Two-flow Model Research Articles

Importance of Magnetic Effects in a Two-Flow Model for Extragalactic Radio Jets

We propose a model for extragalactic radio jets in which two different flows of particles are taken into account, (i) a beam of relativistic electrons and positrons extracted from the funnel of accretion disc and responsible for the observed superluminal motion, (ii) a classical or mildly relativistic wind of electrons and protons coming out from all parts of the disc (Sol et al., 1989). Studying the mutual interaction of the two flows, we show that the configuration is not destroyed by the plasma-beam instability as long as the magnetic field, assumed longitudinal, is strong enough, with an electron gyrofrequency ωc = eB/mec greater than the ambient plasma frequency ωp = (4πnpe2)1/2 (Pelletier et al., 1988). When ωc < ωp, the relativistic beam loses its energy and its momentum mainly through the development of strong Langmuir turbulence in the wind, and disappears quietly after some relaxation zone where heating and entrainment of the wind occur. This emphasizes one aspect of the important role likely played by the magnetic field in the dynamics of extragalactic jets and provides one example in which the magnetic field, acting on the microscopic scale of an interaction, induces strong effects on large–scale structures. Detailed data on the closest known superluminal radio source 3C120 (Walker et al., 1987, 1988; Benson et al., 1988) allow a check on the likelihood of our model. Observational estimates of the variation along the jet of the magnetic field and of the ambient plasma density np suggest that the magnetic field reaches its critical value (corresponding to ωc = ωp) at a minimal distance of about 1.4 kpc from the central engine. This is amazingly close to the location of the 4′–radio knot, a “rather curious structure” described by Walker et al. (1987), which we interpret as the beam relaxation zone in the context of our two–flow model (Sol et al., 1989).

Two-flow model for extragalactic radio jets

Different models of extragalactic jet formation have been proposed in the litterature. They usually considered only one population of particles, ascribing one typical bulk velocity to the jet. However from the point of view of plasma physics it seems very likely that beams of particles with different velocity will be generated in the surroundings of the central engine by any kind of jet acceleration mechanism. This can lead to a typical beam-plasma configuration with a slow ambient plasma pervaded by energetic beams which constitute a population inversion and are a potential source of energy and of instability.

Two-flow simulation of the natural light field within a canopy of submerged aquatic plants

A two-flow model is developed to simulate a light field composed of both collimated and diffuse irradiance within natural waters containing a canopy of bottom-adhering plants. To account for the effects of submerging a canopy, the transmittance and reflectance terms associated with each plant structure (leaves, stems, fruiting bodies, etc.) are expressed as functions of the ratio of the refractive index of the plant material to the refractive index of the surrounding media and the internal transmittance of the plant structure. Algebraic solutions to the model are shown to yield plausible physical explanations for unanticipated variations in volume reflectance spectra. The effect of bottom reflectance on the near-bottom light field is also investigated. These results indicate that within light-limited submerged aquatic plant canopies, substrate reflectance may play an important role in determining the amount of light available to the plants and, therefore, canopy productivity.

Analysis of ocean color spectra (III)

By using the two-flow optical model, the variation in the irradiance reflectance of the ocean just below the surface has been calculated for varying water optical properties, for the interpretation of remotely-sensed ocean color data. The input variables used in our model are the concentration of phytoplankton (chlorophyll-a), the absorption coeffiicient of yellow substance, the particle scattering coefficient, the ratio of the back-scattering coefficient to the total scattering coefficient of particles, and the ratio of the absorption to scattering coefficients for particles.

Applications of a two-flow model for remote sensing of substances in water

A version of the two-flow radiative transfer model is presented as a simple method to study the relationship between substances in water and the backscattered radiation field. It is shown that under the assumption of a diffuse radiative input into a water body, the irradiance attenuation coefficient k can be regarded as an inherent property. A cuvette system is presented which allows one to measure and calculate the attenuation coefficient k, the absorption coefficient a and the backscattering coefficient Bb of various substances. The model can be used to check the applicability of a remote sensing technique for a specific research area and for specific parameters, and to estimate the expected accuracy, and the signal depth. The inversion of the model can be applied as a technique to estimate concentrations in water from the backscattered radiation. The critical assumption of a diffuse radiative input and transfer, which has to be made when using the model for natural conditions, is discussed.

Algebraic expression for the diffuse irradiance reflectivity of water from the two-flow model

A simple expression is obtained for the irradiance reflectance of the ocean based on a two-flow radiative transfer model. This expression is found to reproduce the Monte Carlo calculations to within 7% for scattering albedo values less than 0.8. On the basis of this expression, it is shown that the remotely sensed water color data can be interpreted with the help of iterative optimization techniques, provided that the variations of backscattering coefficient and absorption coefficient with wavelength can be modeled.

Subsurface water parameters: optimization approach to their determination from remotely sensed water color data

A method, using an optimization scheme, has been developed for the interpretation of spectral albedo (or spectral reflectance) curves obtained from remotely sensed water color data. This method used a two-flow model of the radiation flow and solves for the albedo. Optimization fitting of predicted to observed reflectance data is performed by a quadratic interpolation method for the variables chlorophyll concentration and scattering coefficient. The technique is applied to airborne water color data obtained from Kawartha Lakes, Sargasso Sea, and Nova Scotia coast. The modeled spectral albedo curves are compared to those obtained experimentally, and the computed optimum water parameters are compared to ground truth values. It is shown that the backscattered spectral signal contains information that can be interpreted to give quantitative estimates of the chlorophyll concentration and turbidity in the waters studied.