We showed that, in all of the previous studies made of the horizontal circular “Tide-induced residual current (TIRC)”, the velocity field was far beyond the application limit of the TIRC theory and the discussions in previous studies had no physical reality, because in the circular TIRC, the pressure gradient force balances with the centrifugal force and a weak Coriolis' force. We also showed that the Euler numberAP, which is defined by the ratio of the advection term to the pressure gradient term, is useful as a measure of nonlinearity of the temporal tidal velocity field in a numerical model experiment, and that the measureAP must be less than 0.05 or at least less than 0.1 for us to discuss the TIRC as a physical entity of “steady current” in physical space. We proposed another measure,KE, which is defined as the ratio of the sum of kinetic energies of compound- and over-tides to kinetic energies of diurnal- and semi-diurnal tides. We showed that this measure,KE, is also useful as an indicator of the magnitude of nonlinearity of tidal velocity field. We presented the distribution ofKE in the Seto Inland Sea of Japan, showing that the nonlinearity is very large in many places of the basin, which must be considered when analyzing tidal current velocities and the dynamics of the current system or material transport in the Seto Inland Sea.
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