0.3truecm

**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**

We 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
0.01truecm**

In 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
0.01truecm**

Turbulent, 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
0.01truecm**

We 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
0.01truecm**

When 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
0.01truecm**

We 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
0.01truecm**

Soap 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
0.01truecm**

Quasicrystals 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
carried out.
-0.1truecm *P. Alstrøm, M.T. Levinsen, J. Sparre Andersen and (W. Goldburg)
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Mon Feb 6 10:24:27 MET 1995