Tophøj, Laust Emil Hjerrild

Strømninger i vand bemærkes ofte ved at overfladen ændrer form. Vi kender det fra håndvasken, hvor en fordybning i vandoverfladen over afløbet fortæller os, at der er en hvirvel dernede. Men hvad kan man engentlig sige om strømningen, hvis man kender overfladens form? Det viser sig, at man kan sige en hel del. Iafhandlingens første del beskrives en teori for strømningen på en vandoverflade af konstant form. Desuden diskuteres et eksperiment, hvor en roterende væske i en rund beholder pludselig bliver ustabil og går fra en cirkulær til en kantet form. Teorien for overfladestrømninger bruges på dette eksperiment, og jeg fortæller om vores forsøg på at forstå de mystiske kantede former i strømningen. Afhandlingens anden del beskriver dynamikken i en simpel model af hvirvelstrømninger. Jeg præsenterer resultater om kaotisk bevægelse i et system af hvirvler og stabiliteten af den såkaldte “leapfrog”-bevægelse, hvor to par af hvirler overhaler hinanden på skift. Bevægelsen er ustabil under bestemte betingelser, som bestemmes matematisk.This PhD thesis consists of two main parts. The first part describes the dynamics of an ideal fluid on a stationary free surface of a given shape. It turns out that one can formulate a set of self-contained equations of momentum conservation for the tangential flow, with no reference to the flow of the fluid bulk. With these equations, one can in principle predict the surface flow on a given free surface, once its shape has been measured. The equations are expressed for a general surface using Riemannian geometry and their solutions are discussed, including some difficulties that may arise. Furthermore, the equations are applied to an experiment involving a poorly understood symmetry-breaking instability of a rotating fluid with a free surface, cf. Bergmann et al., [J. Fl. Mech. 679, 415-431 (2011)], with the result confirmed by direct measurement. This experiment is discussed in some detail together with an ongoing investigation of the fluid motion in question and the elusive instability mechanism. The second main part of the thesis describes work on point vortex dynamics and instability. The problem of point vortex pair scattering is briefly revisited together with a short discussion of chaotic advection, andthe stability of vortex leapfrogging is investigated within the framework of Floquet theory. An analytical criterion is found, giving the exact location of the transition to instability earlier observed in numerical investigations by Acheson [Eur. J. Phys. 21, 269-273 (2000)]. Finally, an experimental work on elastic collisions of wet spheres is briefly discussed

Online Research Database In Technology

Dynamics and Instabilities of Free Surface and Vortex Flows

http://orbit.dtu.dk/ws/files/9747889/LaustPHD.pdf

Dynamics and Instabilities of Free Surface and Vortex Flows

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Online Research Database In Technology