diffusive convection saturates into a state of homogeneous turbulence, but with turbulent fluxes several orders of magnitude smaller than those expected from direct overturning convection. In other cases the system rapidly and spontaneously develops closely-packed thermo-compositional layers, which later successively merge until a single layer is left. We compare the output of our simulations with an existing theory of layer formation in the oceanographic context, and find very good agreement between the model and our results. The thermal and compositional mixing rates increase significantly during layer formation, and increase even further with each merger. We find that the heat flux through the staircase is a simple function of the layer height. We conclude by proposing a new approach to studying transport by double-diffusive convection in astrophysics.

Dynamics of fingering convection I: Small-scale fluxes and large-scale instabilities

(Received ?? and in revised form ??) Double-diffusive instabilities are often invoked to explain enhanced transport in stablystratified fluids. The most-studied natural manifestation of this process, fingering convection, commonly occurs in the ocean’s thermocline and typically increases diapycnal mixing by two orders of magnitude over molecular diffusion. Fingering convection is also often associated with structures on much larger scales, such as thermohaline intrusions, gravity waves and thermohaline staircases. In this paper, we present an exhaustive study of the phenomenon from small to large scales. We perform the first three-dimensional simulations of the process at realistic values of the heat and salt diffusivities and provide accurate estimates of the induced turbulent transport. Our results are consistent with oceanic field measurements of diapycnal mixing in fingering regions. We then develop a generalized mean-field theory to study the stability of fingering systems to large-scale perturbations, using our calculated turbulent fluxes to parameterize small-scale transport. The theory recovers the intrusive instability, the collective instability, and the instability as limiting cases. We find that the fastest-growing large-scale mode depends sensitively on the ratio of the background gradients of temperature and salinity (the density ratio). While only intrusive modes exist at high density ratios, the collective and -instabilities dominate the system at the low density ratios where staircases are typically observed. We conclude by discussing our findings in the context of staircase formation theory.

Dynamics of Fingering Convection II: The Formation of Thermohaline Staircases

Regions of the oceans thermocline unstable to salt fingering are often observed to host thermohaline staircases, stacks of deep well-mixed convective layers separated by thin stably-stratified interfaces. Decades after their discovery, however, their origin remains controversial. In this paper we use 3D direct numerical simulations to shed light on the problem. We study the evolution of an analogous double-diffusive system, starting from an initial statistically homogeneous fingering state and find that it spontaneously transforms into a layered state. By analysing our results in the light of the mean-field theory developed in Paper I, a clear picture of the sequence of events resulting in the staircase formation emerges. A collective instability of homogeneous fingering convection first excites a field of gravity waves, with a well-defined vertical wavelength. However, the waves saturate early through regular but localized breaking events, and are not directly responsible for the formation of the staircase. Meanwhile, slower-growing, horizontally invariant but vertically quasi-periodic gamma-modes are also excited and grow according to the gamma-instability mechanism. Our results suggest that the nonlinear interaction between these various mean-field modes of instability leads to the selection of one particular gamma-mode as the staircase progenitor. Upon reaching a critical amplitude, this progenitor overturns into a fully-formed staircase. We conclude by extending the results of our simulations to real oceanic parameter values, and find that the progenitor gamma-mode is expected to grow on a timescale of a few hours, and leads to the formation of a thermohaline staircase in about one day with an initial spacing of the order of one to two metres.

Extending Positive CLASS Results Across Multiple Instructors and Multiple Classes of Modeling Instruction

We report on a multiyear study of student attitudes measured with the Colorado Learning Attitudes about Science Survey in calculus-based introductory physics taught with the Modeling Instruction curriculum. We find that five of six instructors and eight of nine sections using Modeling Instruction showed significantly improved attitudes from pre- to postcourse. Cohen’s d effect sizes range from 0.08 to 0.95 for individual instructors. The average effect was d ¼ 0:45, with a 95% confidence interval of (0.26‐0.64). These results build on previously published results showing positive shifts in attitudes from Modeling Instruction classes. We interpret these data in light of other published positive attitudinal shifts and explore mechanistic explanations for similarities and differences with other published positive shifts.

Equity Investigation of Attitudinal Shifts in Introductory Physics

We report on seven years of attitudinal data using the Colorado Learning Attitudes about Science Survey from University Modeling Instruction (UMI) sections of introductory physics at Florida International University. This work expands upon previous studies that reported consistently positive attitude shifts in UMI courses; here, we disaggregate the data by gender and ethnicity to look for any disparities in the pattern of favorable shifts. We find that women and students from statistically underrepresented ethnic groups are equally supported on this attitudinal measure, and that this result holds even when interaction effects of gender and ethnicity are included. We conclude with suggestions for future work in UMI courses and for attitudinal equity investigations generally.

Students’ Use of Symmetry with Gauss’s Law

To study introductory student difficulties with electrostatics, we compared student techniques when finding the electric field for spherically symmetric and non‐spherically symmetric charged conductors. We used short interviews to design a free‐response and multiple‐choice‐multiple‐response survey that was administered to students in introductory calculus‐based courses. We present the survey results and discuss them in light of Singh’s results for Gauss’s Law, Collins and Ferguson’s epistemic forms and games, and Tuminaro’s extension of games and frames.