The propagation of a cylindrical shock wave under the influence of an azimuthal magnetic field in a rotating medium for adiabatic flow conditions is investigated using the Lie group transformation method. The density, magnetic field, and azimuthal and axial fluid velocities are assumed to vary in the undisturbed medium. The arbitrary constants appearing in the expressions for the infinitesimals of the local Lie group of transformations bring about different cases of solutions, i.e., with a power-law shock path, with an exponential-law shock path, and a particular case of a power-law shock path. Numerical solutions are obtained in the case of a power-law shock path and exponential-law shock path. The distributions of gasdynamical quantities are discussed based on figures. The effects of varying the values of the adiabatic exponent \(\gamma \), Alfven–Mach number \(M_\mathrm{A}^{-2}\), ambient azimuthal fluid velocity variation index \(\lambda _{1}\), and ambient density variation index \(\phi \) on the flow variables and shock strength are studied. With an increase in the adiabatic exponent or the strength of the magnetic field, the shock strength decreases. However, an increase in the ambient density variation index or ambient azimuthal fluid velocity variation index results in an increase in the shock strength. The numerical calculations are carried out using Mathematica software.

使用李群变换法研究了在绝热流动条件下旋转介质中方位角磁场作用下圆柱激波的传播。假定密度，磁场以及方位和轴向流体速度在未受干扰的介质中均发生变化。局部李群变换的无穷小表达式中出现的任意常数带来了不同的解情况，即幂律冲击路径，指数律冲击路径以及幂函数的特殊情况。法律冲击路径。在幂律冲击路径和指数律冲击路径的情况下获得数值解。基于数字讨论了气体动力学量的分布。改变绝热指数值的影响\（\ gamma \），Alfven–马赫数\（M_ \ mathrm {A} ^ {-2} \），环境方位角流体速度变化指数\（\ lambda _ {1} \）和环境密度变化指数\ （\ phi \）对流动变量和冲击强度进行了研究。随着绝热指数或磁场强度的增加，冲击强度降低。然而，环境密度变化指数或环境方位角流体速度变化指数的增加导致冲击强度的增加。数值计算使用Mathematica软件进行。