Folding in fluids

• 主讲人：E.A. Kuznetsov (P.N. Lebedev Physical Institute of RAS)
• 举办方： Beijing-Moscow Mathematics Colloquium
• 时间： 2023-05-19 17:00 - 2023-05-19 18:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/69AF81979252F9687C2BA1087CB71CAE
Valid Until: 2027-06-30 23:59

 

Abstract: The formation of the coherent vortical structures in the form of thin pancakes for three-dimensional flows is studied at the high Reynolds regime when, in the leading order, the development of such structures can be described within the Euler equations for ideal incompressible fluids. Numerically and analytically on the base of the vortex line representation [1, 2] we show that compression of such structures and respectively increase of their amplitudes are possible due to the compressibility of the vorticity ω in the 3D case [3]. It is demonstrated that this growth has an exponential behavior and can be considered as folding (analog of breaking) for the divergence-free fields of vorticity. At high amplitudes this process in 3D has a self-similar behavior connected the maximal vorticity and the pancake width by the relation of the universal type [4]: ω_max ∝ l ^−2/3

[1] E.A. Kuznetsov, V.P. Ruban, Hamiltonian dynamics of vortex lines for systems of the hydrodynamic type, Pis’ma ZhETF , 76, 1015 (1998) [JETP Letters, 67, 1076-1081 (1998)].

[2] E.A. Kuznetsov, Vortex line representation for flows of ideal and viscous fluids , Pis’ma v ZHETF, 76, 406-410 (2002) [JETP Letters, 76, 346-350 (2002)].

[3] D.S. Agafontsev, E.A. Kuznetsov, A.A. Mailybaev, and E.V. Sereshchenko, Compressible vortical structures and their role in the hydrodynamical turbulence onset, UFN 192, 205-225 (2022) [Physics Uspekhi, 65 189 - 208 (2022)].

[4] D.S. Agafontsev, E.A. Kuznetsov and A.A. Mailybaev, Development of high vorticity structures and geometrical properties of the vortex line representation, Phys. Fluids 30, 095104-13 (2018); Stability of tangential discontinuity for the vortex pancakes, Pisma ZHETF, 114, 67-71 (2021) [JETP Letters, 2021, 114, 71–75 (2021)]

 

Bio: Evgeny A. Kuznetsov is currently a Principle Research Fellow at Lebedev Physical Institute of RAS and Landau Institute for Theoretical Physics. He graduated from Novosibirsk State University in 1969 and received PhD from the Institute for Nuclear Physics in 1973. In 1981, he obtained the Doctor of Sciences degree at Space Research Institute. Kuznetsov is an Academician of RAS since 2016. His research interests include developed turbulence in plasma physics, hydrodynamics, magnetohydrodynamics, and stability problems of nonlinear waves and solitons.