Motionally induced electric and magnetic fields are investigated in the sea, crust, and mantle for large-scale low-frequency oceanic flows. It is shown that three-dimensional flows generate large-scale horizontal electric currents not present in two-dimensional motions. The resulting induced magnetic fields penetrate into the mantle inducing there electric currents. The degree of mutual induction between the ocean and the mantle depends on the parameter δmL, the ratio of the electromagnetic skin depth of the mantle to the horizontal scale of the flow. For δmL≫1 there is little mutual induction whereas for δmL≪1 there is strong coupling between the ocean and the mantle. It is shown that the variable *, the conductivity-weighted, vertically averaged velocity is important in the generation of both local and large-scale electric currents. Expressions are derived showing that , the vertically averaged velocity, can be determined from measurements of the induced electric and magnetic fields at the sea floor. Several special cases are calculated illustrating the influences of the mantle, the conducting sediments, and the horizontal scales of the motion.

https://www.leif.org/EOS/JC076i015p03476.pdf

Motionally Induced Electric and Magnetic Fields in the Sea

The variability in the volume transport of the Florida Current at 27°N has been observed from the voltage measured between a point 16 km east of Jupiter Inlet, Florida and Settlement Point, Grand Bahama Island by the use of an abandoned communications cable. The voltage is caused by the separation of electric charges in the ocean that are caused by the Florida Current crossing the Earth’s magnetic field (motional induction), by the electric currents induced in the ocean caused by time varying ionospheric and magnetospheric electric currents (geomagnetic induction), and by the voltage bias between the cable-ocean contacts caused by differences in the temperature, salinity and electrochemical state of the contacts. The geomagnetic-induced voltage was removed by the use of shore-based magnetic data and transfer functions. Changes in the voltage bias of the cable-ocean contact at Settlement Point were minimized by the use of a silver-silver-chloride electrode. The comparison of the daily mean motion-induced voltages with 137 daily profiling-derived transports, yields a voltage calibration factor of 24.42 + 0.56 Sv V -1 , a correlation squared of 0.94, and a root mean square misfit of 0.77 Sv (1 Sv = 10 6 m 3 s -1 ). The misfit is consistent with an error of 0.9 Sv in the voltage-derived transport estimated from the velocity and temperature profiling data, the electric current effects, and the profiling derived transport error. Hence the voltages accurately monitor the transport variations. The mean voltage-derived transports for the Florida Current at 27°N is 32.3 + 3.2 Sv based on 4862 daily mean values from 1969 to 1990. The annual variation has a range of 4.4 Sv. There is no evidence since 1969 for any long-term trend in the transport but there are numerous shorter term variations as large as 15 Sv lasting from days to months. The mean northward heat flux is 1.30 + 0.13 PW derived from 130 days of profiling the velocity and temperature of the Florida Current and assuming the North Atlantic has a southward, velocity-weighted temperature of 9.4 °C. The variations in heat flux are, essentially, due to the variations in transport because the velocity weighted temperature estimated by the profiling data has a nearly constant value of 19.1 ± 0 .6°C.

Transport and Heat Flux of the Florida Current at 27 degrees N Derived from Cross-Stream Voltages and Profiling Data: Theory and Observations

Waves approaching a sloping beach induce a tilt in the mean water level within the surf zone. The existence of this ‘set-up’ is here demonstrated by observing the mean flow in a straight tube laid parallel to the incoming waves; also by showing that the waves induce a siphon in a U-tube laid on the sloping bottom. It is argued theoretically, and confirmed by experiment, that the set-up should help to drive an offshore bottom current (the undertow) between the shoreline and the breaker line. Seawards from the breaker line the bottom current is reversed. The consequent convergence of the bottom currents may contribute to building up the ‘breaker bar’. Further experiments show that the mean onshore pressure gradient drives a circulation of water within a porous beach. The associated pattern of streamlines also extends into the land, inshore from the run-up line. Theoretically, the injection of dye at the sediment-water interface might be used to probe the porosity of the beach material.

Wave set-up, percolation and undertow in the surf zone

The theory of electromagnetic induction by motional sources in the ocean is examined from a first principles point of view. The electromagnetic field is expanded mathematically in poloidal and toroidal magnetic modes based on the Helmholtz decomposition. After deriving a set of Green functions for the modes in an unbounded ocean of constant depth and conductivity underlain by an arbitrary one-dimensional conducting earth, a set of exact integral equations are obtained which describe the induction process in an ocean of vertically varying conductivity. Approximate solutions are constructed for the low-frequency (subinertial) limit where the horizontal length scale of the flow is large compared to the water depth, the effect of self induction is weak, and the vertical velocity is negligible, explicitly yielding complex relationships between the vertically-integrated, conductivityweighted horizontal water velocity and the horizontal electric and three component magnetic fields and accounting for interactions with the conductive earth. After introducing geophysically reasonable models for the conductivity structures of the ocean and earth, these reduce to a spatially smoothed proportionality between the electromagnetic field components and the vertically-integrated, conductivity-weighted horizontal water velocity. An upper bound of a few times the water depth for the lateral averaging scale of the horizontal electric field is derived, and its constant of proportionality is shown to be nearly 1 for most of the deep ocean based on geophysical arguments. The magnetic field is shown to have a similar form but is a relatively weak, larger-scale average of the velocity field. Because vertical variations in the conductivity of seawater largely reflect its thermal structure and are weak beneath the thermocline, the horizontal electric field is a spatially filtered version of the true water velocity which strongly attenuates the influence of baroclinicity and accentuates the barotropic component. This is quantified using conductivity profiles and velocity information from a variety of locations.

/pdf/low-frequency-motionally-induced-electromagnetic-fields-in-2nyb1h2zjh.pdf

Low-Frequency, Motionally Induced Electromagnetic Fields in the Ocean 1. Theory

The electrical field induced by ocean currents and waves, with applications to the method of towed electrodes

Summary

The tidal movement of sea water relative to the Earth's magnetic field induces electromotive forces of a few millivolts per kilometre. Recent measurements off Plymouth show that the potential gradient is at right angles to the streams in that part of the English Channel. Observations on cross-channel telephone cables indicate that a considerable flow of electric current takes place, which can be accounted for b assuming the mean conductivity of the sea-bed to be of the order of 6 × 10-5 (ohms-cm.)-1. Tidally generated earth-currents spread into the land on either side of the Channel and have been measured near Lulworth. It may be possible to use them for the measurement of tidal stream velocities.



In the second part of the paper the potential gradients generated by water flow in shallow channels of rectangular or elliptical section are examined. The horizontal gradient in the water is almost independent of vertical variations in water velocity but is affected critically by the depth of the channel and the conductivity of the channel-bed. The induced electric currents can be expected to extend to depths comparable with the width of the channel.

M. S. Longuet-Higgins

Papers

The Electrical and Magnetic Effects of Tidal Streams