caa a22 4500 47574103X CHVBK 20180406123459.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1007/BF02676735 doi (NATIONALLICENCE)springer-10.1007/BF02676735 Yudovich V. Rostov State University, USSR aut On the unbounded increase in vorticity and velocity circulation in stratified and homogenous fluid flows [Elektronische Daten] [V. Yudovich] We consider the Oberbeck-Boussinesq system without dissipation (ideal convection) in a horizontal layer and in a "barrel” with flat bottom and flat cover. It is shown that the velocity circulation along a fluid contour consisting of two fluid curves on the bottom and on the cover connected by two isothermic fluid curves can be calculated explicitly and is a linear function of time. The serre result stating that the azimuthal component of vorticity in rotationally symmetric ideal fluid flows between coaxial cylinders increases linearly is generalized to the case of stratified fluids. It is proved that all plane and axially symmetric isothermic flows in a layer or in a barrel are unstable with respect to nonisothermic perturbations and in the case of a homogenous fluid all axially symmetric flows between coaxial cylinders are unstable in the sense of Lyapunov with respect to perturbations of the azimuthal component of the velocity in any metric including the maximum of magnitude of vorticity. Kluwer Academic/Plenum Publishers, 2000 ideal fluid nationallicence stratified fluid nationallicence plane flow nationallicence axisymmetric flow nationallicence rotationally symmetric flow nationallicence Oberbeck-Boussinesq equations nationallicence vorticity nationallicence velocity circulation nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/4(2000-10-01), 533-540 0001-4346 68:4<533 2000 68 11006 https://doi.org/10.1007/BF02676735 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02676735 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Yudovich V. Rostov State University, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/4(2000-10-01), 533-540 0001-4346 68:4<533 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer