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^‡

The MI gain spectrum Γ_i distributed on the initial amplitude and perturbation wave number space for ω = 3.4 Hz: (a) μ = 2, Ω¯=0 , u¯=−0.2 ; (b) μ = 2, Ω¯=0 , u¯=0 ; (c) μ = 2, Ω¯=0 , u¯=0.2 ; (d) μ = 5, u¯=0 , Ω¯=−0.2 ; (e) μ = 5, u¯=0 , Ω¯=0 ; (f) μ = 5, u¯=0 , Ω¯=0.2 . MI and MS denote modulational instability and modulational stability, respectively.