Related papers: Conformal invariance in water-wave turbulence
We describe a natural inhomogeneous generalization of high frequency plane gravitational waves. The waves are high frequency waves of the Kundt type whose null propagation direction in space-time has vanishing expansion, twist and shear but…
We present a theoretical attack on the classical problem of intermittency and anomalous scaling in turbulence. Our focus is on an ideal situation: high Reynolds number isotropic turbulence driven by steady large scale forcing. Moreover, the…
The stability analysis of self-similar solutions is an important approach to confirm whether they act as an attractor in general non-self-similar gravitational collapse. Assuming that the collapsing matter is a perfect fluid with the…
We present experimental results for water wave turbulence excited by piston-like programmed wavemakers in a water flume with horisontal dimensions 6x12x1.5 meters. Our main finding is that for a wide range of excitation amplitudes the…
Domain walls, optimal droplets and disorder chaos at zero temperature are studied numerically for the solid-on-solid model on a random substrate. It is shown that the ensemble of random curves represented by the domain walls obeys Schramm's…
We present a conformal theory for intermittent scalar fields. As an example, we consider the energy flux from large to small scales in the developed turbulent flow. The conformal correlation functions are found in the inertial range of…
It is well-known that shear flows in a strip or in the half plane are unstable for the Navier-Stokes equations if the viscosity $\nu$ is small enough, provided the horizontal wave number $\alpha$ lies in a small interval, between the so…
We show how to relate Schramm-Loewner Evolutions (SLE) to highest-weight representations of infinite dimensional Lie Algebras using the conformal restriction properties studied by Lawler, Schramm and Werner in the paper…
Linear stability analysis currently fails to predict turbulence transition in canonical viscous flows. We show that two alternative models of the boundary condition for incipient perturbations at solid walls produce linear instabilities…
Simplicity of fundamental physical laws manifests itself in fundamental symmetries. While systems with an infinity of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often…
Self-similar curves arise naturally as the tension-free equilibrium states of conformally invariant bending energies. The simplest example is the M\"obius invariant conformal arc-length on planar curves, dependent on the Frenet curvature…
We consider the linear stability of shear banded planar Couette flow of the Johnson-Segalman fluid, with and without the addition of stress diffusion to regularise the equations. In particular, we investigate the effect of two-dimensional…
Schramm-Loewner evolution (SLE$_\kappa$) is classically studied via Loewner evolution with half-plane capacity parametrization, driven by $\sqrt{\kappa}$ times Brownian motion. This yields a (half-plane) valued random field $\gamma = \gamma…
The problem of existence of stable nonlinear groups of gravity waves in deep water is revised by means of laboratory and numerical simulations with the focus on intense waves. Wave groups with steepness up to $A_{cr} \omega_m^2 /g \approx…
The role of short-wave instabilities on geostrophic turbulence is studied in a simplified model consisting of three layers in the quasi-geostrophic approximation. The linear stability analysis shows that short-wave instabilities are created…
Reduced wavenumber models of turbulence, shell models, show cascade processes and anomalous scaling of correlators which might be analogous to what is observed in Navier-Stokes (N-S) turbulence. The scaling properties of the shell models…
High-resolution numerical simulations are utilized to examine isotropic turbulence in a compressible fluid when long wavelength velocity fluctuations approach light speed. Spectral analysis reveals an inertial sub-range of relativistic…
Greuel, Lossen and Shustin gave a general sufficient numerical condition for the T-smoothness (smoothness and expected dimension) of equisingular families of plane curves. This condition involves a new invariant \gamma for plane curve…
An experimental study is reported of the near-critical reflection of internal gravity waves over sloping topography in a stratified fluid. An overturning instability close to the slope and triggering the boundary-mixing process is observed…
Continuously self-similar (CSS) solutions for the gravitational collapse of a spherically symmetric perfect fluid, with the equation of state p=kappa rho, with 0<kappa<1 a constant, are constructed numerically and their linear…