Abstract
The general initial value problem for the linearized von Karman vortex trail is solved. In particular, the fundamental differences between von Karman’s normal mode solutions and aperiodic solutions with compact support are discussed. Within the natural space ℓ 2 {\ell _2} , it is shown that the von Karman trail at its special aspect ratio (neutrally stable case) supports unbounded solutions. Two invariants of the equations determine whether a solution is bounded or unbounded. The asymptotic behaviour of aperiodic solutions is discussed. It is found that unbounded solutions grow at the rate O ( l n τ ) O\left ( {ln \tau } \right ) in ℓ ∞ {\ell _\infty } while bounded solutions decay as O ( 1 / τ ) O\left ( {1/\sqrt \tau } \right ) . In addition, a Loschmidt’s demon is constructed for the reversible dispersive equations which demonstrates the focussing effect in the von Karman trail.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
