正压海洋地形拦截波的不稳定

INSTABILITY OF BAROTROPIC COASTAL TRAPPED WAVES

从描述f平面上的正压地形拦截波的非线性动力方程出发,利用常微分方程定性理论研究了海底地形坡度和海底摩擦对线性和非线性地形拦截波的动力不稳定性的影响,分析了不稳定的性质,找出了不稳定的判据。还在特定的海底地形坡度和海底摩擦条件下,建立了线性和非线性波的频散关系,并比较了两者的差别。

Based on the nonlinear dynamical equations ignoring the shearing basic currents and the stability theory of ordinary differential equation, the author investigates the effects of the bottom friction and slope on the instability of linear and nonlinear barotropic coastal trapped waves on an f-plane. An attempt is also made to reveal the stability of both linear and nonlinear coastal trapped waves. The main results are summarized as follows:1. The linear continental shelf wave tends to be unstable (or stable) if the slope of seabed is smaller (or greater) than its positive critical value (dh/dx)c. The bottom fractional effect will enlarge the critical value for the bottom slope.2. The edge wave propagating along positive y-axis are always stable. For the edge wave propagating along negative y-axis, (i) if the bottom slope is smaller than (dh/dx)c, (dh/dx)'d is of critical value which enables the waves to change their stability feature; (ii) if the bottom slope is equal to (dh/dx)d but smaller than (dh/dx)c, the linear edge wave will have a stable sinusoidal solution, and the nonlinear edge wave become unstable in the special case where the bottom frictional effect is small enough; (iii) if the bottom slope is greater than(dh/dx)c, the edge wave may be unstable.3. In majority, the stability feature of the nonlinear coastal trapped wave is the same as those of the linear ones, but it may be different in certain cases.4. The characteristics of the nonlinear edge wave under the special bottom topography or friction differ from those of the linear ones. The nonlinear wave is not only related to the wave number, frequency and other physical parameters, (just as the linear ones do), but also depends on wave amplitude.