Folding in fluids

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 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].

[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 vortex 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)].

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic

Mathematical models and integration methods