两层海洋对风场气候异常响应的解析解及其讨论

Study of Two-Layer Ocean Model Forced by Climate Wind Anomalies

利用一个β通道线性化两层正压准平衡海洋模型,解析求解了两层海洋流场对时变风场(风场异常)的响应,得到了时变风场强迫下该海洋流场响应的斜压模态,而该模型中的正压模态则因其与实际情况不符,应弃之。在海洋上层该斜压模态中,西边界附近的海洋流场响应表现为一对由气旋性曲率和反气旋性曲率组成的涡旋偶;在时刻t=0和t=T/2(T为风场变化周期),β通道中线上分别有西风异常和东风异常最大,故响应表现为东向流和西向流;而在β通道的南北侧边界上响应表现为逆流;此时响应变化较缓慢,但强度大。在时刻t=T/4和t=3T/4,虽无大气风场异常强迫,但因海洋运动的惯性,响应仍不为0;此时,响应变化较剧烈,但强度小,且其流向也发生反转,这时上述涡旋偶也表现得最清晰。在海洋下层,海洋流场响应的强度和时间变化与上层相似,但流向却相反,而这体现了响应的斜压性。该海洋流场响应的频率与时变风场异常的频率相同,但存在位相差。因模型中采用了无辐散近似,故响应的性质为准平衡涡旋波,当风应力强迫和瑞利摩擦不太大时,即为海洋Rossby波。对该流场响应的振幅做了估计,发现风应力越大,β通道半宽越大,耗散越小,风应力变化的频率越低,则该响应就越大;在其他因子相同时,低频的风应力异常比高频的能激发出更大的海洋流场响应。得到的斜压模态的解析解与中纬度北太平洋在日本本州岛以东、以南的实际海洋上层流场异常相像,故其在一定程度上能够反映中纬度北太平洋海洋上层流场对实际风应力异常的响应情况;且其较我们以前得到的结果要优,适用性也更广,而这有助于揭示该响应的性质和机理。

In this paper, a β channel linear two-layer barotropic quasi-equilibrium ocean model forced by time-varying wind, that is wind anomalies, is established, and its analytical solutions are obtained. It should be noted that the following discussions pertain to the baroclinic mode because the barotropic mode is inconsistent with actual ocean conditions. In the western boundary, the upper corresponding flow field to time-varying wind is expressed as a couple of vortices with cyclonic and anti-cyclonic curvatures. In the upper ocean, obvious western and eastern flow can be forced on the β channel centerline at t=0 and t=T/2, where T is the varying period of wind field, because west and east wind are strongest at that time. Moreover, an obvious countercurrent appears at the south–north lateral boundary of the β channel. Although the forcing of wind disappears near t=T/4 and t=3T/4, oceanic flow anomalies remain due to inertia. In addition, the abnormal flow is strong and changes slowly at t=0 and t=T/2 but becomes weak, acute, and reverses its direction at t=T/4 and t = 3T/4. The corresponding ocean mode also shows that the strength of the lower flow is similar to that of the upper flow; however, the flow is in an opposite direction, which denotes the baroclinicity of the ocean. In analytical solutions, the fluctuation frequency of the ocean flow is the same as its forcing wind field with the exception of a fixed phase difference. Although the nature of the flow anomalies is a quasi-equilibrium vortex wave because only the vortex wave is included in the model, it will transform to a Rossby wave when the forcing wind stress and Rayleigh friction is small. Estimation of the flow amplitude shows that the corresponding flow anomalies become stronger with a higher wind stress, a wider half-width of β channel, a smaller dissipation and a slower changing frequency of wind stress. In addition, the low-frequency wind stress can initiate stronger flow anomalies than those for high-frequency wind stress under the same conditions. The spatial pattern of the corresponding ocean mode is similar to that of the flow anomalies over southeast Honshu Island in Japan. The analytical solutions obtained in this paper can reflect the upper flow anomalies forced by actual wind in the mid-latitude North Pacific to some extent; therefore, these results are helpful for demonstrating the corresponding mechanism of the upper flow to time-varying wind fields.