Nonlinear dynamics of slope flows: Simple models and exact solutions

Руденко, О. В.; Собисевич, А. Л.; Собисевич, Л. Е.

doi:10.1134/s1028334x07070288

Cited by 4 publications

(6 citation statements)

References 2 publications

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“…The solution of Eq. ( 12) corresponding to the initial power profile ρ(T, Z = 0) = ρ 0 P (T /T 0 ) can be written in implicit form as [21] ρ(T, Z) = ρ 0 P T − 3Z ρ(T, Z) /T 0 (13) or, in more compact notation, as…”

Section: Nonlinear Riemann Wavesmentioning

confidence: 99%

Optical tsunamis: shoaling of shallow water rogue waves in nonlinear fibers with normal dispersion

Wabnitz¹

2013

J. Opt.

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Abstract. In analogy with ocean waves running up towards the beach, shoaling of prechirped optical pulses may occur in the normal group-velocity dispersion regime of optical fibers. We present exact Riemann wave solutions of the optical shallow water equations and show that they agree remarkably well with the numerical solutions of the nonlinear Schrödinger equation, at least up to the point where a vertical pulse front develops. We also reveal that extreme wave events or optical tsunamis may be generated in dispersion tapered fibers in the presence of higher-order dispersion.

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Section: Nonlinear Riemann Wavesmentioning

confidence: 99%

Optical tsunamis: shoaling of shallow water rogue waves in nonlinear fibers with normal dispersion

Wabnitz¹

2013

J. Opt.

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“…The solution (24) has been obtained by Rudenko et al [2007] for the particular case of free gravity flow (no friction) above an inclined plate ( m → ∞). Similar solutions have been studied for water waves above a horizontal bottom and in channels with parabolic‐like cross section [ Pelinovsky and Troshina , 1994; Zahibo et al , 2008a].…”

Section: Nonlinear (Riemann) Wave Presentation Of the Gravity Driven mentioning

confidence: 99%

“…[15] The solution (24) has been obtained by Rudenko et al [2007] for the particular case of free gravity flow (no friction) above an inclined plate (m ! 1).…”

Section: Nonlinear (Riemann) Wave Presentation Of the Gravity Driven mentioning

confidence: 99%

“…Some attempts have been made to simulate submarine landslides using the full three‐dimensional (3‐D) Navier‐Stokes equations [ Heinrich et al , 1998, 1999; Mangeney et al , 2000b]. Similar models developed to describe dry subaerial avalanches, pyroclastic and debris flows including possible sources of tsunami, have aroused much interest in the last decade [see also Gray et al , 1999; Mangeney et al , 2000b; Heinrich et al , 2001; Bouchut et al , 2003; Mangeney‐Castelnau et al , 2003, 2005; Le Friant et al , 2006; Fernandez‐Feria , 2006; Rudenko et al , 2007; Mangeney et al , 2007a; Bouchut et al , 2008; Pirulli and Mangeney , 2008; Pelanti et al , 2008; Yu et al , 2009; Luca et al , 2009]. Most of such models of landslides and avalanches are based on homogeneous shallow water flows that are deformed during propagation.…”

Section: Introductionmentioning

confidence: 99%

“… Fernandez‐Feria [2006] extended this analysis to arbitrary bottom slopes; the axisymmetric dam break problem is solved by Kerswell [2005]. Rudenko et al [2007] found the exact solution that represented the nonlinear deformed wave in an ideal flow (neglected friction) along a plate of a constant slope.…”

Section: Introductionmentioning

confidence: 99%

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Savage‐Hutter model for avalanche dynamics in inclined channels: Analytical solutions

et al. 2010

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[1] The Savage-Hutter model is applied to describe gravity driven shallow water flows in inclined channels of parabolic-like shapes modeling avalanches moving in mountain valleys or landslide motions in underwater canyons. The Coulomb (sliding) friction term is included in the model. Several analytical solutions describing the nonlinear dynamics of avalanches are obtained: the nonlinear deformed (Riemann) wave, the dam break problem, self-similar solutions and others. Some of them extend the known solution for an inclined plate (one-dimensional geometry). The cross-section shape of the inclined channels significantly influences the speed of avalanche propagation and characteristic time of dynamical processes. Obtained analytical solutions can be used to test numerical models and to give insights into the structure of avalanche flow and to highlight basic mechanisms of avalanche dynamics.

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