Dynamics of Internal Envelope Solitons in a Rotating Fluid of a Variable Depth

• Published in: Fluids (Basel) Vol. 4; no. 1; p. 56
• Main Author: Stepanyants, Yury
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 21.03.2019
• Subjects: Carrier waves; Coastal zone; Conservation laws; Earth’s rotation; envelope soliton; Growth rate; internal waves; modulation instability; nonlinear Schrödinger equation; Rotating fluids; Schrodinger equation; Solitary waves; two-layer fluid; variable bottom; Velocity
• ISSN: 2311-5521; 2311-5521
• DOI: 10.3390/fluids4010056

We consider the dynamics of internal envelope solitons in a two-layer rotating fluid with a linearly varying bottom. It is shown that the most probable frequency of a carrier wave which constitutes the solitary wave is the frequency where the growth rate of modulation instability is maximal. An envelope solitary wave of this frequency can be described by the conventional nonlinear Schrödinger equation. A soliton solution to this equation is presented for the time-like version of the nonlinear Schrödinger equation. When such an envelope soliton enters a coastal zone where the bottom gradually linearly increases, then it experiences an adiabatical transformation. This leads to an increase in soliton amplitude, velocity, and period of a carrier wave, whereas its duration decreases. It is shown that the soliton becomes taller and narrower. At some distance it looks like a breather, a narrow non-stationary solitary wave. The dependences of the soliton parameters on the distance when it moves towards the shoaling are found from the conservation laws and analysed graphically. Estimates for the real ocean are presented.