Dynamics of fingering convection II: The formation of thermohaline staircases

Regions of the ocean's 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.Comment: 18 pages, 9 figures, associated mpeg file at http://earth.uni-muenster.de/~stellma/movie_small.mp4, submitted to JF

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

Double-diffusive instabilities are often invoked to explain enhanced transport in stably-stratified 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 gamma-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 gamma-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.Comment: 23 pages, 9 figures, submitted to JF

Geometry of integrable dynamical systems on 2-dimensional surfaces

This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous invariants involved in this classification are the left equivalence classes of period or monodromy functions, and the cohomology classes of period cocycles, which can be expressed in terms of Puiseux series. We also study the problem of Hamiltonianization of these integrable vector fields by a compatible symplectic or Poisson structure.Comment: 31 pages, 12 figures, submitted to a special issue of Acta Mathematica Vietnamic

Boosting Local Field Enhancement by on-Chip Nanofocusing and Impedance-Matched Plasmonic Antennas

Strongly confined surface plasmon-polariton modes can be used for efficiently delivering the electromagnetic energy to nano-sized volumes by reducing the cross sections of propagating modes far beyond the diffraction limit, i.e., by nanofocusing. This process results in significant local-field enhancement that can advantageously be exploited in modern optical nanotechnologies, including signal processing, biochemical sensing, imaging and spectroscopy. Here, we propose, analyze, and experimentally demonstrate on-chip nanofocusing followed by impedance-matched nanowire antenna excitation in the end-fire geometry at telecom wavelengths. Numerical and experimental evidences of the efficient excitation of dipole and quadrupole (dark) antenna modes are provided, revealing underlying physical mechanisms and analogies with the operation of plane-wave Fabry-P\'erot interferometers. The unique combination of efficient nanofocusing and nanoantenna resonant excitation realized in our experiments offers a major boost to the field intensity enhancement up to $\sim 12000$, with the enhanced field being evenly distributed over the gap volume of $30\times 30\times 10\ {\rm nm}^3$, and promises thereby a variety of useful on-chip functionalities within sensing, nonlinear spectroscopy and signal processing

Efficient unidirectional nanoslit couplers for surface plasmons

Plasmonics is based on surface plasmon polariton (SPP) modes which can be laterally confined below the diffraction limit, thereby enabling ultracompact optical components. In order to exploit this potential, the fundamental bottleneck of poor light-SPP coupling must be overcome. In established SPP sources (using prism, grating} or nanodefect coupling) incident light is a source of noise for the SPP, unless the illumination occurs away from the region of interest, increasing the system size and weakening the SPP intensity. Back-side illumination of subwavelength apertures in optically thick metal films eliminates this problem but does not ensure a unique propagation direction for the SPP. We propose a novel back-side slit-illumination method based on drilling a periodic array of indentations at one side of the slit. We demonstrate that the SPP running in the array direction can be suppressed, and the one propagating in the opposite direction enhanced, providing localized unidirectional SPP launching.Comment: 13 pages, 4 figure

An Efficient Large-Area Grating Coupler for Surface Plasmon Polaritons

We report the design, fabrication and characterization of a periodic grating of shallow rectangular grooves in a metallic film with the goal of maximizing the coupling efficiency of an extended plane wave (PW) of visible or near-infrared light into a single surface plasmon polariton (SPP) mode on a flat metal surface. A PW-to-SPP power conversion factor > 45 % is demonstrated at a wavelength of 780 nm, which exceeds by an order of magnitude the experimental performance of SPP grating couplers reported to date at any wavelength. Conversion efficiency is maximized by matching the dissipative SPP losses along the grating surface to the local coupling strength. This critical coupling condition is experimentally achieved by tailoring the groove depth and width using a focused ion beam.Comment: The final publication is available at http://www.springerlink.com. http://dx.doi.org/10.1007/s11468-011-9303-

Efficient Excitation of Channel Plasmons in Tailored, UV-Lithography-Defined V-Grooves

[Image: see text] We demonstrate the highly efficient (>50%) conversion of freely propagating light to channel plasmon-polaritons (CPPs) in gold V-groove waveguides using compact 1.6 μm long waveguide-termination coupling mirrors. Our straightforward fabrication process, involving UV-lithography and crystallographic silicon etching, forms the coupling mirrors innately and ensures exceptional-quality, wafer-scale device production. We tailor the V-shaped profiles by thermal silicon oxidation in order to shift initially wedge-located modes downward into the V-grooves, resulting in well-confined CPPs suitable for nanophotonic applications

Thermochemical conversion of plant biomass in the energotechnological complex with heat recovery

Basic performance principles of the energotechnological complex used for thermochemical conversion of plant biomass with the influence of a magnetic field and high recovery of spent heat carrier energy have been developed. The concurrent saturation of a spent heat carrier in a loading bunker with the steam from humid biomass aimed at using a certain part of a spent heat carrier, which is clear from oxygen and nitrogen oxide, and moisture in thermochemical recovery has been considered as an important aspect of recuperation processes. A mathematical model has been developed and the results of numerical simulation have been presented for determining the distribution of temperature, velocity and pressure fields in a loading bunker. Prospective assessment of the engineering solutions developed for heat energy recovery of a double-flow spent heat carrier has been conducted