Topographic waves in a stratified elliptical basin, with application to the Lake of Lugano
Topographic waves in a stratified elliptical basin, with application to the Lake of Lugano
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分层椭圆盆地中的地形波，及其在卢加诺湖中的应用
DOI：
10.1098/rsta.1985.0055
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发表时间：
1985
期刊：
影响因子：
--
通讯作者：
T. Scheiwiller
中科院分区：
文献类型：
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作者：
L. Mysak;G. Salvadé;K. Hutter;T. Scheiwiller
本文提出了一种在分层的细长湖泊中风力产生地形波的理论。分层由上层厚度为D1的双层流体模拟，< D2，即特征下层深度。通过尺度分析表明，正压流函数和界面位移控制方程对在O（D1/D2）时解耦，而Jr满足包含风应力强迫的线性化位涡方程。然后将该方程的解代入ε的控制方程，现在可以根据已知的强迫x]s求解ε。Jr和ε的解接下来用于分别求出上层和下层速度u1和u2。对于O（D1/D2），速度场u2是正压的，而u1由正压部分、斜压部分和直接强迫风分量组成。水平海流一般是表层增强的。所描述的一般理论被应用到一个椭圆形的盆地中，其中的海岸线和深度轮廓线形成一个家庭ofconcentric椭圆。对于指数型的深度剖面，用变分法得到了描述自由椭圆行波的径向和方位正压模式的简单解。如果r21 < L2，则可以用初等函数来表示ε，u1和u2的相应解，其中r1是两层内部Rossby变形半径，L是湖的半长。该理论被应用到卢加诺湖，瑞士，在1979年夏季观察到一个明显的74小时振荡的温度和电流记录。它示出的周期，相位传播的方向，等温线深度振幅分布沿着湖，和水平电流运动与此信号是一致的模型的一个自由的，基本模式的地形波，周围的椭圆形盆地的代表性的卢加诺湖anticipally旅行。从尺度参数和交叉谱分析，它也表明，这波的能量来源可能是风沿着海岸在南端的湖泊。然而，一个完整的解决方案，强迫问题的观测风谱作为输入没有给出。地形波（旋转模式）在卢加诺湖的存在是令人惊讶的，考虑到这个阿尔卑斯湖的水平尺寸小（约17公里x1.5公里）。因此，将这里开发的理论应用于其他山间湖泊，看看这种尺度的低频地形波是否在自然界中普遍存在，这将是相当有趣的。
A theory is presented for the wind generation of topographic waves in a stratified, elongated lake. The stratification is modelled by a two-layer fluid with upper layer thickness D1, < D2, the characteristic lower layer depth. It is shown by means of scale analysis that to O(D1/D2), the governing pair of equations for the barotropic stream function ]s and interfacial displacement £ decouple, with Jr satisfying the linearized potential vorticity equation, which includes wind stress forcing. The solution of this equation is then substituted into the governing equation for £, which can now be solved in terms of the known forcing x]s. The solutions for Jr and £ are next used to find u1 and u2, the upper and lower layer velocities respectively. To O(D1/D2) the velocity field u2 is barotropic, whereas u1 consists of a barotropic part, a baroclinic part, and a directly forced wind component. The horizontal currents are generally surface intensified. The general theory described is applied to an elliptically shaped basin in which the shoreline and depth contours form a family ofconfocal ellipses. For an exponential depth profile, simple solutions for the radial and azimuthal barotropic modes describing free, elliptically travelling waves are obtained by using a variational method. The corresponding solutions for £, u1 and u2 can be expressed in terms of elementary functions provided r21 < L2, where r1 is the two-layer internal Rossby radius of deformation and L is the half-length of the lake. The theory is applied to the Lake of Lugano, Switzerland, where a distinct 74 h oscillation in both the temperature and current records was observed during summer 1979. It is shown that the period, direction of phase propagation, isotherm-depth amplitude distribution along the lake, and horizontal current motion associated with this signal are consistent with the model of a free, fundamental-mode topographic wave that travels anticlockwise around an elliptical basin representative of the Lake of Lugano. From scaling arguments and cross-spectral analysis it is also demonstrated that the energy source for this wave is probably the wind along the shore at the southern end of the lake. However, a complete solution to the forced problem with the observed wind spectrum as input is not given. The existence of topographic waves (rotational modes) in the Lake of Lugano is surprising, considering the small horizontal dimensions of this Alpine lake (approximately 17 km x 1.5 km). Thus it would be of considerable interest to apply the theory developed here to other intermontane lakes to see whether low-frequency topographic waves of this scale are a common occurrence in nature.