Numerical Solution of Unsteady Ekman Equation Modified by Wave and Linear Friction Term

Abstract

Based on the assumption that taking the KPP model as the vertical vortex viscosity coefficient, the unsteady Ekman equation modified by wave and linear friction terms is solved numerically with the finite difference method and the influence of wave and linear friction terms on the unsteady Ekman current are studied. Based on the measured data of AWAC, the Stokes drift is calculated by the Stokes drift formula; and on the basis of the measured data of wind speed, the average wind speed of the 3 hours is divided into three different sections: low wind speed (0∼4) m/s, medium -low wind speed (4∼8) m/s and medium-high wind speed (8∼12) m/s. The results show that: Stokes drift has the greatest impact on Ekman current under the low wind speed, which is accounted for 27.4%, the second is under the medium-low wind speed of 7.5%, and the smallest effect is under the medium-high wind speed of 4.2%. In additon, the effect of linear friction term on Ekman current is also studied. It is shown that under the medium-high wind speed and the medium-low wind speed, together with the ratio of the linear friction term to the Coriolis force is, the influence of the linear friction term on the Ekman current has exceeded that of the Stokes drift on the Ekman current; while under the low wind speed, the effect of linear friction term on Ekman current can not exceed that of Stokes drift on Ekman current until. Furthermore, the comparison between the numerical solution and the actual measured data also shows different characteristics. In the perspective of relevance, the correlation between the numerical simulation results and the measured data is above 0.7 under the medium-high wind speed, which is higher than the correlation between the both of 0.4∼0.5 under the low wind speed and the medium-low wind speed; and in the perspective of the root mean square deviation degree, the root mean square deviation between the numerical simulation results and the measured data under the medium-high wind speed is lower than that under the low wind speed and the medium-low wind speed. The above results show that the influence of Stokes drift, linear friction term and the unsteady wind on Ekman model can not be ignored.