地球物理流体力学课件：Lecture 6 Ekman flows 和海洋风生环流

dVh dt
1
p
f
k Vh
We saw that the acceleration term is relatively small. Omitting it, we get a diagnostic relationship called geostrophic balance:
1
p
f
k Vh
0
Vh
1
f
k p
矢量形式
fv 1 p
0 x
1 p fu
0 y
分量形式
地转流
在远离边界层，赤道及极地的地方，大尺度流动以准水平 （w0=0), 静力平衡的地转流（压强梯度力与科氏力平衡）为主要特征
k p
vg f
地转流在北半球（f>0) 和南半球 （f<0)， 高压中心附近沿等压线 呈顺和逆时针运动；在低压中心附近则相反
direction normal to flow. Thus a layer establishes itself close to the
wall with a velocity gradient. This is what we call the Boundary 9
Layer.
Planetary boundary layer 行星边界层
Shallow water model 浅水模型
Βιβλιοθήκη Baidu平运动(u, v)与高度z无关
准水平 u v 0 z z
For equation of horizontal velocity (u, v, 0)
1
dVh
/
dt
h p 2 V h
du / dt 1 p
fv
x
V h (u , v,0 )
(2.) Theory for solutions and mechanisms: • inviscid shallow-water theory无粘旋转流体的浅水理论 • friction and viscous flow,摩擦和粘性流 • wind-driven oceanic circulation,海洋风生环流
浅水模型中
• 粘性，斜压性和涡管的倾斜机制均不存在，所以 改变涡度的唯一机制是涡管的伸缩效应，或水平 辐散/辐合效应
da
dt
( a )V
a V
p ( 1
2
ij )
d [z f ] 0 absolute vorticity
dt H
fluid depth
4
地转流 Geostropic flow, 当大尺度时Ro<<1
• Objectives: to understand the common character of large scale atmospheric dynamics and oceanic dynamics.大尺度 大气和海洋动力学的共性特征.
• Major Contents:
(1.) Dynamic behavior of geophysical fluid under conditions of gravitation, rotation, stratification层结, viscosity and heating粘性和加热;
大气边界层（百度）
• 近地面层或表面层（亦称常通量层constant fluxes layer ）：是大气边界层最接 近地表面的部分。厚度为100米左右，该层内湍流黏性力为主导力。风速与高 度同增。湍流动量通量(湍流切应力)、热通量和水汽通量近似不随高度变化的 气层。按照稳定度性质区分为不稳定近地面层、中性近地面层和稳定近地面 层。厚度在十米至百米左右，不稳定或地面粗糙度大的情形下厚度较大，稳 定或地面粗糙度小的时候较浅薄。近地面层中温度、湿度、风速等气象。要 素随高度的变化很大，湍流运动对该层的性质起着决定性的作用，进而又决 定了整个大气边界层的特征。近地面层是人类和生物直接接触的气层和大气 污染影响最主要的表现场所。
8
Boundary Layer
Figure : Formation of a Boundary Layer
Let us now follow the effects as a flow approaches a flat plate,
Consider a uniform (inviscid) flow in front of a flat plate at a
dv / dt 1 p fu
y
We assumed that, the velocity (u, v) is independent of depth, z.
Examining the equations for u and v, we note that the
accelerations do not vary with depth z. (du/dz=dv/dz=0)
H
L
Eq
H
L
Chapter 6 Ekman flows
• Near wall surfaces
• Near free surfaces
Ekman模型 (考虑粘性和湍流的情况 viscosity and turbulence effect) (~Ekman flows/layers)
6.1 考虑粘性效应的边界层
to the solid surface continuously decreases towards downstream. But
away from the flat plate the speed is equal to the free stream value
of . Consequently a velocity gradient is set up in the fluid in a
speed
. As soon as the flow 'hits' the plate No Slip Conditions
gets into action. As a result, the velocity on the body becomes zero.
Since the effect of viscosity is to resist fluid motion, the velocity close