The effects of vertical viscosity coefficients with different distribution characteristics on classical Ekman spiral structure

The classical Ekman theory tells us that the ocean surface current turns to the right(left) side of wind direction with 45° in the north(south) hemisphere,but the observation and research results show that the surface current deflexion angle is smaller than 45° in the Arctic and high latitude areas while larger than 45° in the low latitude areas.In order to explain these phenomena,a series of idealized numerical experiments are designed to investigate the influence of vertical viscosity coefficients with different vertical distribution characteristics on the classical and steady Ekman spiral structure.Results show that when the vertical viscosity coefficient decreases with water depth,the surface current deflexion angle is larger than 45°,whereas the angle is smaller than 45° when the vertical viscosity coefficient increases with water depth.So the different observed surface current deflexion angles in low latitude sea areas and the Arctic regions should be attributed to the different vertical distribution characteristics of vertical viscosity coefficients in the upper ocean.The flatness of the Ekman spiral is not equal to one and does not show regular behaviors for the numerical experiments with different distribution of vertical viscosity.However,the magnitudes and directions of volume transport of Ekman spirals are almost the same as the results of classical Ekman theory,i.e.,vertical viscosity coefficient distributions have no effect on the magnitudes and directions of volume transport.