Numerical Solution Of Unsteady Ekman Equation Modified By Wave And Linear Friction Term

In this thesis,the unsteady Ekman equation modified by wave and linear friction terms is discretized by the finite difference method.On the basis of this,we study the effects of Stokes drift,linear friction,vertical eddy viscous coefficient and unsteady wind on Ekman current.Firstly,it discusses the sensitivity of Ekman current to wind-stress,Stokes drift,linear friction as well as vertical eddy viscosity.In the partial sensitivity analysis method,conduct sensitivity calculation by adopting one-variable-at-a-time approach,the result shows that under condition of U10=5m/s and U10=10m/s,sensitivities size rank successively are wind-stress,vertical eddy viscosity,Stokes drift,linear friction,but under condition of U10=15m/s,U10=20m/s as well as U10=25m/s,sensitivity of linear friction bigger than Stokes drift.In the global sensitivity analysis approach,conduct sensitivity calculation by adopting Morris method,the result shows that sensitivities size rank successively are linear friction term,vertical eddy viscosity,wind-stress term,Stokes drift term.Additionally,from calculation result of interaction among all parameters,we can see interaction between linear friction term and other parameters are the strongest,next is eddy viscosity,then is wind-stress,however,smallest interaction with other parameters is the Stokes drift.No matter one-variable-at-a-time approach or Morris method,the result of its sensitivity analysis all indicate the effect of linear friction term in Ekman model can not be underestimated,should consider the effect of linear friction term in Ekman model.Secondly,it conducts ideal experiment on the basis of sensitivity of Ekman current to all parameters and researches the effect of three kinds of different Stokes drift formula to Ekman current and discusses the effect of vertical eddy viscosity for KPP and MY2.5 form to Ekman current.The result shows that Ekman current calculated out by the monochromatic wave formula,the exponential integral formula and the Phillips spectrum approximation formula is not obvious,indicating that the selection of these three Stokes drift formula has little effect on Ekman current.Additionally,under the condition that wind speed,Stokes drift formula,linear friction term are the same,Ekman current calculated out by vertical eddy viscosity under MY2.5 form is bigger than Ekman current calculated out under KPP form.From this it can indicates that adoption of vertical eddy viscosity formula has great effect on Ekman current.Finally,it carries out measured data inspection on the basis of sensitivity analysis and ideal experiment and adopts vertical eddy viscosity of KPP form and one-dimensional sea spectra integral formula to discuss the effect of Stokes drift and linear friction term to unsteady Ekman current.The result shows that:under low wind speed,the effect of Stokes drift to Ekman current is the biggest(27.4%),under medium-low wind speed,it is smaller(7.5%),medium-high wind speed is the smallest(4.2%).Additionally,under medium-high and medium-low wind speed,when λ=r/fcor=0.5(the ratio of the linear friction term to the Coriolis force),the effect of linear friction term to Ekman current has already exceeded the effect of Stokes drift to Ekman current,however under low wind speed condition,when λ=1,the effect of linear friction term to Ekman current only exceeds the effect of Stokes drift to Ekman current.