三维非静力平衡大气中平行切变流上重力内波的不稳定及半椭圆定理

本文应用守恒型非弹性模式研究了三维非静力平衡大气中平行切变流上重力内波的不稳定，推广了Miles定理和半圆定理，得到了有限深度气层的半椭圆定理。该定理指出不稳定波的复波速被限制在相速复平面上一个内接于霍华德（Howard）半圆的半椭圆内。该半椭圆长轴重合于半圆的直径，而短轴则取决于最小Ri数、波长、波宽等因素。

Instability and Semi-Ellipse Theorem of lnternal Gravity Wave on a Three Dimensional Non-Hydrostatic Shear Flow

By use of an energy--conservated anelastic model, the instability of stratified shear flow ina finite depth invisid atmosphere has been studied. The semi--ellipse theorem of unstable modes has been established. The theorem means that the complex wave velocity for any unstable modes lies in a semi--ellipse whose major axis coincides with the diameter of the Howard's semi--circle, while its minor axis depends not only on the minimum Richardson number and the wave number but also on the depth of the atmosphere.