Relationship between ocean velocity and motionally induced electrical signals: 1. In the presence of horizontal velocity gradients

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Motionally induced electric fields and electric currents in the ocean depend to first order solely on the vertical dimension. We investigate the significance of two‐dimensional (2‐D) perturbations that arise in the presence of horizontal velocity gradients. The full electric response is calculated for two schematic geometries that contain horizontal velocity gradients, have a two‐layer ocean with a layer of sediment beneath, and are described by four nondimensional parameters. When considered over the realistic ranges of oceanic aspect ratio (the ratio of water depth to the width of velocity), sediment thickness, and sediment conductivity, velocity errors arising from 2‐D perturbations are found to be less than a few percent of the dominant one‐dimensional (1‐D) signal. All errors depend on the aspect ratio to the power of 1.9 (1) for signals induced by the vertical (horizontal) component of the Earth's magnetic field. Depth‐uniform velocity errors are proportional to the 1‐D sediment conductance ratio, whereas depth‐varying velocity errors are independent of sediment thickness or conductivity. Errors are weakly (proportionally) dependent on the jet depth for signals induced by the vertical (horizontal) component of the magnetic field. Two‐dimensional perturbations decay away from the forcing region with a half width of 0.2–1 times the 1‐D effective water depth. This study extends the first‐order theory to the maximum expected aspect ratios for oceanic flow and finds small perturbations with simple dependencies on the nondimensional parameters.