Cross-equatorial flow of grounded abyssal ocean currents

Abstract

The cross-equatorial flow of grounded abyssal ocean currents in a differentially rotating meridional channel with parabolic bottom topography is examined. In particular, the dependence is determined of the cross-equatorial volume flux on the underlying flow parameters including the slope of the channel’s walls , the half-width of the channel , the half-width and height of the abyssal current and , respectively, the magnitude of the rotation vector , the Earth’s radius , and the reduced gravity . In addition, it is shown that the ratio between the width of the channel and the zonal wavelength of a narrow wave structure that is formed by the current in the equatorial region plays a crucial role in determining into which hemisphere the current flows after its interaction with the equator. It is found that some parameters (e.g. and ) do not have any significant effect on the zonal wavelength, while variations in other parameters (e.g. , , , and ) change the zonal wavelength and, consequently, can dramatically alter the qualitative trans-equatorial behavior of the abyssal current. After examining an auxiliary model of a particle in a rotating equatorial channel, it is shown that the zonal wavelength of the equatorial wave is linearly proportional to the equatorial length scale defined as , where is the equatorial value of the beta-parameter.