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Taylor's problem and morphodynamics

机译：泰勒问题和形态动力学

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In the fundamental process of reflection of Kelvin waves in a rectangular semi-enclosed basin, known as Taylor Problem, the generation of Poincare waves and sandbank formation are investigated applying a two-dimensional, vertically integrated numerical model. The Taylor problem separates clearly areas where Kelvin and Poincare waves exist. Without consideration of morphodynamics, the calculated pattern of currents agrees with previous solutions of Taylor Problem. If morphodynamics is allowed in the numerical modeling of the Taylor problem, sandbank-like bed forms appear at the closed boundary on the side where the incident Kelvin wave transforms into Poincare waves. The presence of sandbanks modifies the wavelength of Poincare waves generated in the vicinity of the closed boundary in relation to those produced in the calculation without consideration of morphodynamics. The Poincare waves are evanescent in both cases. The presence of sandbanks influences the generation of Poincare waves whereas the formation of sandbanks itself is initiated by Poincare waves. Using calculated wavelengths of Poincare waves and wavelengths of sandbanks, we show that sandbanks could be generated through a nonlinear interaction where friction and advection terms seem to play a relevant role. Numerical experiments reveal that a bay, located in the neighborhood of the closed boundary, diffracts the incident Kelvin wave producing also evanescent Poincare waves and modifying the generation of bed forms. A bay, located far away of the closed boundary generates Poincare waves which propagate in all directions. Trapped Poincare waves seem to favor the development of bed forms.
机译：在矩形半封闭盆地中的开尔文波反射的基本过程（称为泰勒问题）中，使用二维垂直积分数值模型研究了庞加莱波的产生和沙洲的形成。泰勒问题清楚地将开尔文波和庞加莱波存在的区域分开。在不考虑形态动力学的情况下，计算出的电流模式与泰勒问题的先前解一致。如果在泰勒问题的数值模型中允许形态动力学，则在入射开尔文波转换为庞加莱波的一侧的封闭边界处会出现沙丘状的床形。相对于计算中产生的波峰，沙洲的存在改变了在封闭边界附近产生的庞加莱波的波长，而无需考虑形态动力学。在这两种情况下，庞加莱波都是渐逝的。沙堤的存在影响庞加莱波的产生，而沙堤的形成本身是由庞加莱波引发的。使用庞加莱波的计算波长和沙洲的波长，我们表明，沙洲可以通过非线性相互作用产生，其中摩擦和对流项似乎起着重要作用。数值实验表明，位于封闭边界附近的海湾对入射的开尔文波产生了衍射，还产生了van灭的庞加莱波，并改变了床形的产生。距离封闭边界较远的海湾会产生庞加莱波，该波向各个方向传播。受困的庞加莱海浪似乎有利于床形的发展。

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