Finite Time Singularities in Interface Dynamics 0.01truecm
There is some evidence that certain models of dynamical interfaces
have singularities, which develop at a finite time, after which they
blow up. We are developing a new technique, based on projection
from a space with one more spatial dimension, to check this.
-0.1truecm V. Putkaradze, T. Bohr, and (J. Krug)
0.3truecm Advection of Particles and Passive Scalars in Nonlinear Field Theories
0.01truecm Growth Shapes of Turbulent Spots in Unstable Systems
0.01truecm Space-Time Correlations in Turbulent Systems
0.01truecm Predictability in Turbulence
0.01truecm Experimental Study of the Circular Hydraulic Jump
0.01truecm Shell Models for 2-d Turbulence
0.01truecm Experimental and Theoretical Studies of
Turbulence in Soap Films and Pipe Flows
Advection of Particles and Passive Scalars in Nonlinear Field Theories 0.01truecmWe have developed a new method for studying the statistical properties of the turbulent states of non-linear PDE's especially the so-called Kuramoto-Sivashinsky equation and its generalizations. We seed the flow with fictitious particles (or a whole passively advected field). In this way one can study a wide class of transport phenomena in a setting which is much simpler than real 3d hydrodynamical turbulence, but has many of the same properties. We look at scaling properties (e.g. anomalous diffusion) and qualitative transitions, e.g. between pinned and flowing states in the presence of symmetry breaking terms. -0.1truecm T. Bohr and (A. Pikovsky) 0.3truecm
Growth Shapes of Turbulent Spots in Unstable Systems 0.01truecmIn a convectively unstable system, a localized disturbance will move "down-stream", while amplifying and spreading. We have studied the asymptotic form of such local disturbances in a very general setting of a PDE in one or 2 dimensions for a scalar field. In one dimension we have found analytically the form of the asymptotic field and predicted a novel type of instability for a generalized Kuramoto-Sivashinsky equation (NBI preprint 93-61). In two dimensions we show how to find the spatial shape of the spreading spots and note the transitions between different shapes and the appearance of non-convex growth forms (C. Conrado: Localized Disturbances in Chaotic and Unstable Systems. Ph.D. Thesis, University of Copenhagen 1993). -0.1truecm C. Conrado and T. Bohr 0.3truecm
Space-Time Correlations in Turbulent Systems 0.01truecmTurbulent, or space-time chaotic, systems are characterized by a set of Lyapunov exponents of which the number of positive ones are believed to be an extensive quantity (i.e. proportional to the system volume). This implies that distant parts are decorrelated. Often, however, the systems can have long range correlations e.g. like the scale invariant structure functions of fully developed fluid turbulence or interface models. The chaotic fluctuations should show the lack of correlations and we are trying to figure out the best ways of showing this for various systems. Further we are studying the influence of conservation laws, e.g. on the Lyapunov spectra. -0.1truecm T. Bohr, (G. Grinstein), C. Jayaprakash, and (W. van de Water) 0.3truecm
Predictability in Turbulence 0.01truecmWe study the growth of small perturbations in fully developed turbulence. By using approximations to the Navier-Stokes equations, so-called shell models, we have shown that the predictability time in strongly turbulent flows depends crucially on the strength of the intermittency of the energy dissipation at the small scales. A shell model is local in k-space and therefore non-local in real space as is the Navier-Stokes equations due to the pressure term. To check the generality our results we must therefore formulate models in real space which include non-local interactions. One may for instance study simple systems of coupled maps which contain non-local couplings. Preliminary results indicate good agreement with our results obtained using the shell models and we plan to pursue this question in more details. -0.1truecm M.H. Jensen (A. Crisanti), (G. Paladin), and (A. Vulpiani) 0.3truecm
Experimental Study of the Circular Hydraulic Jump 0.01truecmWhen a vertical jet of fluid is directed upon a horizontal surface, it spreads out radially and it is observed that at a certain radius the height of the fluid increases abruptly. This is known as the circular hydraulic jump. It is an interesting example of a nontrivial structure appearing on a fluid surface which, on average, remains fixed and shows a transition to turbulence. The height fluctuations of the surface have been studied using the absorption of a light beam. The resulting power spectra show interesting structures which may be understood in terms of classical orbits. -0.1truecm S. Hansen, S. Hørlück, D. Zauner, P. Dimon, C. Ellegaard, T. Sams, and S.C. Creagh 0.3truecm
Shell Models for 2-d Turbulence 0.01truecmWe investigate 2-d turbulence using shell models in k-space. A key point is to observe whether there are two scaling laws present for the energy spectrum, namely an inverse cascade with Kolmogorov scaling -5/3 and a forward cascade of scaling -3 below and above the point of energy input, respectively. All shell models, however, exhibit an inverse cascade with scaling -1, in contradiction to simple arguments based on dimensional analysis. We consider whether this discrepancy is due to fundamental reasons, and might thus be found in 2-d Navier-Stokes, or is due to the limitations of the shell models. -0.1truecm M.H. Jensen and (A. Brandenburg) 0.3truecm
Experimental and Theoretical Studies of Turbulence in Soap Films and Pipe Flows 0.01truecmSoap films have attracted much interest because of their two-dimensional nature. Our laboratory soap film flows last up to 1 hour, with the flow velocity determined by the viscosity and the height difference between the two containers between which the soap film is spanned, and measured by He-Ne laser-Doppler anemometry. Turbulence is produced at sufficiently high velocities. The theoretical problem is to describe the flow and the boundary air layer.
Velocity fluctuations in a turbulent state
We have recently developed equipment that
with good precision measure velocity changes over
short space scales .
Traditionally, the Taylor hypothesis is invoked
to replace by .
An important question is to test the extent to
which this assumption is justified in studying the
scaling properties for turbulence.
We have therefore initiated theoretical as well
as experimental research on a pipe flow to resolve what role the Taylor
hypothesis plays in extracting the scaling properties for the velocity
fluctuations in a three-dimensional turbulent flow behind a grid. For
this experiment, back-scatter Argon-Ion laser-Doppler anemometry is
used to measure the velocity fluctuations.
-0.1truecm P. Alstrøm, Mogens T. Levinsen and J. Zhang
0.3truecm Experimental and Theoretical Studies of
Pattern Formation and Turbulence in Capillary Waves
Experimental and Theoretical Studies of Pattern Formation and Turbulence in Capillary Waves 0.01truecmQuasicrystals were observed in solid-state physics in 1984. Eight years later, we observed the first quasicrystal pattern in a fluid, a discovery that went into widely read journals like Nature, Science, and Discovery. The quasicrystal pattern was made out of four standing capillary waves, formed on a water or alcohol surface undergoing vertical oscillations at high frequencies. At sufficient forcing capillary waves are formed with a frequency-dependent wavelength; we can attain about 50 wavelengths across the cell.
Besides the quasicrystal pattern, square and hexagonal patterns are observed. patterns are formed. We investigate experimentally how the patterns change when changing the viscosity of the fluid. Theoretically, the instability by which the surface waves are formed is an important issue in nonlinear hydrodynamics. A good theoretical project is to develop the nonlinear theory further.
At higher drive, the flow becomes turbulent. In this regime we consider
diffusion and relative diffusion of particles placed on the surface.
This is done using image processing and particle tracking programs.
For comparison, simulations on particle diffusion in chaotic fields are
-0.1truecm P. Alstrøm, M.T. Levinsen, J. Sparre Andersen and (W. Goldburg)