课程名称︰流体力学 课程性质︰大气系必修 课程教师︰林和 开课学院：理学院 开课系所︰大气科学系 考试日期（年月日）︰2012/06/18 考试时限（分钟）：180min 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1.20% (a)What is a linear system in the sense of differential equations and matrix? Please give some examples. (b)Eigen function?Example? (c)Orthogonality?How to expand an arbitrary function on an eigenbasis? 2.20% (a)What is the meaning of dispersion relationship? Can you give an example? (b)Derive the disperative relationship of internal energy wave from the follow -ing Boussinesq Approximation.(Hint:linearize equations first) (∂u/∂t)+u(∂u/∂x)+v(∂u/∂y)+w(∂u/∂z)=-ρs (∂p/∂x) (∂v/∂t)+u(∂v/∂x)+v(∂v/∂y)+w(∂v/∂z)=-ρs (∂p/∂y) (∂w/∂t)+u(∂w/∂x)+v(∂w/∂y)+w(∂w/∂z)=-(ρ/ρs)-ρs (∂p/∂z) (∂u/∂x)+(∂u/∂y)+(∂u/∂z)+(w/H)=0 (∂θ/∂t)+u(∂θ/∂x)+v(∂θ/∂y)+w*(∂θ/∂z)+(w*σ)=0 θ/θs=-(ρ/ρs) 3.20% (a)Explain the advantage and disadvantage of using Fourier transformation part -icularly when dealing with a local disturbance in physical space. (b)Try your best to explain group velocity. 4.20% (a)Derive vorticity equation,with and without the assumption of incompressibil -ity. (b)Explain the meaning of Jacobian term,give example. (c)What is the Bernoulli equation?Meaning? (d)Explain the effect of tilting-stretching term. 5.20% (a)Explain the meaning of viscosity,for the views of both molecular and turbul -ent scale. (b)Derive Renold's decompisition. (c)Show how to parameterize Renold's stress term in the form of Laplacian,try to justify the process. --

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