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SUMMARY:Nonlinear dynamics of slipping flows - Evgenii Kuznetsov (Lebedev 
 Physical Institute)
DTSTART:20221017T150000Z
DTEND:20221017T153000Z
UID:TALK182489@talks.cam.ac.uk
DESCRIPTION:The process of breaking of inviscid incompressible flows along
  a rigid body with slipping boundary conditions is studied. Such slipping 
 flows may be considered compressible on the rigid surface\, where the norm
 al velocity vanishes. It is the main reason for the formation of a singula
 rity for the gradient of the velocity component parallel to rigid border. 
 Slipping flows are studied analytically in the framework of two- and three
 -dimensional inviscid Prandtl equations. Criteria for a gradient catastrop
 he are found in both cases. For 2D Prandtl equations breaking takes place 
 both for the parallel velocity along the boundary and for the\nvorticity g
 radient. For three-dimensional Prandtl flows\, breaking\, i.e. the formati
 on of a fold in a finite time\, occurs for the symmetric part of the veloc
 ity gradient tensor\, as well as for the antisymmetric part - vorticity. T
 he problem of the formation of velocity gradients for flows between two pa
 rallel plates is studied numerically in the framework of two-dimensional E
 uler equations. It is shown that the maximum velocity gradient grows expon
 entially with time on a rigid boundary with a simultaneous increase in the
  vorticity gradient according to a double exponential law. Careful analysi
 s shows that this process is nothing more than the folding\, with a power-
 law relationship between the maximum velocity gradient and its width: $\\m
 ax|u_x|\\propto \\ell^{-2/3}$.\n&nbsp\;\nCo-author: Evgenii A. MIkhailov (
 Moscow State University\, Moscow\, Russia)\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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