平方根深度波方程
The Square Root Depth Wave Equations
摘要：
我们引入了一组耦合方程的多层水波，消除了不适定性的多层Green-Naghdi（MGN）方程中存在的剪切。新的适定方程是哈密顿的，在没有施加背景剪切的情况下，它们保留了与MGN相同的行波解。我们称之为平方根深度方程，从他们的垂直运动的动能的修改形式的新模型。我们的数值结果显示了如何平方根深度方程模型的多层波的传播和相互作用的影响，有和没有剪切。
英文摘要：
We introduce a set of coupled equations for multilayer water waves that removes the ill-posedness of the multilayer Green-Naghdi (MGN) equations in the presence of shear. The new well-posed equations are Hamiltonian and in the absence of imposed background shear they retain the same travelling wave solutions as MGN. We call the new model the Square Root Depth equations, from the modified form of their kinetic energy of vertical motion. Our numerical results show how the Square Root Depth equations model the effects of multilayer wave propagation and interaction, with and without shear.
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