In this paper, we study three-dimensional equatorial flows with constant vorticity beneath a wave train and above a flat bed in the $\beta$-plane approximation with centripetal forces by adopting higher order approximation about the Coriolis terms. We show that the new approximation about the Coriolis forces is also applicable for certain problem, which help us to derive the same result.

中文翻译：

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一种用向心力研究 $\beta$ 平面近似中恒定涡度水流的新方法

在本文中，我们通过采用关于科里奥利项的高阶近似，在具有向心力的 $\beta$ 平面近似中研究波列下方和平台上方具有恒定涡量的三维赤道流。我们表明关于科里奥利力的新近似也适用于某些问题，这有助于我们得出相同的结果。