Relationship between ocean velocity and motionally induced electrical signals: 2. In the presence of sloping topography

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 sloping topography. The full electric response is calculated for a schematic geometry that contains a topographic slope, has a two‐layer ocean with a layer of sediment beneath, and is described by five nondimensional parameters. When considered over the realistic ranges of topographic aspect ratio (the ratio of mean water depth to topographic width), topographic relief, 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 topographic aspect ratio to the power of 1.9 and have linear dependence on topographic relief and the depth of the surface jet. Depth‐uniform velocity errors are roughly proportional to the 1‐D sediment conductance ratio, whereas depth‐varying velocity errors are independent of sediment thickness or conductivity. Two‐dimensional perturbations decay with a half width of 0.2–1 times the 1‐D effective water depth. The magnitude of estimated errors is consistent with those found at a measurement location with strong 2‐D perturbations. This study extends the first‐order theory to the maximum expected aspect ratios for topography and finds small perturbations with simple dependencies. Overall, the 1‐D approximation is found to be adequate for interpreting observations at all but the most extreme locations.