Gravity wave turbulence revealed by horizontal vibrations of the container

We experimentally study the role of the forcing on gravity-capillary wave turbulence. Previous laboratory experiments using spatially localized forcing (vibrating blades) have shown that the frequency power-law exponent of the gravity wave spectrum depends on the forcing parameters. By horizontally vibrating the whole container, we observe a spectrum exponent that does not depend on the forcing parameters for both gravity and capillary regimes. This spatially extended forcing leads to a gravity spectrum exponent in better agreement with the theory than by using a spatially localized forcing. The role of the vessel shape has been also studied. Finally, the wave spectrum is found to scale linearly with the injected power for both regimes whatever the forcing type used

Comparing the statistics of interstellar turbulence in simulations and observations: Solenoidal versus compressive turbulence forcing

We study two limiting cases of turbulence forcing in numerical experiments: solenoidal (divergence-free) forcing, and compressive (curl-free) forcing, and compare our results to observations reported in the literature. We solve the equations of hydrodynamics on grids with up to 1024^3 cells for purely solenoidal and purely compressive forcing. Eleven lower-resolution models with mixtures of both forcings are also analysed. We find velocity dispersion--size relations consistent with observations and independent numerical simulations, irrespective of the type of forcing. However, compressive forcing yields stronger turbulent compression at the same RMS Mach number than solenoidal forcing, resulting in a three times larger standard deviation of volumetric and column density probability distributions (PDFs). We conclude that the strong dependence of the density PDF on the type of forcing must be taken into account in any theory using the PDF to predict properties of star formation. We supply a quantitative description of this dependence. We find that different observed regions show evidence of different mixtures of compressive and solenoidal forcing, with more compressive forcing occurring primarily in swept-up shells.Comment: 28 pages, 20 figures, published as Highlight Paper in A&A, 512, A81 (2010); simulation movies available at http://www.ita.uni-heidelberg.de/~chfeder/videos.shtml?lang=e

Steady free-surface flow over spatially periodic topography

Two-dimensional free-surface flow over a spatially periodic channel bed topography is examined using a steady periodically forced Korteweg-de Vries equation. The existence of new forced solitary-type waves with periodic tails is demonstrated using recently developed non-autonomous dynamical-systems theory. Bound states with two or more co-existing solitary waves are also identified. The solution space for varying amplitude of forcing is explored using a numerical method. A rich bifurcation structure is uncovered and shown to be consistent with an asymptotic theory based on small forcing amplitude..J. Binder, M.G. Blyth and S. Balasuriy

Symplectomorphisms and discrete braid invariants

Area and orientation preserving diffeomorphisms of the standard 2-disc, referred to as symplectomorphisms of $\mathbb{D}^{2}$, allow decompositions in terms of positive twist diffeomorphisms. Using the latter decomposition we utilize the Conley index theory of discrete braid classes as introduced in [Ghrist et al., C. R. Acad. Sci. Paris S\'er. I Math., 331(11), 2000, Invent. Math., 152(2), 2003] in order to obtain a Morse type forcing theory of periodic points: a priori information about periodic points determines a mapping class which may force additional periodic points.Comment: 31 pages, in print in Journal of Fixed Point Theory and Application