Erratum and Errata

ERRATUM in On properties of seawater defined by temperature, salinity, and pressure, by George Veronis; Journal of Marine Research 30(2): 227–255. ERRATA in On the estimation of surface gravity-wave fields in the vicinity of an array of wave recorders, by R. L. Snyder and Linda Smith; Journal of Marine Research 31(1): 51–60

Solving dielectric and plasmonic waveguide dispersion relations with a pocket calculator

We present a robust iterative technique for solving complex transcendental dispersion equations routinely encountered in integrated optics. Our method especially befits the multilayer dielectric and plasmonic waveguides forming the basis structures for a host of contemporary nanophotonic devices. The solution algorithm ports seamlessly from the real to the complex domain--i.e., no extra complexity results when dealing with leaky structures or those with material/metal loss. Unlike several existing numerical approaches, our algorithm exhibits markedly-reduced sensitivity to the initial guess and allows for straightforward implementation on a pocket calculator.Comment: 18 pages, 11 Figures, 5 Tables, added references, Submitted to Optics Expres

Modal Analysis and Coupling in Metal-Insulator-Metal Waveguides

This paper shows how to analyze plasmonic metal-insulator-metal waveguides using the full modal structure of these guides. The analysis applies to all frequencies, particularly including the near infrared and visible spectrum, and to a wide range of sizes, including nanometallic structures. We use the approach here specifically to analyze waveguide junctions. We show that the full modal structure of the metal-insulator-metal (MIM) waveguides--which consists of real and complex discrete eigenvalue spectra, as well as the continuous spectrum--forms a complete basis set. We provide the derivation of these modes using the techniques developed for Sturm-Liouville and generalized eigenvalue equations. We demonstrate the need to include all parts of the spectrum to have a complete set of basis vectors to describe scattering within MIM waveguides with the mode-matching technique. We numerically compare the mode-matching formulation with finite-difference frequency-domain analysis and find very good agreement between the two for modal scattering at symmetric MIM waveguide junctions. We touch upon the similarities between the underlying mathematical structure of the MIM waveguide and the PT symmetric quantum mechanical pseudo-Hermitian Hamiltonians. The rich set of modes that the MIM waveguide supports forms a canonical example against which other more complicated geometries can be compared. Our work here encompasses the microwave results, but extends also to waveguides with real metals even at infrared and optical frequencies.Comment: 17 pages, 13 figures, 2 tables, references expanded, typos fixed, figures slightly modifie

Instability of small-amplitude convective flows in a rotating layer with stress-free boundaries

We consider stability of steady convective flows in a horizontal layer with stress-free boundaries, heated below and rotating about the vertical axis, in the Boussinesq approximation (the Rayleigh-Benard convection). The flows under consideration are convective rolls or square cells, the latter being asymptotically equal to the sum of two orthogonal rolls of the same wave number k. We assume, that the Rayleigh number R is close to the critical one, R_c(k), for the onset of convective flows of this wave number: R=R_c(k)+epsilon^2; the amplitude of the flows is of the order of epsilon. We show that the flows are always unstable to perturbations, which are a sum of a large-scale mode not involving small scales, and two large-scale modes, modulated by the original rolls rotated by equal small angles in the opposite directions. The maximal growth rate of the instability is of the order of max(epsilon^{8/5},(k-k_c)^2), where k_c is the critical wave number for the onset of convection.Comment: Latex, 12 pp., 15 refs. An improved version of the manuscript submitted to "Mechanics of fluid and gas", 2006 (in Russian; English translation "Fluid Dynamics"

Statistical mechanics of Fofonoff flows in an oceanic basin

We study the minimization of potential enstrophy at fixed circulation and energy in an oceanic basin with arbitrary topography. For illustration, we consider a rectangular basin and a linear topography h=by which represents either a real bottom topography or the beta-effect appropriate to oceanic situations. Our minimum enstrophy principle is motivated by different arguments of statistical mechanics reviewed in the article. It leads to steady states of the quasigeostrophic (QG) equations characterized by a linear relationship between potential vorticity q and stream function psi. For low values of the energy, we recover Fofonoff flows [J. Mar. Res. 13, 254 (1954)] that display a strong westward jet. For large values of the energy, we obtain geometry induced phase transitions between monopoles and dipoles similar to those found by Chavanis and Sommeria [J. Fluid Mech. 314, 267 (1996)] in the absence of topography. In the presence of topography, we recover and confirm the results obtained by Venaille and Bouchet [Phys. Rev. Lett. 102, 104501 (2009)] using a different formalism. In addition, we introduce relaxation equations towards minimum potential enstrophy states and perform numerical simulations to illustrate the phase transitions in a rectangular oceanic basin with linear topography (or beta-effect).Comment: 26 pages, 28 figure

Quasiperiodic waves at the onset of zero Prandtl number convection with rotation

We show the possibility of quasiperiodic waves at the onset of thermal convection in a thin horizontal layer of slowly rotating zero-Prandtl number Boussinesq fluid confined between stress-free conducting boundaries. Two independent frequencies emerge due to an interaction between a stationary instability and a self-tuned wavy instability in presence of coriolis force, if Taylor number is raised above a critical value. Constructing a dynamical system for the hydrodynamical problem, the competition between the interacting instabilities is analyzed. The forward bifurcation from the conductive state is self-tuned.Comment: 9 pages of text (LaTex), 5 figures (Jpeg format

Thermohaline structure in the California Current System : observations and modeling of spice variance

Author Posting. © American Geophysical Union, 2012. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 117 (2012): C02008, doi:10.1029/2011JC007589.Upper ocean thermohaline structure in the California Current System is investigated using sustained observations from autonomous underwater gliders and a numerical state estimate. Both observations and the state estimate show layers distinguished by the temperature and salinity variability along isopycnals (i.e., spice variance). Mesoscale and submesoscale spice variance is largest in the remnant mixed layer, decreases to a minimum below the pycnocline near 26.3 kg m−3, and then increases again near 26.6 kg m−3. Layers of high (low) meso- and submesoscale spice variance are found on isopycnals where large-scale spice gradients are large (small), consistent with stirring of large-scale gradients to produce smaller scale thermohaline structure. Passive tracer adjoint calculations in the state estimate are used to investigate possible mechanisms for the formation of the layers of spice variance. Layers of high spice variance are found to have distinct origins and to be associated with named water masses; high spice variance water in the remnant mixed layer has northerly origin and is identified as Pacific Subarctic water, while the water in the deeper high spice variance layer has southerly origin and is identified as Equatorial Pacific water. The layer of low spice variance near 26.3 kg m−3 lies between the named water masses and does not have a clear origin. Both effective horizontal diffusivity, κh, and effective diapycnal diffusivity, κv, are elevated relative to the diffusion coefficients set in the numerical simulation, but changes in κh and κv with depth are not sufficient to explain the observed layering of thermohaline structure.We gratefully acknowledge funding from the Gordon and Betty Moore Foundation, the Coastal Ocean Currents Monitoring Project (COCMP), and NOAA. R. E. Todd was partially supported by the Postdoctoral Scholar Program at the Woods Hole Oceanographic Institution, with funding provided by the Cooperative Institute for the North Atlantic Region.2012-08-0

CS22964-161: A Double-Lined Carbon- and s-Process-Enhanced Metal-Poor Binary Star

A detailed high-resolution spectroscopic analysis is presented for the carbon-rich low metallicity Galactic halo object CS 22964-161. We have discovered that CS 22964-161 is a double-lined spectroscopic binary, and have derived accurate orbital components for the system. From a model atmosphere analysis we show that both components are near the metal-poor main-sequence turnoff. Both stars are very enriched in carbon and in neutron-capture elements that can be created in the s-process, including lead. The primary star also possesses an abundance of lithium close to the value of the ``Spite-Plateau''. The simplest interpretation is that the binary members seen today were the recipients of these anomalous abundances from a third star that was losing mass as part of its AGB evolution. We compare the observed CS 22964-161 abundance set with nucleosynthesis predictions of AGB stars, and discuss issues of envelope stability in the observed stars under mass transfer conditions, and consider the dynamical stability of the alleged original triple star. Finally, we consider the circumstances that permit survival of lithium, whatever its origin, in the spectrum of this extraordinary system.Comment: manuscript, 7 tables, 13 figures. ApJ, in pres

The spatial distribution and annual cycle of upper ocean thermohaline structure

Author Posting. © American Geophysical Union, 2012. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 117 (2012): C02027, doi:10.1029/2011JC007033.Observations of the spatial distribution and persistence of thermohaline structure are presented, and show how advection and diffusion affect a passive tracer. More than two years of underwater glider observations in the central subtropical North Pacific showed thermohaline variability over horizontal scales from 5 to 1300 km. Thermohaline fluctuations along isopycnals (spice fluctuations) were elevated in layers throughout the water column with the largest fluctuations near the surface and subtropical frontal regions. Fluctuations were uncorrelated between the layers but stirred by the same velocity field. Spice variance had local extrema in the vertical because of differences in source water properties and the influence of neighboring water masses. Spice variance spanned about three orders of magnitude along deeper isopycnals with larger variance where different water masses met and where velocity and vorticity variance were elevated. Horizontal wave number spectra of spice had slopes of −2 everywhere in the upper 1000 m. Submesoscale spice fluctuations had slopes in physical space near the ratio of the Coriolis parameter to the buoyancy frequency (f/N), consistent with predictions of quasi-geostrophic theory. In the mixed layer, thermohaline structure had a significant annual cycle with smaller interannual differences. Thermohaline fluctuations left behind during restratification and isolated from the mixed layer decayed with time because of diffusion along isopycnals. Horizontal diffusivity estimates in the remnant mixed layer were 0.4 m2 s−1 at 15–28 km wavelengths and 0.9 m2 s−1 at 35–45 km wavelengths.We gratefully acknowledge the National Science Foundation for funding this work under grant number OCE0452574.2012-08-1