arXiv subjects

D. S. Agafontsev

Publications and source records attributed to D. S. Agafontsev.

23 records · Page 2Linked to original sources

arXiv2015

Development of high vorticity structures in incompressible 3D Euler equations

We perform the systematic numerical study of high vorticity structures that develop in the 3D incompressible Euler equations from generic large-scale initial conditions. We observe that a multitude of high vorticity structures appear in the form of thin vorticity sheets (pancakes). Our analysis reveals the self-similarity of the pancakes evolution, which is governed by two different exponents $e^{-t/T_{\ell}}$ and $e^{t/T_ω}$ describing compression in the transverse direction and the vorticity growth respectively, with the universal ratio $T_{\ell}/T_ω \approx 2/3$. We relate development of these structures to the gradual formation of the Kolmogorov energy spectrum $E_{k}\propto\, k^{-5/3}$, which we observe in a fully inviscid system. With the spectral analysis we demonstrate that the energy transfer to small scales is performed through the pancake structures, which accumulate in the Kolmogorov interval of scales and evolve according to the scaling law $ω_{\max} \propto \ell^{-2/3}$ for the local vorticity maximums $ω_{\max}$ and the transverse pancake scales $\ell$.

physics.flu-dyn↗

arXiv2014

Oscillatory dynamics of the classical Nonlinear Schrodinger equation

We study numerically the statistical properties of the modulation instability (MI) developing from condensate solution seeded by weak, statistically homogeneous in space noise, in the framework of the classical (integrable) one-dimensional Nonlinear Schrodinger (NLS) equation. We demonstrate that in the nonlinear stage of the MI the moments of the solutions amplitudes oscillate with time around their asymptotic values very similar to sinusoidal law. The amplitudes of these oscillations decay with time $t$ as $t^{-3/2}$, the phases contain the nonlinear phase shift that decays as $t^{-1/2}$, and the period of the oscillations is equal to $π$. The asymptotic values of the moments correspond to Rayleigh probability density function (PDF) of waves amplitudes appearance. We show that such behavior of the moments is governed by oscillatory-like, decaying with time, fluctuations of the PDF around the Rayleigh PDF; the time dependence of the PDF turns out to be very similar to that of the moments. We study how the oscillations that we observe depend on the initial noise properties and demonstrate that they should be visible for a very wide variety of statistical distributions of noise.

nlin.SI↗

arXiv2013

Waves statistics for generalized one-dimensional Nonlinear Schrodinger Equation with saturated nonlinearity

We measure spectra, spatial correlation functions and probability density functions (PDFs) for waves amplitudes for generalized one-dimensional nonlinear Schrodinger (NLS) equation of focusing type with saturated nonlinearity. All additional terms beyond the classical NLS equation are small. As initial conditions we use perturbed by weak noise modulationally unstable condensate. On the PDFs we observe power-law region for small and medium amplitudes followed by intermediate region and then Rayleigh far tail. Power-law region appears starting from some critical levels of average amplitude and coefficient related to saturated nonlinearity, and then becomes more pronounced with average amplitude and saturation coefficient. Correlation of phases becomes significant for large wave events and contributes about one order of magnitude to the frequencies of their occurrence. Waves statistics for the considered systems turns out to be exceptionally stable against additional stochastic forces.

physics.optics↗

arXiv2008

Collapse of solitary waves near transition from supercritical to subcritical bifurcations

We study both analytically and numerically the nonlinear stage of the instability of one-dimensional solitons in a small vicinity of the transition point from supercritical to subcritical bifurcations in the framework of the generalized nonlinear Schrödinger equation. It is shown that near the collapsing time the pulse amplitude and its width demonstrate the self-similar behavior with a small asymmetry at the pulse tails due to self-steepening. This theory is applied to both solitary interfacial deep-water waves and envelope water waves with a finite depth and short optical pulses in fibers as well.

nlin.PS↗

arXiv2005

Deep-water internal solitary waves near critical density ratio

Bifurcations of solitary waves propagating along the interface between two ideal fluids are considered. The study is based on a Hamiltonian approach. It concentrates on values of the density ratio close to a critical one, where the supercritical bifurcation changes to the subcritical one. As the solitary wave velocity approaches the minimum phase velocity of linear interfacial waves (the bifurcation point), the solitary wave solutions transform into envelope solitons. In order to describe their behavior and bifurcations, a generalized nonlinear Schrödinger equation describing the behavior of solitons and their bifurcations is derived. In comparison with the classical NLS equation this equation takes into account three additional nonlinear terms: the so-called Lifshitz term responsible for pulse steepening, a nonlocal term analogous to that first found by Dysthe for gravity waves and the six-wave interaction term. We study both analytically and numerically two solitary wave families of this equation for values of the density ratio $ρ$ that are both above and below the critical density ratio $ρ_{cr}$. For $ρ>ρ_{cr}$, the soliton solution can be found explicitly at the bifurcation point. The maximum amplitude of such a soliton is proportional to $\sqrt{ρ-ρ_{cr}}$, and at large distances the soliton amplitude decays algebraically. A stability analysis shows that solitons below the critical ratio are stable in the Lyapunov sense in the wide range of soliton parameters. Above the critical density ratio solitons are shown to be unstable with respect to finite perturbations.

physics.flu-dyn↗