The probability density function (PDF) for a decaying passive scalar advected by a deterministic, periodic, incompressible fluid flow is numerically studied using a variety of random and coherent initial scalar fields. We establish the dynamic emergence at large Péclet numbers of a broad-tailed PDF for the scalar initialized with a Gaussian random measure, and further explore a rich parameter space involving scales of the initial scalar field and the geometry of the flow. We document that the dynamic transition of the PDF to a broad tailed distribution is similar for shear flows and time-varying non-sheared flows with positive Lyapunov exponent, thereby showing that chaos in the particle trajectories is not essential to observe intermittent scalar signals. The role of the initial scalar field is carefully explored. The long time PDF is sensitive to the scale of the initial data. For shear flows we show that heavy-tailed PDFs appear only when the initial field has sufficiently small-scale variation. We also connect geometric features of the scalar field with the shape of the PDFs. We document that the PDF is constructed by a subtle balance between spatial regions of strong and weak shear in conjunction with the presence of

We investigate the interaction of two ellipsoidal vortices in the three-dimensional quasigeostrophic fluid equations by first studying a reduced model of vortex interaction, the ellipsoidal moment model, and second by comparing the results to corresponding numerical simulations. The ellipsoidal moment model approximates the interaction of two ellipsoidal lumps of potential vorticity by a finite-degree-of-freedom Hamiltonian system. This approximation is derived explicitly in the natural moment coordinate system to first order in the ratio of the size of the vortices to their separation. Using this Hamiltonian system for the case of initially spheroidal identical vortices, the linear stability of vertically aligned vortices is analyzed. A new dynamical criterion for vortex merger and alignment is proposed and shown to give a clear and reasonable boundary for vortex merger. A similar boundary is shown to exist in the size of the largest Lyapunov exponent, although not in the chaotic region as measured by the 0-1 test of Gottwald and Melbourne ͓Proc. R. Soc. London, Ser. A 460, 603 ͑2004͔͒. There is no such sharp boundary for vortex alignment in this reduced model. A series of numerical experiments confirms the accuracy of the merger criterion used in the ellipsoidal moment model. The numerical simulations also suggest a mechanism for understanding the process of vortex alignment in terms of vortex Rossby waves.

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