A self-similar solution of a curved shock wave and its time-dependent force variation for a starting flat plate airfoil in supersonic flow

The problem of aeroelasticity and maneuvering of command surface and gust wing interaction involves a starting flow period which can be seen as the flow of an airfoil attaining suddenly an angle of attack. In the linear or nonlinear case, compressive Mach or shock waves are generated on the windward side and expansive Mach or rarefaction waves are generated on the leeward side. On each side, these waves are composed of an oblique steady state wave, a vertically-moving one-dimensional unsteady wave, and a secondary wave resulting from the interaction between the steady and unsteady ones. An analytical solution in the secondary wave has been obtained by Heaslet and Lomax in the linear case, and this linear solution has been borrowed to give an approximate solution by Bai and Wu for the nonlinear case. The structure of the secondary shock wave and the appearance of various force stages are two issues not yet considered in previous studies and has been studied in the present paper. A self-similar solution is obtained for the secondary shock wave, and the reason to have an initial force plateau as observed numerically is identified. Moreover, six theoretical characteristic time scales for pressure load variation are determined which explain the slope changes of the time-dependent force curve.     

Numerical modeling of propagation of breaking nonlinear acoustic-gravity waves from the lower to the upper atmosphere

Acoustic-gravity waves (AGWs) observed in the upper atmosphere may be generated near the Earth’s surface due to a variety of meteorological sources. Two-dimensional simulations of vertical propagation and breaking of nonlinear AGWs in the atmosphere are performed. Forcing near the Earth’s surface is used as the AGW source in the model. We use a numerical method based on finite-difference analogues of fundamental conservation laws for solving atmospheric hydrodynamic equations. This approach selects physically correct generalized solutions of the wave hydrodynamic equations. Numerical simulations are performed in a representative region of the Earth’s atmosphere up to altitude 500 km. Vertical profiles of temperature, density, molecular viscosity and heat conductivity were taken from the standard atmosphere model MSIS-90 for January. Calculations were made for different amplitudes and frequencies of lower boundary wave forcing. It is shown that after activating the tropospheric wave forcing, the initial pulse of AGWs may very quickly propagate to altitudes of 100 km and above and relatively slowly dissipate due to molecular viscosity and heat conduction. This may increase the role of transient nonstationary waves in effective energy transport and variations of atmospheric parameters and gas admixtures in a broad altitude range.     

Effect of q-nonextensive hot electrons on bifurcations of nonlinear and supernonlinear ion-acoustic periodic waves

Nonlinear and supernonlinear ion-acoustic periodic waves are investigated in a three-component unmagnetized plasma which consists of mobile fluid cold ions, Maxwellian cold electrons and q-nonextensive hot electrons employing phase plane analysis. Using the traveling wave transformation, the plasma system is reduced to a planar autonomous dynamical system. Utilizing phase plane analysis of planar dynamical systems, all possible phase portraits including nonlinear homoclinic orbit, nonlinear periodic orbit, supernonlinear homoclinic orbit and supernonlinear periodic orbit are presented depending on physical parameters $q,\alpha ,\sigma$ and V. Using numerical simulations, nonlinear and supernonlinear ion-acoustic periodic waves are shown for different conditions. It is found that the nonextensive parameter q plays a crucial role in the bifurcations of nonlinear and supernonlinear ion-acoustic periodic waves. Our study may be applicable to understand the nonlinear and supernonlinear periodic features in auroral plasma.     

Kink mode m = 1 in magnetic tube with discontinuous magnetic field

In this paper, we study conditions of realization and stability of kink modes with azimuthal wave numbers $m=\pm 1$ in cylindrical plasma flex with twisted magnetic field and homogeneous current along its axis. We assume permanent axial magnetic field both inside and outside the flex, surrounded by currentless plasma. Azimuthal magnetic field decreases inversely proportional to the distance from the boundary beyond the flex. We derived dispersion equations for stable and unstable modes in approximation of “thin” plasma flex. The analysis of equations has been provided for the case of discontinuous axial magnetic field on flex’s boundary. Conditions of propagation of wave modes have been defined. It was shown, that unstable modes can be implemented in certain interval of longitudinal wavenumbers. Results can be applied for the interpretation of solar magnetic tubes behavior, using measurements, provided by spacecrafts.     

声重波激发的赤道Spread—F的拓扑特性研究

本文对声重波激发的Spread-F扰动的非线性制约方程的拓扑特性进行了定性讨论和数值计算．研究了Spread-F的混沌特征及参数范围．结果表明声重波在不同条件时对Spread-F的激发作用有本质的不同．     

Alfvén gravity waves in viscous solar plasma: Effect of the background flow

We study the Propagation and damping properties of Alfvén gravity waves in the presence of the vertical magnetic field in the viscous solar plasma under influence of the background flow by deriving a fourth order dispersion relation in terms of the Doppler shifted frequency. We derive the dispersion relation under WKB and Boussinesq approximation. We study the damping of Alfvén gravity waves for the wave frequencies less than and greater than the Brunt-Väisälä frequency. We find that the Brunt-Väisälä frequency divides the frequency ranges where the weakly or strongly damped oscillations occur. The background flow exhibits a strong effect on weakly damped oscillations and a weak effect on the strongly damped oscillations. We also notice that the damping of both the strong and weakly damped oscillations depend on the Brunt-Väisälä frequency and wave number. The effect of the background flow is also being governed by the Brunt-Väisälä frequency and wave number. We also study the properties of gravity wave mode after filtering the Alfvén wave mode by minimizing the magnetic field and noticed that the background flow shows a very strong effect on the gravity wave mode.