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Session: Vortex Dynamics 2
Session starts: Tuesday 25 August, 15:00
Presentation starts: 15:00
Room: Room B

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Dmitry Agafontsev (P. P. Shirshov Institute of Oceanology of RAS)
Evgenii Kuznetsov (P. N. Lebedev Physical Institute of RAS)
Alexey Mailybaev (Instituto Nacional de Matematica Pura e Aplicada)

Abstract:
This work is aimed for understanding nonlinear mechanisms at early stages of turbulence, when the flow is not yet affected by viscosity. Based on numerical simulations of the 3D incompressible Euler equations with generic large-scale initial conditions, we show that the exponential growth of vorticity developing in thin vortex sheets (pancake structures) leads to formation of Kolmogorov energy spectrum in fully inviscid flow. This direct observation yields the decoupling of the finite-time blowup problem from the Kolmogorov theory of turbulence. We demonstrate that the pancake structures have self-similar dynamics and evolve according to the scaling law W(t) ~ l(t)^(-2/3) for the local vorticity maximums W(t) and the transverse pancake scales l(t). Then, we argue that the energy spectrum requires an increasing number of such structures developing densely through the Kolmogorov range of wavenumbers, in good agreement with numerical data.