• G. NATH

      Articles written in Journal of Astrophysics and Astronomy

    • Cylindrical ionizing shock waves in a self-gravitating gas with magnetic field: Power series method

      G. NATH SUMEETA SINGH

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      The propagation of cylindrical ionizing shock waves in a self-gravitating ideal gas with axial magnetic field is investigated. The density and magnetic pressure are assumed to be varying according to power law with distance in the undisturbed medium. Approximate analytical solutions are obtained by expanding the flow variables in power series. The zeroth order and first order approximate solutions are discussed. Solutions for zeroth order approximation are constructed in analytical form. Distributions of hydrodynamical quantities for zeroth order approximation are discussed. Also, the effect of various flow parameters, namely shock Cowling number, adiabatic exponent, gravitational parameter and ambient density variation exponent are studied on the flow variables.

    • Approximate analytical solution for shock wave in rotational axisymmetric perfect gas with azimuthal magnetic field: Isothermal flow

      G. NATH SUMEETA SINGH

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      The propagation of cylindrical shock wave in rotational axisymmetric perfect gas under isothermal flow condition with azimuthal magnetic field is investigated. Distributions of gas dynamical quantities are discussed. The density, magnetic pressure, azimuthal fluid velocity and axial fluid velocity are assumed to bevarying according to power law with distance from the axis of symmetry in the undisturbed medium. Approximate analytical solutions are obtained by expanding flow variables in power series. Zeroth-order and first-order approximations are discussed with the aid of power series method. Solutions for zeroth-order approximation are constructed in approximate analytical form. The effect of flow parameters namely: shock Cowling number $C_0$, ambient density variation index $q$ and adiabatic exponent $\gamma$ are studied on the flow variables. Consideration of magnetic pressure increases the total energy of disturbance of zeroth order while with increase in ambient density variation index or adiabatic exponent, the total energy of disturbance decreases.

    • Approximate analytical solution for the propagation of shock waves in selfgravitating perfect gas via power series method: isothermal flow

      G. NATH

      More Details Abstract Fulltext PDF

      For the propagation of a shock (blast) in a self-gravitating perfect gas in case of spherical and cylindrical symmetry, an approximate analytical solution is investigated. The shock wave is considered to be a strong one, with the ratio $(C/V_S)^2$ to be a small quantity, where $C$ is the sound speed in an undisturbed medium and $V_S$ is the shock wave velocity. The initial density in the undisturbed medium is taken to be varying according to a power law. To obtain the approximate closed-form similarity solution, the flow variables are expanded in a power series of $(C/V_S)^2$. The first- and second-order approximations are discussed with the help of power series expansion. The analytical solutions are constructed for the first-order approximation. The distribution of the flow variables for first-order approximation in the flow field region behind the shock wave is shown in graphs for both the cylindrical and spherical geometries. The effect of flow parameters, namely, ambient density variation index $\alpha$, adiabatic exponent $\gamma$ and gravitational parameter $G_0$, are studied on the flow variables and on the total energy of disturbance in the case of the first approximation to the solutions. It is shown that the total energy of the disturbance in the flow field region behind the shock wave decreases with an increase in initial density variation index or adiabatic exponent, i.e. shock strength increases with increase in the value of adiabatic exponent or initial density variation index. A comparison is also made between the solutions obtained for non-gravitating and self-gravitating gases.

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