Effects of density differences on lateral mixing in open-channel flows

This study investigates lateral mixing of tracer fluids in turbulent open-channel flows when the tracer and ambient fluids have different densities. Longitudinal dispersion in flows with longitudinal density gradients is investigated also.

Lateral mixing was studied in a laboratory flume by introducing fluid tracers at the ambient flow velocity continuously and uniformly across a fraction of the flume width and over the entire depth of the ambient flow. Fluid samples were taken to obtain concentration distributions in cross-sections at various distances, x, downstream from the tracer source. The data were used to calculate variances of the lateral distributions of the depth-averaged concentration. When there was a difference in density between the tracer and the ambient fluids, lateral mixing close to the source was enhanced by density-induced secondary flows; however, far downstream where the density gradients were small, lateral mixing rates were independent of the initial density difference. A dimensional analysis of the problem and the data show that the normalized variance is a function of only three dimensionless numbers, which represent: (1) the x-coordinate, (2) the source width, and (3) the buoyancy flux from the source.

A simplified set of equations of motion for a fluid with a horizontal density gradient was integrated to give an expression for the density-induced velocity distribution. The dispersion coefficient due to this velocity distribution was also obtained. Using this dispersion coefficient in an analysis for predicting lateral mixing rates in the experiments of this investigation gave only qualitative agreement with the data. However, predicted longitudinal salinity distributions in an idealized laboratory estuary agree well with published data.

Infiltration of fine and coarse sand into an open-work gravel bed

The siltation of an experimental gravel bed, with three grades of sand moving in suspension and as bedload, was examined. The rate of infiltration of sand into the void space of the gravel was determined under differing conditions of discharge, water depth, and velocity (jointly expressed as variation in the Froude Number) and suspended sediment concentration. The downstream reduction in siltation from the point source was also examined.

Development of roll waves in open channels

This study is concerned with some of the properties of roll waves that develop naturally from a turbulent uniform flow in a wide rectangular channel on a constant steep slope . The wave properties considered were depth at the wave crest, depth at the wave trough, wave period, and wave velocity . The primary focus was on the mean values and standard deviations of the crest depths and wave periods at a given station and how these quantities varied with distance along the channel.

The wave properties were measured in a laboratory channel in which roll waves developed naturally from a uniform flow . The Froude number F (F = u_n/√gh_n, u_n = normal velocity , h_n = normal depth, g =acceleration of gravity) ranged from 3. 4 to 6. 0 for channel slopes S_o of . 05 and . 12 respectively . In the initial phase of their development the roll waves appeared as small amplitude waves with a continuous water surface profile . These small amplitude waves subsequently developed into large amplitude shock waves. Shock waves were found to overtake and combine with other shock waves with the result that the crest depth of the combined wave was larger than the crest depths before the overtake. Once roll waves began to develop, the mean value of the crest depths h_nmax increased with distance . Once the shock waves began to overtake, the mean wave period T_av increased approximately linearly with distance.

For a given Froude number and channel slope the observed quantities h^-_max/h_n , T' (T' = S_o T_av √g/h_n), and the standard deviations of h^-_max/h_n and T', could be expressed as unique functions of l/h_n (l = distance from beginning of channel) for the two-fold change in h_n occurring in the observed flows . A given value of h^-_max/h_n occurred at smaller values of l/h_n as the Froude number was increased. For a given value of h /hh^-_max/h_n the growth rate of δh^-_max/h^-_maxδl of the shock waves increased as the Froude number was increased.

A laboratory channel was also used to measure the wave properties of periodic permanent roll waves. For a given Froude number and channel slope the h^-_max/h_n vs. T' relation did not agree with a theory in which the weight of the shock front was neglected. After the theory was modified to include this weight, the observed values of h^-_max/h_n were within an average of 6.5 percent of the predicted values, and the maximum discrepancy was 13.5 percent.

For h^-_max/h_n sufficiently large (h^-_max/h_n > approximately 1.5) it was found that the h^-_max/h_n vs. T' relation for natural roll waves was practically identical to the h^-_max/h_n vs. T' relation for periodic permanent roll waves at the same Froude number and slope. As a result of this correspondence between periodic and natural roll waves, the growth rate δh^-_max/h^-_maxδl of shock waves was predicted to depend on the channel slope, and this slope dependence was observed in the experiments.

Characteristics of 980/1550 nm WDM coupler based on planar curved waveguides

A wavelength division multiplexer (WDM) for 980/1550 nm based on planar curved waveguide coupler (CWC) is proposed. Compared with conventional parallel straight waveguide coupler (SWC), this structure has more flexibility with two variable parameters of bending radius R and minimum edge-to-edge spacing do, which are the two main parameters for the splitting ratio of coupler and decrease the complexity of device design and fabrication. Based on coupled mode theory (CMT) and waveguide theory, R and do of the WDM CWC are designed to be R = 13.28 m and d(0) = 4.39 mu m. The contrast ratio (CR) and insertion loss (IL) for 980 and 1550 nm are CR1 = 24.62 dB, CR2 = 24.56 dB and IL1 = 0.014 dB, IL2 = 0.015 dB, respectively. The 3D beam propagation method (BPM) is used to verify the validity of the design result. The influence of R and d(0) variations on the device performance is analyzed. For CR > 20 dB, the variation ranges of R and d(0) should be within -0.10 to +0.44 m and -0.05 to + 0.02 mu m, respectively. (c) 2006 Elsevier GmbH. All rights reserved.

Prism coupling of ultrashort light pulses into waveguides

We discuss coupling of ultrashort light pulses into waveguides by use of a prism waveguide coupler configuration. Theoretical analysis indicates that an extra loss induced by the short coherence times of ultrashort pulses, which has a strong effect on the reflected light and the optimum coupling condition, appears in the waveguide. Numerical simulations show that the reflectance strongly depends on the coherence times of ultrashort pulses. A method for realizing optimum coupling by compensating for the extra loss is proposed as well in this paper. A preliminary experiment of employing ultrashort pulses with different coherence times was carried out, and good agreement between theory and experiment was obtained. (c) 2006 Optical Society of America.

Construction of the refractive index profiles for few-mode planar optical waveguides

We present a nondestructive technique to predict the refractive index profiles of isotropic planar waveguides, on which a thin gold film is deposited to as the cladding. The negative dielectric constant of the metal results in significant differences of effective indices between TE and TM modes. The two polarized modes and a surface plasmon resonance (SPR) with abundant information of the surface index can be used to construct the refractive index profiles of single-mode and two-mode waveguides at a fixed wavelength. (c) 2005 Elsevier B.V. All rights reserved.

Electromagnetic fields and transmission properties in tapered hollow metallic waveguides

We analyze the electromagnetic spatital distributions and address an important issue of the transmission properties of spherical transverse-electric (TE) and transverse-magnetic (TM) eigenmodes within a tapered hollow metallic waveguide in detail. Explicit analytical expressions for the spatital distributions of electromagnetic field components, attenuation constant, phase constant and wave impedance are derived. Accurate eigenvalues obtained numerically are used to study the dependences of the transmission properties on the taper angle, the mode as well as the length of the waveguide. It is shown that all modes run continuously from a propagating through a transition to an evanescent region and the value of the attenuation increases as the distance from the cone vertex and the cone angle decrease. A strict distinction between pure propagating and pure evanescent modes cannot be achieved. One mode after the other reaches cutoff in the tapered hollow metallic waveguide as the distance from the cone vertex desreases. (C) 2008 Optical Society of America

Low-loss planar and stripe waveguides in Nd3+-doped silicate glass produced by oxygen-ion implantation

We report on the fabrication and characterization of low-loss planar and stripe waveguides in a Nd3+-doped glass by 6 MeV oxygen-ion implantation at a dose of 1x10(15) ions/cm(2). The dark mode spectroscopy of the planar waveguide was measured using a prism coupling arrangement. The refractive index profile of the planar waveguide was reconstructed from a code based on the reflectivity calculation method. The results indicate that a refractive index enhanced region as well as an optical barrier have been created after the ion beam processing. The near-field mode profiles of the stripe waveguide were obtained by an end-fire coupling arrangement, by which three quasitransverse electric modes were observed. After annealing, the propagation losses of the planar and stripe waveguides were reduced to be similar to 0.5 and similar to 1.8 dB/cm, respectively. (c) 2007 American Institute of Physics.

Planar waveguides formed in a new chemically stable Er3+/Yb3+ co-doped phosphate glass

A new Er(3+)/Yb(3+) co-doped phosphate glass has been prepared, which exhibits good chemical durability and spectralproperties. Planar graded index waveguides have been fabricated in the glass by (Ag+)-Na(+) ion exchange in a mixed melt of silver nitrate and potassium nitrate. Ion exchange is carried out by varying the process parameters such as temperature, diffusion time, and molten salt compositions. The diffusion parameters, diffusion coefficients, and activation energy are determined by the guidelines of fabricated waveguides, which are determined by the input prism coupling technique.