A nonlinear Schrödinger equation for gravity waves slowly modulated by linear shear flow<xref rid="cpb_28_12_124701_fn1" ref-type="fn">*</xref><fn id="cpb_28_12_124701_fn1"><label>*</label><p>Project supported by the National Key Research and Development Program of China (Grant Nos. 2016YFC1401404 and 2017YFA0604102) and the National Natural Science Foundation of China (Grant No. 41830533).</p></fn>

A nonlinear Schrödinger equation for gravity waves slowly modulated by linear shear flow**

Project supported by the National Key Research and Development Program of China (Grant Nos. 2016YFC1401404 and 2017YFA0604102) and the National Natural Science Foundation of China (Grant No. 41830533).

Li Shaofeng, Chen Juan, Cao Anzhou^†, Song Jinbao^‡

Schematic of the Eulerian framework for two-dimensional propagating gravity waves with a linear shear flow. Here ζ(x,t) is the free surface elevation and c is the wave velocity. (a) Waves propagating upstream with uniform up-flow (U < 0) and negative vorticity (Ω < 0). (b) Waves propagating downstream with uniform down-flow (U > 0) and positive vorticity (Ω > 0).