Blowup phenomena in hydrodynamics, mechanism of developed turbulence, spontaneously stochastic solutions, shell models
We discuss a theoretical framework to define an optimal sub-grid closure for shell models of turbulence. The closure is based on the ansatz that consecutive shell multipliers are short-range correlated, following the third hypothesis of Kolmogorov formulated for similar quantities for the original three dimensional Navier-Stokes turbulence.
We present a theoretical argument showing that a classical deterministic solution before a finite-time blowup must be continued as a stochastic process after the blowup, representing a unique physically relevant description in the inviscid limit.
Incompressible 3D Euler equations develop high vorticity in very thin pancake-like regions from generic large-scale initial conditions. In this work we propose an exact solution of the Euler equations for the asymptotic pancake evolution.
Exceptional points in non-Hermitian systems, applications in optics and quantum physics
Systems with loss or gain have resonant modes that decay or grow with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, an ‘exceptional point’ occurs. We present an experiment with a waveguide that steers incoming waves around an exceptional point during the transmission. The induced transitions transform this device into an asymmetric switch between different waveguide modes.
J. Doppler, A.A. Mailybaev, J. Böhm, U. Kuhl, A. Girschik, F. Libisch, T.J. Milburn, P. Rabl, N. Moiseyev, S. Rotter, Dynamically encircling an exceptional point for asymmetric mode switching, Nature (2016) 537:7618, 76-79.
Selected for: Nature Physics News & Views.
Almost twenty years ago the light was slowed down to less than 10−7 of its vacuum speed in a cloud of ultracold atoms. Here we extend the phenomenon of stopped light to the new field of parity-time (PT) symmetric systems. We show that zero group speed in PT symmetric optical waveguides can be achieved if the system is prepared at an exceptional point, where two optical modes coalesce.
Singularities, instabilities, droplets formation
We disclose a new multiscale mechanism in which small-scale perturbations (ripples) on water surface are controlled by the large-scale wave dynamics in a way analogous to the adiabatic transport in quantum mechanics. Unlike classical hydrodynamic instabilities, this results in a super-exponential steepness amplification for small-scale ripples. We propose that this explosive increase of ripple steepness explains the breakdown of a smooth water surface into a spray with small droplets, commonly observed in ocean waves prior to overturning even in the absence of wind. The developed quantitative theory is shown to be in excellent agreement with numerical simulations.
(photo courtesy of Keahi de Aboitiz)
A.A. Mailybaev and A. Nachbin, Breakdown along an ocean wave surface prior to overturning, 2017. ArXiv:1707.07516.
Singular traveling waves in conservation laws, in-situ combustion, enhanced oil recovery (EOR)
This paper combines analytical and numerical studies of light oil recovery by air injection. Our solution shows that between regimes of total and partial oxygen consumption there is a change in the oxidation wave, which may have negative implications for oxygen breakthrough.
F.P. Santos, A.A. Mailybaev and D. Marchesin, Oxidation wave structure and oxygen breakthrough for air injection into light oil reservoirs, Computational Geosciences (2016) 20, 1095-1107. [Link] [PDF]
We study a nonlinear wave for a system of balance laws, which describes combustion for two-phase (gas and liquid) flow in a porous medium. The problem is formulated for a general N-component liquid for modeling multicomponent effects. Despite the immense complexity of the model, the problem allows an analytic solution. The clue to this solution is a special form of a folding singularity at an internal point of the wave profile.
M.A. Endo Kokubun and A.A. Mailybaev, Singularity of a combustion wave profile: a clue to the multicomponent theory for liquid-gas filtration, SIAM Journal on Applied Mathematics 77 (2017), 1375–1396. [Link] [PDF]