The barotropic vorticity equation is a classical model in atmospheric sciences. In this paper, we study the symmetry invariance properties of multipliers (integrating factors) admitted by this equation. The results are classified according to the ratio of the characteristic length scale to the Rossby radius of deformation and the variation of earth’s angular rotation. A plethora of conservation laws can be obtained by studying the interaction between Lie point symmetry generators and multipliers.

中文翻译：

---

正压涡度方程的新乘数

正压涡度方程是大气科学中的经典模型。在本文中，我们研究了该方程承认的乘数（积分因子）的对称不变性。根据特征长度尺度与Rossby变形半径之比和地球角旋转的变化将结果分类。通过研究李点对称发生器与乘子之间的相互作用，可以获得大量的守恒定律。