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A multiple scales analysis is used to derive a mixed Burgers-Korteweg-de Vries (BKdV) equation in the long wavelength regime for a two-fluid MHD model used to describe cosmic-ray acceleration by the first-order Fermi process in astrophysical shocks. The BKdV equation describes the time evolution of weak shocks in the theory of diffusive shock acceleration for all possible cosmic-ray pressures. Previous work on weak shocks in the cosmic-ray MHD model has assumed that dissipation alone is sufficient to balance nonlinearity, but, as cosmic-ray pressures become small, the weak shock becomes discontinous. By including Hall current effects into the MHD model, the low cosmic-ray pressure limit leads smoothly into solitary wave behaviour. For low cosmic-ray pressures, the shock has a downstream oscillatory precursor which is smoothed into the standard Taylor shock profile with increasing cosmic-ray pressure. As a by-product of the perturbation analysis, a dissipative KdV equation is derived. In conclusion, dispersive effects on Alfvén waves are discussed and a modulational stability analysis is presented.  相似文献   
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We investigate cosmic ray scattering in the direction perpendicular to a mean magnetic field. Unlike in previous articles we employ a general form of the turbulence wave spectrum with arbitrary behavior in the energy range. By employing an improved version of the nonlinear guiding center theory we compute analytically the perpendicular mean free path. As shown, the energy range spectral index, has a strong influence on the perpendicular diffusion coefficient. If this parameter is larger than one we find for some cases a perpendicular diffusion coefficient that is independent of the parallel mean free path and particle energy. Two applications are considered, namely transport of Galactic protons in the solar system and diffusive particle acceleration at highly perpendicular interplanetary shock waves.  相似文献   
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G. M. Webb  G. P. Zank 《Solar physics》1990,127(2):229-252
Solutions of the sine-Poisson equation are used to construct a class of isothermal magnetostatic atmospheres, with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model j is directed along the x-axis, where x is the horizontal ignorable coordinate. The current j varies as the sine of the magnetostatic potential and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. We investigate in detail solutions for the magnetostatic potential A corresponding to the one-soliton, two soliton, and breather solutions of the sine-Gordon equation. Depending on the values of the free parameters in the soliton solutions, horizontally, periodic magnetostatic structures are obtained possessing either (a) a single X-type neutral point, (b) multiple neutral X-points, or (c) solutions without X-points. The solution cases (b) and (c) contain two families of intersecting current sheets, in which the line of intersection forms flux concentration points (or singularities) for the magnetic field. The solutions illustrate the contribution of the anisotropic J × B force (B, magnetic field induction), the gravitational force, and the gas pressure gradient to the force balance.  相似文献   
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This paper describes the influence of noise on the u, v, and w wind components, which are measured by commonly used rectangular hot-film or hot-wire probes. It is shown that the distortion of the u, v, and w turbulence spectra may be entirely different, even if all three measured cooling velocities are equally disturbed by the same noise signal. A practical formalism is given for estimating the influence of any cooling velocity noise on the spectra and cospectra of u, v, and w. With inverted matrices, the original spectrum of a noise signal in the cooling velocities can be calculated from the observed u, v, and w spectra, assuming that the undisturbed shape of them is known.This work was supported by the Sonderforschungsbereich Meeresforschung of the Deutsche Forschungsgemeinschaft.  相似文献   
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The relationship between satellite-derived low-level cloud motion, surface wind and geostrophic wind vectors is examined using GATE data. In the trades, surface wind speeds can be derived from cloud motion vectors by the linear relation: V = 0.62 V s + 1.9 m s–1 with a mean scatter of ±1.3 m s–1. The correlation coefficient between surface and satellite wind speed is 0.25. Considering baroclinicity, i.e., the influence of the thermal wind, the correlation coefficient does not increase, because of the uncertainty of the thermal wind vectors. The ratios of surface to geostrophic wind speed and surface to satellite wind speed are 0.7 and 0.8, respectively, with a statistical uncertainty of ±0.3. Calculations of the ratio of surface to geostrophic wind speed on the basis of the resistance law yield V/V g = 0.8 ± 0.2, in agreement with experimental results. The mean angle difference between the surface and the satellite wind vectors amounts to - 18 °, taking into account baroclinicity. This value is in good agreement with the mean ageostrophic angle - 25 °.  相似文献   
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Crossings of the heliospheric current sheet (HCS) at the Earth’s orbit are often associated with observations of anisotropic beams of energetic protons accelerated to energies from hundreds of keV to several MeV and above. A connection between this phenomenon and the occurrence of small-scale magnetic islands (SMIs) near reconnecting current sheets has recently been found. This study shows how pre-accelerated protons can be energized additionally due to oscillations of multiple SMIs inside the ripple of the reconnecting HCS. A model of the electromagnetic field of an oscillating 3D SMI with a characteristic size of ~0.001 AU is developed. A SMI is supposed to be bombarded by protons accelerated by magnetic reconnection at the HCS to energies from ~1keV to tens of keV. Numerical simulations have demonstrated that the resulting longitudinal inductive electric fields can additionally reaccelerate protons injected into a SMI. It is shown that there is a local “acceleration” region within the island in which particles gain energy most effectively. As a result, their average escape energies range from hundreds of keV to 2 MeV and above. There is almost no particle acceleration outside the region. It is shown that energies gained by protons significantly depend on the initial phase and the place of their entry into a SMI but weakly depend on the initial energy. Therefore, low-energy particles can be accelerated more efficiently than high-energy particles, and all particles can reach the total energy limit upon their escape from a SMI. It is also found that the escape velocity possesses a strong directional anisotropy. The results are consistent with observations in the solar wind plasma.

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The structure of atmospheric turbulence in the surface layer over the open ocean is examined under conditions of local free convection. The raw data consist of profile and fluctuation measurements of wind and temperature as obtained from a meteorological buoy. For near neutral conditions and for waves running approximately along the wind direction, wave-induced wind fluctuations can be described by a simplified linear theory based on Miles (1957). In this case, the spectrum of wind velocity is given as the sum of two parts; for the turbulent part, the parameterization as obtained by Kaimal et al. (1972) applies, while the wave-induced part is parameterized using a simplification of Miles' linear theory. For cases of local free convection, the measurements of the vertical component of the wind velocity are well described by similarity theory; as expected, w /(-uw)1/2 is proportional to (- z/L)1/3. In order to scale the longitudinal wind velocity component, it seems to be reasonable to extend the list of relevant parameters by the height of the mixed layer z i. We obtain u /(- uw)1/2 (z/z i)1/3(- z/L)1/3 with only a poor correlation coefficient of r = 0.6. Overall, the results of local free convection scaling obtained from direct measurements show good agreement with those obtained from profile measurements. A comparison between direct and indirect determination of turbulent fluxes of momentum shows an unexplained difference of about 20%. This discrepancy is mainly due to a gap in the uw-cospectrum at the swell frequency.  相似文献   
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