arXiv subjects

A. Tilgner

Publications and source records attributed to A. Tilgner.

At least 19 recordsLinked to original sources

arXiv2025

Finger properties in bounded double diffusive finger convection

We analyze experimental data on double diffusive convection in an electrochemical cell in the finger regime. All fingers in the experiments are bounded on at least one end by a solid wall. The properties of these fingers are compared with those of fingers in other experiments which are surrounded by fluid on all sides. The compositional boundary layers are found to be thinner than the finger width. The finger thickness agrees well with half the wavelength of the fastest growing mode obtained in linear stability analysis. The ion transport through the boundary layers is reduced by two orders of magnitude compared with unbounded fingers. The overturning layers in staircases contribute negligibly to salinity mixing because of efficient transport between finger layers and convection rolls.

physics.flu-dyn↗

arXiv2023

Thermal convection in compressible gas with spanwise rotation

We simulate numerically convection in a rectangular cell filled with an ideal gas rotating about an axis perpendicular to the direction of gravity. This configuration corresponds to an experiment with a convection cell placed in a rapidly rotating centrifuge in which the centrifugal force plays the role of gravity. The compressibility of the gas in combination with the rotation of the cell leads to a drifting mode at the onset of convection. The drift persists despite the presence of sidewalls and is rapid enough to cause the anelastic approximation to fail at parameters typical of realizable laboratory experiments. The global spanwise rotation forces the flow to be 2D unless the Rayleigh number is sufficiently large. The main properties of compressible convection in 2D and 3D are compared.

physics.flu-dyn↗

arXiv2022

Staircase formation in unstably stratified double diffusive finger convection

Double diffusive staircases are investigated experimentally in a fluid layer with a stabilizing temperature gradient and a destabilizing gradient of ion concentration. Gradients of temperature and ion concentration are maintained in a steady state within an electrochemical system. Staircases are observed even if the density stratification is unstable. None of the previously proposed mechanisms for staircase formation can be recognized in the experiments. Ion transport through fingers which are part of a staircase is not the same as transport through fingers extending through the entire cell. Fingers cease to exist if the diffusive heat transport between neighboring fingers is insufficient.

physics.flu-dyn↗

arXiv2022

Bounds for rotating convection at infinite Prandtl number from semidefinite programs

Bounds for the poloidal and toroidal kinetic energies and the heat transport are computed numerically for rotating convection at infinite Prandtl number with both no slip and stress free boundaries. The constraints invoked in this computation are linear or quadratic in the problem variables and lead to the formulation of a semidefinite program. The bounds behave as a function of Rayleigh number at fixed Taylor number qualitatively in the same way as the quantities being bounded. The bounds are zero for Rayleigh numbers smaller than the critical Rayleigh number for the onset of convection, they increase rapidly with Rayleigh number for Rayleigh numbers just above onset, and increase more slowly at large Rayleigh numbers. If the dependencies on Rayleigh number are approximated by power laws, one obtains larger exponents from bounds on the Nusselt number for Rayleigh numbers just above onset than from the actual Nusselt number dependence known for large but finite Prandtl number. The wavelength of the linearly unstable mode at the onset of convection appears as a relevant length scale in the bounds.

physics.flu-dyn↗

arXiv2022

Transition to three dimensional flow in thermal convection with spanwise rotation

We investigate by direct numerical simulation Rayleigh-Bénard convection in a rotating rectangular cell with rotation vector and gravity perpendicular to each other. The flow is two dimensional near the onset of convection with convection rolls aligned parallel to the rotation axis of the boundaries. At a sufficiently large Rayleigh number, the flow becomes unstable to three dimensional disturbances which changes the scaling of heat transport and kinetic energy with Rayleigh number. The mechanism leading to the instability is identified as an elliptical instability. At the transition, the Reynolds and Rossby numbers $\mathrm{Re}$ and $\mathrm{Ro}$ based on the kinetic energy of the flow are related by $\mathrm{Re} \propto \mathrm{Ro}^{-2}$ at small $\mathrm{Ro}$ with a geometry dependent prefactor.

physics.flu-dyn↗

arXiv2019

The time evolution equation for advective heat transport as a constraint for optimal bounds in Rayleigh-Bénard convection

Upper bounds on the heat transport and other quantities of interest in Rayleigh-Bénard convection are derived in previous work from constraints resulting from the equations of time evolution for kinetic energy, the root mean square of temperature, and the temperature averaged over horizontal planes. Here, we investigate the effect of a new constraint derived from the time evolution equation for the advective heat transport. This additional constraint leads to improved bounds on the toroidal dissipation.

physics.flu-dyn↗

arXiv2018

Mechanisms for magnetic Field generation in precessing cubes

It is shown that flows in precessing cubes develop at certain parameters large axisymmetric components in the velocity field which are large enough to either generate magnetic fields by themselves, or to contribute to the dynamo effect if inertial modes are already excited and acting as a dynamo. This effect disappears at small Ekman numbers. The critical magnetic Reynolds number also increases at low Ekman numbers because of turbulence and small scale structures.

physics.flu-dyn↗

arXiv2017

Bounds on poloidal kinetic energy in plane layer convection

A numerical method is presented which conveniently computes upper bounds on heat transport and poloidal energy in plane layer convection for infinite and finite Prandtl numbers. The bounds obtained for the heat transport coincide with earlier results. These bounds imply upper bounds for the poloidal energy which follow directly from the definitions of dissipation and energy. The same constraints used for computing upper bounds on the heat transport lead to improved bounds for the poloidal energy.

physics.flu-dyn↗

arXiv2017

Scaling laws and bounds for the turbulent G.O. Roberts dynamo

Numerical simulations of the G.O. Roberts dynamo are presented. Dynamos both with and without a significant mean field are obtained. Exact bounds are derived for the total energy which conform with the Kolmogorov phenomenology of turbulence. Best fits to numerical data show the same functional dependences as the inequalities obtained from optimum theory.

physics.flu-dyn↗

arXiv2014

Transition to finger convection in double-diffusive convection

Finger convection is observed experimentally in an electrodeposition cell in which a destabilizing gradient of copper ions is maintained against a stabilizing temperature gradient. This double-diffusive system shows finger convection even if the total density stratification is unstable. Finger convection is replaced by an ordinary convection roll if convection is fast enough to prevent sufficient heat diffusion between neighboring fingers, or if the thermal buoyancy force is less than 1/30 of the compositional buoyancy force. At the transition, the ion transport is larger than without an opposing temperature gradient.

physics.flu-dyn↗

arXiv2014

Magnetic energy dissipation and mean magnetic field generation in planar convection driven dynamos

A numerical study of dynamos in rotating convecting plane layers is presented which focuses on magnetic energies and dissipation rates, and the generation of mean fields (where the mean is taken over horizontal planes). The scaling of the magnetic energy with the flux Rayleigh number is different from the scaling proposed in spherical shells, whereas the same dependence of the magnetic dissipation length on the magnetic Reynolds number is found for the two geometries. Dynamos both with and without mean field exist in rapidly rotating convecting plane layers.

physics.flu-dyn↗

arXiv2013

Elliptical instability of compressible flow in ellipsoids

Elliptical instability is due to a parametric resonance of two inertial modes in a fluid velocity field with elliptical streamlines. This flow is a simple model of the motion in a tidally deformed, rotating body. Elliptical instability typically leads to three-dimensional turbulence. The associated turbulent dissipation together with the dissipation of the large scale mode may be important for the synchronization process in stellar and planetary binary systems. In order to determine the influence of the compressibility on the stability limits of tidal flows in stars or planets, we calculate the growth rates of perturbations in flows with elliptical streamlines within ellipsoidal boundaries of small ellipticity. In addition, the influence of the orbiting frequency of the tidal perturber $Ω_P$ and the viscosity of the fluid are taken into account.

astro-ph.EP↗

arXiv2012

Transitions in rapidly rotating convection driven dynamos

Numerical simulations of dynamos in rotating Rayleigh-Bénard convection in plane layers are presented. Two different types of dynamos exist which obey different scaling laws for the amplitude of the magnetic field. The transition between the two occurs within a hydrodynamically uniform regime which can be classified as rapidly rotating convection.

physics.flu-dyn↗

arXiv2012

Simulations of the kinematic dynamo onset of spherical Couette flows with smooth and rough boundaries

We study numerically the dynamo transition of an incompressible electrically conducting fluid filling the gap between two concentric spheres. In a first series of simulations, the fluid is driven by the rotation of a smooth inner sphere through no-slip boundary conditions, whereas the outer sphere is stationary. In a second series a volume force intended to simulate a rough surface drives the fluid next to the inner sphere within a layer of thickness one tenth of the gap width. We investigate the effect of the boundary layer thickness on the dynamo threshold in the turbulent regime. The simulations show that the boundary forcing simulating the rough surface lowers the necessary rotation rate, which may help to improve spherical dynamo experiments.

physics.flu-dyn↗

arXiv2011

Convection in an ideal gas at high Rayleigh numbers

Numerical simulations of convection in a layer filled with ideal gas are presented. The control parameters are chosen such that there is a significant variation of density of the gas in going from the bottom to the top of the layer. The relations between the Rayleigh, Peclet and Nusselt numbers depend on the density stratification. It is proposed to use a data reduction which accounts for the variable density by introducing into the scaling laws an effective density. The relevant density is the geometric mean of the maximum and minimum densities in the layer. A good fit to the data is then obtained with power laws with the same exponent as for fluids in the Boussinesq limit. Two relations connect the top and bottom boundary layers: The kinetic energy densities computed from free fall velocities are equal at the top and bottom, and the products of free fall velocities and maximum horizontal velocities are equal for both boundaries.

physics.flu-dyn↗

arXiv2011

Global fluctuations in magnetohydrodynamic dynamos

The spectrum of temporal fluctuations of total magnetic energy for several dynamo models is different from white noise at frequencies smaller than the inverse of the turnover time of the underlying turbulent velocity field. Examples for this phenomenon are known from previous work and we add in this paper simulations of the G.O. Roberts dynamo and of convectively driven dynamos in rotating spherical shells. The appearance of colored noise in the magnetic energy is explained by simple phenomenological models. The Kolmogorov theory of turbulence is used to predict the spectrum of kinetic and magnetic energy fluctuations in the inertial range.

physics.geo-ph↗

arXiv2010

Transitions in turbulent rotating Rayleigh-Bénard convection

Numerical simulations of rotating Rayleigh-Bénard convection are presented for both no slip and free slip boundaries. The goal is to find a criterion distinguishing convective flows dominated by the Coriolis force from those nearly unaffected by rotation. If one uses heat transport as an indicator of which regime the flow is in, one finds that the transition between the flow regimes always occurs at the same value of a certain combination of Reynolds, Prandtl and Ekman numbers for both boundary conditions. If on the other hand one uses the helicity of the velocity field to identify flows nearly independent of rotation, one finds the transition at a different location in parameter space.

physics.flu-dyn↗

arXiv2009

Wave-driven dynamo action in spherical MHD systems

Hydrodynamic and magnetohydrodynamic numerical studies of a mechanically forced two-vortex flow inside a sphere are reported. The simulations are performed in the intermediate regime between the laminar flow and developed turbulence where a hydrodynamic instability is found to generate internal waves with a characteristic m=2 zonal wave number. It is shown that this time-periodic flow acts as a dynamo although snapshots of the flow as well as the mean flow are not dynamos. The magnetic fields' growth rate exhibits resonance effects depending on the wave frequency. Furthermore, a cyclic self-killing and self-recovering dynamo based on the relative alignment of the velocity and magnetic fields is presented. The phenomena are explained in terms of a mixing of non-orthogonal eigenstates of the time dependent linear operator of the magnetic induction equation. The potential relevance of this mechanism to dynamo experiments is discussed.

physics.flu-dyn↗