Unbalanced instabilities of rapidly rotating stratified shear flows

The linear stability of a rotating, stratified, inviscid horizontal plane Couette flow in a channel is studied in the limit of strong rotation and stratification. An energy argument is used to show that unstable perturbations must have large wavenumbers. This motivates the use of a WKB-approach which, in the first instance, provides an approximation for the dispersion relation of the various waves that can propagate in the flow. These are Kelvin waves, trapped near the channel walls, and inertia-gravity waves with or without turning points. Although, the wave phase speeds are found to be real to all algebraic orders in the Rossby number, we establish that the flow, whether cyclonic or anticyclonic, is unconditionally unstable. This is the result of linear resonances between waves with oppositely signed wave momenta. We derive asymptotic estimates for the instability growth rates, which are exponentially small in the Rossby number, and confirm them by numerical computations. Our results, which extend those of Kushner et al (1998) and Yavneh et al (2001), highlight the limitations of the so-called balanced models, widely used in geophysical fluid dynamics, which filter out Kelvin and inertia-gravity waves and hence predict the stability of the Couette flow. They are also relevant to the stability of Taylor-Couette flows and of astrophysical accretion discs.Comment: 6 figure

Congregational Honors: A Model for Inclusive Excellence

This essay proposes a conception of honors programs and colleges as sacred communities that acknowledge and embrace the unique human dignity of each of their members. Drawing on Ron Wolfson’s congregational model articulated in Relational Judaism, McMillan and Chavis’s definition of “sense of community,” and the pedagogy of educators such as Paolo Freire and bell hooks, I argue that to create a true culture of inclusive excellence, an honors program or college should not be constructed as a checklist of “exceptional experiences for exceptional students” but rather as a “community of relationships.” Leading with a student-centered, holistic focus that recognizes and cherishes the specific students served by an institution enables proactive engagement with what Richard Badenhausen has termed the “monumental demographic shifts” in higher education and expands the frequently too narrow conception of who belongs in honors. It also requires grounding our efforts in the data (from the American College Health Association and the U.S. Governmental Affairs Office, among others) reflecting that 55% of U.S. college students reported being diagnosed with or treated for an illness or disability in the past twelve months, more than 88% have felt overwhelmed, 64% report anxiety, and 30% are food insecure, while 51.7% have found academics “traumatic or very difficult.” The essay concludes by offering concrete strategies for creating authentically relational communities by ensuring that honors programs, advising, and coursework are specifically designed to recognize and welcome the diverse and complex intersectional identities of students and to address the myriad challenges they may face

On MMSE and MAP Denoising Under Sparse Representation Modeling Over a Unitary Dictionary

Among the many ways to model signals, a recent approach that draws considerable attention is sparse representation modeling. In this model, the signal is assumed to be generated as a random linear combination of a few atoms from a pre-specified dictionary. In this work we analyze two Bayesian denoising algorithms -- the Maximum-Aposteriori Probability (MAP) and the Minimum-Mean-Squared-Error (MMSE) estimators, under the assumption that the dictionary is unitary. It is well known that both these estimators lead to a scalar shrinkage on the transformed coefficients, albeit with a different response curve. In this work we start by deriving closed-form expressions for these shrinkage curves and then analyze their performance. Upper bounds on the MAP and the MMSE estimation errors are derived. We tie these to the error obtained by a so-called oracle estimator, where the support is given, establishing a worst-case gain-factor between the MAP/MMSE estimation errors and the oracle's performance. These denoising algorithms are demonstrated on synthetic signals and on true data (images).Comment: 29 pages, 10 figure

Thinking Critically, Acting Justly

In October 2011, just two months after I became Director of the University Honors Program at Loyola New Orleans, my new home town was simultaneously proclaimed both “America’s Best City for Foodies” (Forbes) and the country’s “Worst Food Desert” (Lammers). The city known for beignets and crawfish, Mardi Gras and jazz, was revealed to have only one supermarket for each 16,000 residents (half the national average), with some residents traveling over fifteen miles from their homes to purchase fresh produce. In the past six years, the situation has been somewhat ameliorated by multiple farmers markets throughout the city that accept food stamps and by an urban farm movement that has been repurposing land, abandoned and overgrown since Katrina, in the Lower 9th Ward and St. Bernard Parish. Even so, one of six children in New Orleans experiences food insecurity, and food injustice is not the only challenge facing this city of tremendous inequities: ・ 40% of adults are illiterate; ・ 39% of New Orleans’ children live in poverty; and ・ 1 in 14 black males is incarcerated in a city where 60.2% of the population is African American. (Louisiana has the highest incarceration rate in the world.) I emphasize my city’s inequities because Loyola, a Jesuit university located in uptown New Orleans, intertwines with its community as both a place of privilege and a point of access. Loyola, a masters-level institution, is far more diverse than Tulane, the much larger, less “artsy,” and more affluent research university next door. In 2017, Loyola was ranked #4 in the region for ethnic diversity by the U.S. News & World Report and, according to The Princeton Review, #13 in the country for race/class interaction (Loyola). Although the Loyola University Honors Program is, like many other honors programs and colleges, somewhat “whiter” than the rest of the institution (half of whose undergraduates are students of color), approximately 30% of honors students are people of color, 30% are the first in their families to attend college, and 26% are Pell-eligible. Geographically, 60% of honors students come from outside of Louisiana; some may come for our nationally ranked music industries program, knowing nothing about the city’s social justice challenges, while others may decide to come after a “Voluntourism” service or mission trip here in high school. At least 25% of honors students, however, are from the greater New Orleans area and so have experienced in some way the loss and displacement of Katrina regardless of their childhood social and economic backgrounds. More recently, a number of our students lost their homes (some for the second time) or were otherwise affected by the flooding near Baton Rouge in the summer of 2016. Now, as I write this essay, images of devastation from Houston, along with our own city’s torrential rain and dysfunctional pumps, are bringing up painful memories and raising anxiety. I suspect that my colleagues on the provost council at Loyola have turned our conversations into a virtual drinking game, betting on how quickly I will say the word “honors.” NCHC board members, in turn, may secretly promise themselves a shot each time I bring up Loyola or New Orleans. I do think my program is special, as each of us does, or at least should, but I am starting my discussion with Loyola because our story crystallizes two essential questions about honors education and social justice: first, how to engage our highestability and most motivated students in questions of justice; and second, how honors can be a place of access, equity, and excellence in higher education