Determination of the coronal magnetic field by coronal loop oscillations

We develop a new method for the determination of the absolute value of the magnetic field strength in coronal closed magnetic structures, based on the analysis of flare-generated oscillations of coronal loops. Interpretation of the oscillations observed in terms of global standing kink waves allows to connect the period of the oscillations and the loops length with the magnetic field strength in the loops. For loop oscillations observed with TRACE on 14th July 1998 and 4th July 1999, we estimate the magnetic field strength as 4-30 G. Using TRACE 171 Å and 195 Å images of the loop, taken on 4th July 1999 to determine the plasma density, we estimate the magnetic field in the loop as 13 +- 9 G. Improved diagnostic of the loop length, the oscillation period, and the plasma density in the loop will significantly improve the method's precision

High-frequency Alfven waves in multi-ion coronal plasma : observational implications

We investigate the effects of high-frequency (of order ion gyrofrequency) Alfvén and ion-cyclotron waves on ion emission lines by studying the dispersion of these waves in a multi-ion coronal plasma. For this purpose we solve the dispersion relation of the linearized multifluid and Vlasov equations in a magnetized multi-ion plasma with coronal abundances of heavy ions. We also calculate the dispersion relation using nonlinear one-dimensional hybrid kinetic simulations of the multi-ion plasma. When heavy ions are present the dispersion relation of parallel propagating Alfvén cyclotron waves exhibits the following branches (in the positive Ω − k quadrant): right-hand polarized nonresonant and left-hand polarized resonant branch for protons and each ion. We calculate the ratio of ion to proton velocities perpendicular to the direction of the magnetic field for each wave modes for typical coronal parameters and find strong enhancement of the heavy ion perpendicular fluid velocity compared with proton perpendicular fluid velocity. The linear multifluid cold plasma results agree with linear warm plasma Vlasov results and with the nonlinear hybrid simulation model results. In view of our findings we discuss how the observed nonthermal line broadening of minor ions in coronal holes may relate to the high-frequency wave motions

Nonlinear Discrete Systems with Nonanalytic Dispersion Relations

A discrete system of coupled waves (with nonanalytic dispersion relation) is derived in the context of the spectral transform theory for the Ablowitz Ladik spectral problem (discrete version of the Zakharov-Shabat system). This 3-wave evolution problem is a discrete version of the stimulated Raman scattering equations, and it is shown to be solvable for arbitrary boundary value of the two radiation fields and initial value of the medium state. The spectral transform is constructed on the basis of the D-bar approach.Comment: RevTex file, to appear in Journ. Math. Phy

Rectangular Cutthroat Flow Measuring Flumes

Introduction: Procedures and methods for more accurate measurement and improved management of water are continually being sought to make better use of our water resources. Of all the devices and structures developed for measuring water, measuring flumes are among the most widely accepted and used. The most common measuring flume is the Parshall flume developed by Ralph Parshall at Colorado State University. Common to most flumes is the basic geometry consisting of a converging inlet section, a throat, and a diverging outlet section. Occasionally, the diverging outlet section is removed under free flow conditions, and the water is allowed to jet directly from the throat section into the downstream channel. This is not always permissible, however, in unlined channels because of possible erosion problems. In flat gradient channels, a flume may be installed to operate under conditions of submerged flow rather then free flow in order to (1) reduce energy losses, and (2) allow placement of the flume on the channel bed to minimize the increase in water surface elevation upstream from the flume. The purpose of the research effort reported herein was to develop a flume which would operate satisfactorily under both free flow and submerged flow conditions

Analysis of Submergence in Flow Measuring Flumes

Submerged flow exists in a measuring flume when a change in flow depth downstream from the flume causes a change in flow depth upstream for any particular constant value of discharge. When a change in tailwater depth does not affect the upstream depth, free flow exists. To evaluate the discharge under free-flow conditions, it is necessary to measure only a flow depth upstream from the contracted section (throat) of the flume, whereas two flow depths must be measured to evaluate the discharge under submerged-flow conditions. The two flow depths normally measured when submerged flow exists consist of the same upstream depth used for free flow and a depth measured in the throat, although this need not be the case as will be shown later. Most of the earlier investigations regarding measuring flumes have emphasized the development of free-flow calibrations or ratings for various flume geometries. Notable free flow investigations have been made by V. M. Cone, Parshall, Engel, Khafagi, Robinson and Chamberlain, and Ackers and Harrison, to mention a few. Various methods of analyzing submerged flow have been presented by Parshall, Khafagi, Villemonte and Gunaji, Robinson and Chamberlain, and Robinson. Parameters describing submergence in flow-measuring flumes will be developed from dimensional analysis. A combination of empiricism and dimensional analysis will be used to develop a submerged flow discharge equation. The resulting discharge equation will be compared with the theoretical submerged-flow equation developed from momentum relationships. A rectangular flat-bottomed flow measuring flume was used to generate data necessary for establishing the parameters describing submerged flow. The form of the discharge equations describing submerged flow in a rectangular flume has been verified for a trapezoidal flat-bottomed flume, a rectangular flat-bottomed flume, and a Parshall flume

Subcritical Flow Over Highway Embankments

Introduction: At Utah State University, considerable effort has been devoted to the analysis of submerged flow at open channel constrictions. A method of analyzing subcritical (submerged) flow has been developed for flumes. Because of previous findings, it was felt that this method of analyzing submerged flow could be applied to highway embankments. A highway embankment, when overtopped by flood waters, is a form of broad-crested weir. Being a weir, the flood discharge over the embankment is only a function of the upstream depth for free flow conditions. This paper will present a method for determining the discharge under submerged flow conditions using the upstream and downstream depths. Thus, postflood field measurements and observations, when properly obtained, will provide the necessary information for an accurate determination of the flood discharge for either free or submerged flow conditions. One of the earliest studies regarding flow over an embankment was reported by Yarnell and Nagler. More recent experimental data have been reported by Kindsvater. The data collected by Kindsvater have been reanalyzed in this paper according to recent developments. The experimental models studied by Kindsvater are comparable to a secondary highway embankment. The data resulting from the model studies have been subjected to the method of submerged flow analysis previously employed with flow measuring flumes. The consistency of the data, both for free flow and submerged flow, reflects the quality of the experimental design and procedures used in collecting the data. Although the data presented in this paper apply only to various forms of secondary road embankments, the method of analysis is general

Molecular Gas in the Powerful Radio Galaxies 3C~31 and 3C~264: Major or Minor Mergers?

We report the detection of $^{12}$CO~($1 \to 0$) and $^{12}$CO~($2 \to 1$) emission from the central regions ($\lesssim 5$--$10 {\rm kpc}$) of the two powerful radio galaxies 3C~31 and 3C~264. Their individual CO emission exhibits a double-horned line profile that is characteristic of an inclined rotating disk with a central depression at the rising part of its rotation curve. The inferred disk or ring distributions of the molecular gas is consistent with the observed presence of dust disks or rings detected optically in the cores of both galaxies. For a CO to H$_2$ conversion factor similar to that of our Galaxy, the corresponding total mass in molecular hydrogen gas is $(1.3 \pm 0.2) \times 10^9 {\rm M_{\odot}}$ in 3C~31 and $(0.31 \pm 0.06) \times 10^9 {\rm M_{\odot}}$ in 3C~264. Despite their relatively large molecular-gas masses and other peculiarities, both 3C~31 and 3C~264, as well as many other powerful radio galaxies in the (revised) 3C catalog, are known to lie within the fundamental plane of normal elliptical galaxies. We reason that if their gas originates from the mergers of two gas-rich disk galaxies, as has been invoked to explain the molecular gas in other radio galaxies, then both 3C~31 and 3C~264 must have merged a long time (a few billion years or more) ago but their remnant elliptical galaxies only recently (last tens of millions of years or less) become active in radio. Instead, we argue that the cannibalism of gas-rich galaxies provides a simpler explanation for the origin of molecular gas in the elliptical hosts of radio galaxies. Given the transient nature of their observed disturbances, these galaxies probably become active in radio soon after the accretion event when sufficient molecular gas agglomerates in their nuclei.Comment: 16 pages, 1 JPEG figure attached, accepted for publication in ApJ

Negaton and Positon solutions of the soliton equation with self-consistent sources

The KdV equation with self-consistent sources (KdVES) is used as a model to illustrate the method. A generalized binary Darboux transformation (GBDT) with an arbitrary time-dependent function for the KdVES as well as the formula for $N$-times repeated GBDT are presented. This GBDT provides non-auto-B\"{a}cklund transformation between two KdV equations with different degrees of sources and enable us to construct more general solutions with $N$ arbitrary $t$-dependent functions. By taking the special $t$-function, we obtain multisoliton, multipositon, multinegaton, multisoliton-positon, multinegaton-positon and multisoliton-negaton solutions of KdVES. Some properties of these solutions are discussed.Comment: 13 pages, Latex, no figues, to be published in J. Phys. A: Math. Ge