On a model for internal waves in rotating fluids Publié en ligne: 31 déc. 2018 Pages: 627 - 648 Reçu: 17 oct. 2018 Accepté: 31 déc. 2018 © 2018 A. Durán, published by Sciendo This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.
Fig. 1 Idealized model of internal wave propagation in a two-layer interface. ρ2 > ρ1; d2 > d1; ζ(x, t) denotes the downward vertical displacement of the interface from its level of rest at (x, t). Fig. 2 Amplitude (a) and wavelength (λ) of a wave. Fig. 3 Numerical approximation with α = 0, β = γ = δ = 1. Computed solitary wave profiles. Fig. 4 Numerical approximation with α = 0, β = γ = δ = 1. Phase portraits of the computed solitary wave profiles. Fig. 5 Numerical approximation with α = 0, β = γ = δ = 1. Speed-amplitude relations. Fig. 6 Two-pulse for α = 0, β = −1, γ = δ = 1, p = 2, cs = 1.1 and a negative hyperbolic-secant profile as initial data for the iteration (22), (23). Fig. 7 ω(k)/k vs k. Case β < 0. Fig. 8 ω(k)/k vs k for β > 0. (a) Solid line: A > 0, B > 0 (α = γ = 1/2, β = 2, δ = 1); dashed line: A < 0, B > 0 (α = γ = 1/2, β = 2, δ = 1/4); (b) Solid line: A > 0, B < 0 (α = γ = 1/2, β = δ = 1); dashed line: A < 0, B < 0 (α = 1/2, γ = 5, β = 1, δ = 1/8); (c) Magnification of (a); (d) Magnification of (b) Fig. 9 Amplitude vs β. Fig. 10 c∗=12−β1+β4δ+(4δ−β)γδ+β4δ2$\begin{array}{}
\displaystyle
c^{*} = \frac{1}{2}\left(-\beta\left(1+\frac{\beta}{4\delta}\right)+(4\delta-\beta)\sqrt{\frac{\gamma}{\delta}+\left(\frac{\beta}{4\delta}\right)^{2}}\right)
\end{array}$ vs β with α = 0, γ = δ = 1. Fig. 11 RMBenjamin vs Ostrovsky equations. Computed solitary wave profiles with (a) cs = 0.1, (b) cs = 0.9. Fig. 12 RMBenjamin vs Ostrovsky equations. Speed-amplitude relations.