Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics

Zonal flows have been observed to appear spontaneously from turbulence in a number of physical settings. A complete theory for their behavior is still lacking. Recently, a number of studies have investigated the dynamics of zonal flows using quasilinear theories and the statistical framework of a second-order cumulant expansion (CE2). A geometrical-optics (GO) reduction of CE2, derived under an assumption of separation of scales between the fluctuations and the zonal flow, is studied here numerically. The reduced model, CE2-GO, has a similar phase-space mathematical structure to the traditional wave-kinetic equation, but that wave-kinetic equation has been shown to fail to preserve enstrophy conservation and to exhibit an ultraviolet catastrophe. CE2-GO, in contrast, preserves nonlinear conservation of both energy and enstrophy. We show here how to retain these conservation properties in a pseudospectral simulation of CE2-GO. We then present nonlinear simulations of CE2-GO and compare with direct simulations of quasilinear (QL) dynamics. We find that CE2-GO retains some similarities to QL. The partitioning of energy that resides in the zonal flow is in good quantitative agreement between CE2-GO and QL. On the other hand, the length scale of the zonal flow does not follow the same qualitative trend in the two models. Overall, these simulations indicate that CE2-GO provides a simpler and more tractable statistical paradigm than CE2, but CE2-GO is missing important physics.Comment: 8 pages, 5 figure

Take Me Out to the Metaphor

[Excerpt] “In the fall of 2003, Judge Smith of the United States District Court for the District of Rhode Island wrote that “[c]ases examining the issue of workplace sexual harassment by women against women are about as common as a baseball post-season that includes the Cubs and the Red Sox . . . . Judge Smith’s observation was, of course, rooted in the perception among baseball fans, and in the popular culture, that nothing says “futility” quite like a reference to the Chicago Cubs or the Boston Red Sox. Conversely, there can be little doubt that for one in search of a baseball metaphor for success, all roads lead to the Bronx, home of the New York Yankees. This article examines judicial references to the Cubs, Red Sox, and Yankees that are based on the ongoing ninety-eight-year wait for a World Series championship on the North Side of Chicago, the recently ended eighty-six-year drought between titles in Beantown, and the twenty-six World Series trophies won so far by the men in pinstripes.

Law Clerks Out of Context

[Excerpt] “In a previous article, I examined judicial opinions in cases in which law clerks have gone wild, principally by doing things that law clerks just aren‘t supposed to do, such as convening court, conducting independent factual investigations into matters before their judges, or leaking drafts of opinions to the press. Here, I focus on opinions in federal cases that discuss two other categories of unusual law-clerk activity, serving as a source of evidence, and going to court, as a litigant. The article is informed by my ten years of experience as a trial court law clerk in the state and federal courts of New Hampshire. Things that caught my eye, and made it into the article, are incidents I read about in judicial opinions that struck me as very different from anything I had ever seen or heard about through the law-clerk grapevine. My purpose is two-fold. First, many of the opinions I discuss are downright entertaining. But beyond that, the unusual fact patterns that make those opinions entertaining also serve to point out things that might happen to a law clerk that are not covered in law school or the typical law-clerk training program. Accordingly, I intend for the article to have a practical dimension that underpins its entertainment value. In Part II, I explore opinions in which law clerks have become sources of evidence in cases they were working on, as producers of exhibits, as affiants, or as witnesses. In discussing those opinions, I focus on both the process by which law clerks have become sources of evidence and the topics on which they have been asked to give evidence. Part III is devoted to cases in which law clerks have been litigants, and it serves as a guide to situations in which litigation is, and is not, a productive option for a law clerk who believes that he or she has been wronged.

Revisiting the Scrap Heap: The Decline and Fall of Smith v. F.W. Morse & Co.

[Excerpt] One of the more difficult tasks facing a federal court is trying to predict how a state’s highest court would rule on a question of law it has not yet addressed. That difficulty is well illustrated by the history of Wenners v. Great State Beverages, Inc., and in particular, the interpretation of that opinion contained in Smith v. F.W. Morse & Co. [ . . . ] This article begins with a close examination of Wenners and the two opinions on which Wenners relied for its now-canonical statement of the relationship between statutory and common law remedies. I continue with a discussion of Smith and the two opinions that Wenners purportedly consigned to the scrap heap. The next section explores the two distinctly different shadows cast by Wenners, one in the United States District Court for the District of New Hampshire, the other in the New Hampshire Supreme Court. I conclude by suggesting that, in light of Bliss v. Stow Mills, Inc., the scrap heap may be due for a changing of the guard, with Smith replacing Godfrey.

Magnetic eddy viscosity of mean shear flows in two-dimensional magnetohydrodynamics

Magnetic induction in magnetohydrodynamic fluids at magnetic Reynolds number (Rm) less than~1 has long been known to cause magnetic drag. Here, we show that when $\mathrm{Rm} \gg 1$ and the fluid is in a hydrodynamic-dominated regime in which the magnetic energy is much smaller than the kinetic energy, induction due to a mean shear flow leads to a magnetic eddy viscosity. The magnetic viscosity is derived from simple physical arguments, where a coherent response due to shear flow builds up in the magnetic field until decorrelated by turbulent motion. The dynamic viscosity coefficient is approximately $(B_p^2/2\mu_0) \tau_{\rm corr}$, the poloidal magnetic energy density multiplied by the correlation time. We confirm the magnetic eddy viscosity through numerical simulations of two-dimensional incompressible magnetohydrodynamics. We also consider the three-dimensional case, and in cylindrical or spherical geometry, theoretical considerations similarly point to a nonzero viscosity whenever there is differential rotation. Hence, these results serve as a dynamical generalization of Ferraro's law of isorotation. The magnetic eddy viscosity leads to transport of angular momentum and may be of importance to zonal flows in astrophysical domains such as the interior of some gas giants.Comment: 16 pages, 8 figure

Development of an all-metal thick film cost effective metallization system for solar cells

Electrodes made with pastes produced under the previous contract were analyzed and compared with raw materials. A needle-like structure observed on the electroded solar cell was identified as eutectic copper-silicon, a phase considered to benefit the electrical and metallurgical properties of the contact. Electrodes made from copper fluorocarbon and copper silver fluoride also contained this phase but had poor adhesion. A liquid medium, intended to provide transport during carbon fluoride decomposition was incorporated into the paste resulting in better adhesion. The product survived preliminary environmental tests. A 2 cm by 2 cm solar cell made with fluorocarbon activated copper electrodes and gave 7% AMI efficiency (without AR coating). Both silver fluoride and fluorocarbon screened paste electrodes can be produced for approximately $0.04 per watt