Coriolis force in Geophysics: an elementary introduction and examples

We show how Geophysics may illustrate and thus improve classical Mechanics lectures concerning the study of Coriolis force effects. We are then interested in atmospheric as well as oceanic phenomena we are familiar with, and are for that reason of pedagogical and practical interest. Our aim is to model them in a very simple way to bring out the physical phenomena that are involved.Comment: Accepted for publication in European Journal of Physic

Self Running Droplet: Emergence of Regular Motion from Nonequilibrium Noise

Spontaneous motion of an oil droplet driven by chemical nonequilibricity is reported. It is shown that the droplet undergoes regular rhythmic motion under appropriately designed boundary conditions, whereas it exhibits random motion in an isotropic environment. This study is a novel manifestation on the direct energy transformation of chemical energy into regular spatial-motion under isothermal conditions. A simple mathematical equation including noise reproduces the essential feature of the transition from irregularity into periodic regular motion. Our results will inspire the theoretical study on the mechanism of molecular motors in living matter, working under significant influence of thermal fluctuation.Comment: 4 pages, 4 figure

The Influence of Horizontal Boundaries on Ekman Circulation and Angular Momentum Transport in a Cylindrical Annulus

We present numerical simulations of circular Couette flow in axisymmetric and fully three-dimensional geometry of a cylindrical annulus inspired by Princeton MRI liquid gallium experiment. The incompressible Navier-Stokes equations are solved with the spectral element code Nek5000 incorporating realistic horizontal boundary conditions of differentially rotating rings. We investigate the effect of changing rotation rates (Reynolds number) and of the horizontal boundary conditions on flow structure, Ekman circulation and associated transport of angular momentum through the onset of unsteadiness and three-dimensionality. A mechanism for the explanation of the dependence of the Ekman flows and circulation on horizontal boundary conditions is proposed.Comment: 23 pages, 7 figures; to be published in the Topical Issue of the Physica Scripta in 200

Turbulent states in plane Couette flow with rotation

Shearing and rotational forces in fluids can significantly alter the transport of momentum.A numerical investigation was undertaken to study the role of these forces using plane Couette flow subject to rotation about an axis perpendicular to both wall-normal and streamwise directions. Using a set of progressively higher Reynolds numbers up to Re = 5200, we find that the torque for a given Re is a non-monotonic function of rotation number, Ro. For low-to-moderate turbulent Reynolds numbers we find a maximum that is associated with flow fields that are dominated by downstream vortices and calculations of 2-d vortices capture the maximum also quantitatively. For higher shear Reynolds numbers a second stronger maximum emerges at smaller rotation numbers, closer to non-rotating plane Couette flow. It is carried by flows with a markedly 3-d structure and cannot be captured by 2-d vortex studies. As the Reynolds number increases, this maximum becomes stronger and eventually overtakes the one associated with the 2-d flow state.Comment: 15 pages, 10 figure

Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere

Numerical solutions of the incompressible magnetohydrodynamic (MHD) equations are reported for the interior of a rotating, perfectly-conducting, rigid spherical shell that is insulator-coated on the inside. A previously-reported spectral method is used which relies on a Galerkin expansion in Chandrasekhar-Kendall vector eigenfunctions of the curl. The new ingredient in this set of computations is the rigid rotation of the sphere. After a few purely hydrodynamic examples are sampled (spin down, Ekman pumping, inertial waves), attention is focused on selective decay and the MHD dynamo problem. In dynamo runs, prescribed mechanical forcing excites a persistent velocity field, usually turbulent at modest Reynolds numbers, which in turn amplifies a small seed magnetic field that is introduced. A wide variety of dynamo activity is observed, all at unit magnetic Prandtl number. The code lacks the resolution to probe high Reynolds numbers, but nevertheless interesting dynamo regimes turn out to be plentiful in those parts of parameter space in which the code is accurate. The key control parameters seem to be mechanical and magnetic Reynolds numbers, the Rossby and Ekman numbers (which in our computations are varied mostly by varying the rate of rotation of the sphere) and the amount of mechanical helicity injected. Magnetic energy levels and magnetic dipole behavior are exhibited which fluctuate strongly on a time scale of a few eddy turnover times. These seem to stabilize as the rotation rate is increased until the limit of the code resolution is reached.Comment: 26 pages, 17 figures, submitted to New Journal of Physic

Asymptotic theory for a moving droplet driven by a wettability gradient

An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and the receding side -- to respective solutions of the problem on the microscale. On the microscale the velocity of movement is used as the small parameter of an asymptotic expansion. Matching gives the droplet shape, velocity of movement as a function of the imposed wettability gradient and droplet volume.Comment: 8 fig

Whither Capitalism? Financial externalities and crisis

As with global warming, so with financial crises – externalities have a lot to answer for. We look at three of them. First the financial accelerator due to ‘fire sales’ of collateral assets -- a form of pecuniary externality that leads to liquidity being undervalued. Second the ‘risk- shifting’ behaviour of highly-levered financial institutions who keep the upside of risky investment while passing the downside to others thanks to limited liability. Finally, the network externality where the structure of the financial industry helps propagate shocks around the system unless this is checked by some form of circuit breaker, or ‘ring-fence’. The contrast between crisis-induced Great Recession and its aftermath of slow growth in the West and the rapid - and (so far) sustained - growth in the East suggests that successful economic progress may depend on how well these externalities are managed

Bubble Shape Oscillations and the Onset of Sonoluminescence

An air bubble trapped in water by an oscillating acoustic field undergoes either radial or nonspherical pulsations depending on the strength of the forcing pressure. Two different instability mechanisms (the Rayleigh--Taylor instability and parametric instability) cause deviations from sphericity. Distinguishing these mechanisms allows explanation of many features of recent experiments on sonoluminescence, and suggests methods for finding sonoluminescence in different parameter regimes.Comment: Phys. Rev. Lett., in pres

A magnetic field diagnostic for sonoluminescence

This study is motivated by the extraordinary process of single bubble sonoluminescence (SBSL), where an acoustically driven spherical shock is thought to power the emitted radiation. We propose new experiments using an external magnetic field which can induce anisotropies in both the shock propagation and radiation pattern. The effects will depend on the temperature, conductivity, and size of the radiating region. Our predictions suggest that such a laboratory experiment could serve as an important diagnostic in placing bounds on these parameters and understanding the physics of sonoluminescence.Comment: Latex File, Two .eps files, 5 pages, submitted to PR

Fuzzy Fibers: Uncertainty in dMRI Tractography

Fiber tracking based on diffusion weighted Magnetic Resonance Imaging (dMRI) allows for noninvasive reconstruction of fiber bundles in the human brain. In this chapter, we discuss sources of error and uncertainty in this technique, and review strategies that afford a more reliable interpretation of the results. This includes methods for computing and rendering probabilistic tractograms, which estimate precision in the face of measurement noise and artifacts. However, we also address aspects that have received less attention so far, such as model selection, partial voluming, and the impact of parameters, both in preprocessing and in fiber tracking itself. We conclude by giving impulses for future research