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<p>In this paper, we focus on the characteristics of the velocity field described by the Navier-Stokes equations for a compressible viscous fluid with the dynamic eddy viscosity varying only in the vertical direction in spherical coordinates. Considering non-equatorial zonal flows with longitudinal invariance, we reduce the governing equations to a linear parabolic evolution equation, which can be solved employing the method of separation of variables. By prescribing the dynamic eddy viscosity as a power function of height above the ground–a profile that can be either monotonically increasing or decreasing depending on the parameter–we obtain an exact velocity field that varies with time, radial distance, and latitude.</p>

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Exact viscous flow describing the dynamics of the atmosphere away from the Equator

  • 期刊论文

  • 发表日期：

    2026年7月8日

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  • Lili Fan,
  • Xin Zhang

摘要

In this paper, we focus on the characteristics of the velocity field described by the Navier-Stokes equations for a compressible viscous fluid with the dynamic eddy viscosity varying only in the vertical direction in spherical coordinates. Considering non-equatorial zonal flows with longitudinal invariance, we reduce the governing equations to a linear parabolic evolution equation, which can be solved employing the method of separation of variables. By prescribing the dynamic eddy viscosity as a power function of height above the ground–a profile that can be either monotonically increasing or decreasing depending on the parameter–we obtain an exact velocity field that varies with time, radial distance, and latitude.