三维重力波非线性传播数值模型的一种求解格式

A STUDY OF NONLINEAR PROPAGATION OF 3D GRAVITY-WAVE MCKETS IN A COMPRESSIBLE ATMOSPHERE BY USING ADI SCHEME

采用交替方向隐格式（ＡＤＩ）求解三维可压大气中重力波非线性传播的数值模型．经过几个波周期后，重力波波包仍然沿着线性理论射线方向稳定地传播，波包保持着很好的形状，内点和边界保持稳定；水平风与垂直运动的振幅随着传播高度的增加而增加．这说明ＡＤＩ格式是模拟三维可压大气中重力波传播的一种可靠的格式．模拟结果也表明，在非线性情况下，重力波仍可保持线性传播的某些特征，非线性效应主要表现在对波包传播速度的修正．

By using an Alternative- Direction- Implicit (ADI) scheme, a numerical model for nonlinear propagation of gravity-wave packets in a three-dimensional compressible atmosphere is solved. Results of numerical simulation show that after several periods, the gravity-wave packets propagate steadily upward and keep its shape well. The interior points and boundaries of the calculating region are stable. During the propagation the amplitude of wave-associated perturbation velocities increase with the increasing height. This shows that ADI scheme is reliable for simulating the nonlinear propagation of gravity-wave packets in a three-dimensional compressible atmosphere. From the results, It's also found that under nonlinear condition, a gravity wave packet is still able to keep some characterizations as under linear propagation. The nonlinear effect mainly impacts the propagation velocity of gravity-wave packets.