Determination of ocean transports and velocities by electromagnetic effects

The electric potentials in and about an ocean current are shown to be related in a simple fashion to the total fluid transport. In many waters, surface measurements alone permit the determination of this total transport. It is also established that the local vertical potential gradient is a measure of the local velocity. Several techniques of measurement, including the Geomagnetic electrokinetograph method, and the errors which may be involved in each, are discussed

The Malkus–Robbins dynamo with a linear series motor

Hide [1997] has introduced a number of different nonlinear models to describe the behavior of n-coupled self-exciting Faraday disk homopolar dynamos. The hierarchy of dynamos based upon the Hide et al. [1996] study has already received much attention in the literature (see [Moroz, 2001] for a review). In this paper we focus upon the remaining dynamo, namely Case 3 of [Hide, 1997] for the particular limit in which the Malkus–Robbins dynamo [Malkus, 1972; Robbins, 1997] obtains, but now modified by the presence of a linear series motor. We compare and contrast the linear and the nonlinear behaviors of the two types of dynamo

Destabilizing Taylor-Couette flow with suction

We consider the effect of radial fluid injection and suction on Taylor-Couette flow. Injection at the outer cylinder and suction at the inner cylinder generally results in a linearly unstable steady spiralling flow, even for cylindrical shears that are linearly stable in the absence of a radial flux. We study nonlinear aspects of the unstable motions with the energy stability method. Our results, though specialized, may have implications for drag reduction by suction, accretion in astrophysical disks, and perhaps even in the flow in the earth's polar vortex.Comment: 34 pages, 9 figure

Stability of the thermohaline circulation examined with a one-dimensional fluid loop

The Stommel box model elegantly demonstrates that the oceanic response to mixed boundary conditions, combining a temperature relaxation with a fixed salt flux forcing, is nonlinear owing to the so-called salt advection feedback. This nonlinearity produces a parameter range of bi-stability associated with hysteresis effects characterised by a fast thermally-driven mode and a slow salinity-driven mode. Here we investigate whether a similar dynamical behaviour can be found in the thermohaline loop model, a one-dimensional analogue of the box model. A semi-analytical method to compute possible steady states of the loop model is presented, followed by a linear stability analysis carried out for a large range of loop configurations. While the salt advection feedback is found as in the box model, a major difference is obtained for the fast mode: an oscillatory instability is observed near the turning point of the fast mode branch, such that the range of bi-stability is systematically reduced, or even removed, in some cases. The oscillatory instability originates from a salinity anomaly that grows exponentially as it turns around the loop, a situation that may occur only when the salinity torque is directed against the loop flow. Factors such as mixing intensity, the relative strength of thermal and haline forcings, the nonlinearity of the equation of state or the loop geometry can strongly affect the stability properties of the loop

Electroconvection in a Suspended Fluid Film: A Linear Stability Analysis

A suspended fluid film with two free surfaces convects when a sufficiently large voltage is applied across it. We present a linear stability analysis for this system. The forces driving convection are due to the interaction of the applied electric field with space charge which develops near the free surfaces. Our analysis is similar to that for the two-dimensional B\'enard problem, but with important differences due to coupling between the charge distribution and the field. We find the neutral stability boundary of a dimensionless control parameter ${\cal R}$ as a function of the dimensionless wave number ${\kappa}$. ${\cal R}$, which is proportional to the square of the applied voltage, is analogous to the Rayleigh number. The critical values ${{\cal R}_c}$ and ${\kappa_c}$ are found from the minimum of the stability boundary, and its curvature at the minimum gives the correlation length ${\xi_0}$. The characteristic time scale ${\tau_0}$, which depends on a second dimensionless parameter ${\cal P}$, analogous to the Prandtl number, is determined from the linear growth rate near onset. ${\xi_0}$ and ${\tau_0}$ are coefficients in the Ginzburg-Landau amplitude equation which describes the flow pattern near onset in this system. We compare our results to recent experiments.Comment: 36 pages, 7 included eps figures, submitted to Phys Rev E. For more info, see http://mobydick.physics.utoronto.ca

Experiments with a Malkus-Lorenz water wheel: Chaos and Synchronization

We describe a simple experimental implementation of the Malkus-Lorenz water wheel. We demonstrate that both chaotic and periodic behavior is found as wheel parameters are changed in agreement with predictions from the Lorenz model. We furthermore show that when the measured angular velocity of our water wheel is used as an input signal to a computer model implementing the Lorenz equations, high quality chaos synchronization of the model and the water wheel is achieved. This indicates that the Lorenz equations provide a good description of the water wheel dynamics.Comment: 12 pages, 7 figures. The following article has been accepted by the American Journal of Physics. After it is published, it will be found at http://scitation.aip.org/ajp

Waves attractors in rotating fluids: a paradigm for ill-posed Cauchy problems

In the limit of low viscosity, we show that the amplitude of the modes of oscillation of a rotating fluid, namely inertial modes, concentrate along an attractor formed by a periodic orbit of characteristics of the underlying hyperbolic Poincar\'e equation. The dynamics of characteristics is used to elaborate a scenario for the asymptotic behaviour of the eigenmodes and eigenspectrum in the physically relevant r\'egime of very low viscosities which are out of reach numerically. This problem offers a canonical ill-posed Cauchy problem which has applications in other fields.Comment: 4 pages, 5 fi

Magnetic field induced by elliiptical instability in a rotating tidally distorded sphere

It is usually believed that the geo-dynamo of the Earth or more generally of other planets, is created by the convective fluid motions inside their molten cores. An alternative to this thermal or compositional convection can however be found in the inertial waves resonances generated by the eventual precession of these planets or by the possible tidal distorsions of their liquid cores. We will review in this paper some of our experimental works devoted to the elliptical instability and present some new results when the experimental fluid is a liquid metal. We show in particular that an imposed magnetic field is distorted by the spin- over mode generated by the elliptical instability. In our experiment, the field is weak (20 Gauss) and the Lorenz force is negligible compared to the inertial forces, therefore the magnetic field does not modify the fluid flow and the pure hydrodynamics growth rates of the instability are recovered through magnetic measurements