Previously, we have reported theory and experiments on the spin-up of a linearly stratified fluid contained in a sealed square cylinder with a bottom sloped at angle \(\alpha\) (Munro & Foster, Phys. Fluids, 26, 026603, 2014). The motion is characterized by the small Rossby number, \(\epsilon\), the fractional change in the rotation rate, the Ekman number, E, and the Burger number, S, the square of the ratio of the buoyancy frequency (or Brunt-Väisälä frequency) to the base rotation rate. This paper, supplementing what has gone before, is focused on the horizontal and vertical structure of the propagating vorticity waves (Rossby waves), with alternating anti-cyclonic and cyclonic cells, which move across the tank from east to west, thereby accomplishing at least the early stages of the spin-up. We find strong dependence of the modal structure of these Rossby waves, and their speed, on the Burger number. However, what is particularly noteworthy is the observed strong north-south asymmetry of the wave field. We find that the asymmetry is not consistent with typical Rossby-wave theories (Pedlosky and Greenspan, J. Fluid Mech., 27, p. 291, 1967), but is attributable to second-order effects in the asymptotic expansion of the streamfuntion in powers of \(\alpha\).

以前，我们已经报道了关于线性分层流体旋转的理论和实验，该流体包含在一个底部倾斜角度为\(\alpha\)的密封方形圆柱体中(Munro & Foster, Phys. Fluids , 26 , 026603, 2014 ）。运动的特征在于小罗斯比数\(\epsilon\)、旋转速率的分数变化、埃克曼数E和伯格数S，浮力频率（或 Brunt-Väisälä 频率）与基本旋转速率之比的平方。本文作为对前文的补充，重点研究了传播涡度波（罗斯比波）的水平和垂直结构，具有交替的反气旋和气旋单元，它们从东向西穿过水箱，从而至少完成旋转的早期阶段。我们发现这些罗斯比波的模态结构及其速度对伯格数有很强的依赖性。然而，特别值得注意的是观察到的波场强烈的南北不对称性。我们发现不对称与典型的罗斯贝波理论不一致（Pedlosky and Greenspan, J. Fluid Mech. , 27，页。291, 1967)，但归因于\(\alpha\)幂的流函数的渐近展开中的二阶效应。