2-2014-09-中尺度-方程组G
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Ｔ１
> = <
Ｔ’
１
Ｔ０
Ｔ’
０
赤道
Ｔ－１
Ｔ’－
１
Brunt-Vä isä lä
Wave equation Frequency Period scale Physicsimplication
dw / dt ( ' / 0 ) g d ' / dt w 0 / z
Inertial
On the other hand, if the inertial forces dominate, the result is geostrophic adjustment. The atmospheric response is dependent upon the scale of the disturbance.
大气运动系统的尺度划分的基本方法
经验、实用（几何）、理论 中尺度系统的定义
Based on his research on radar storm-echoes collected at the MIT Weather Radar Research Project, Ligda (1951) made the foresighted statement,” It is anticipated that radar will provide useful information concerning the structure and behavior of that portion of the atmosphere which is not covered by either micro- or synoptic meteorological studies. We have already observed with radar that precipitation formations which are undoubtedly of significance occur on a scale too gross to
注：ν为运动粘滞性
量纲参数(表中均为常用符号)(阿特金森，1987)
q F 2N 2 S 4
N2, f, P(b), U/ Ri=N2/(U/ Z)2
ห้องสมุดไป่ตู้
z
F 2 f ( f v / x), S 2 fv / z g / 0 Q x , N 2 g / 0 Q x
§1.1 大气运动系统的尺度划分
Richardson (1922): “big whirls have little whirls which feed on their velocity and little whirls have lesser whirls and so on to viscosity.”
(After from T.T. Fujita: Review of the history of mesoscale meteorology and forecasting)
Ligda (1951) : the
phenomena that are too large to be observed by in-situ sensors at a single station, but too small to be resolved by the conventional upperair network.
be observed from a single station, yet too small to appear even on sectional synoptic charts. Phenomena of this size might will be designated as “mesometeorological”.
Ro=V/fL Ri=N2/Uz2
0.1 100
1.0 1.0
>1.0 <1.0
Typical mesoscale is the scale, which is large enough so that the static equilibrium is kept ,while is small enough so that the motion is ageostrophic. (Pielke,R.A.1984) 定义3 典型中尺度指这样的尺度: 其水平尺度足够大以至 于可适用静力平衡关系；水平尺度足够小以至于地转风关系 不成立。
中尺度气象学
Mesoscale Meteorology
（2）
寿绍文 南京信息工程大学大气科学学院 201４.0９
第一章 中尺度运动的特征 及方程组
§1.1 §1.2 §1.3 §1.4 大气运动系统的尺度划分 中尺度大气运动的基本特征 包辛尼斯克(Boussinesq)近似方程组 滞弹性(Anelastic )近似方程组
Small scale
L 2pU / N
f FN
Mesoscale
PF f
Synoptic scale
FP
Planetary scale
2pU / N L 2pU / f
L 2p (U / b )1/ 2
2pU / f L 2p (U / b )1/ 2
Mesoscale refers to as the scale of flow with a frequency larger than f but smaller than N. Buoyancy and rotation are the two fundamental variables describing the mesoscale circulation.
Adjustment of the pressure and wind fields
Large scale : wind field adjusted pressure field
Meso scale: pressure field adjusted wind field
( E / P) geo LR / L2 , ( E / P) geo ( E / P) geo
2 2
2
LR gH / f
Rossby radius of deformation
1/ 2
g RN / L RN HN / f , N z 2 2 V N 2 2 RN / L2 R synoptic o Ri B 2 Ri 100 2 2 V f L Ro 0.1 z
参数 弗劳德数Fr 雷利数Ra 雷诺数Re 里查森数Ri 罗斯贝数Ro 斯特劳哈尔 数St
形式 Ｕ２/ｇＬ(Δ ρ ／ρ ) ｇＬ(Δ ρ ／ρ )ａν ＵＬ／ν (Δ ρ ／ρ )／Ｌ(u ／ｚ)２ Ｕ／Ω Ｌ Ｕ／ｆＬ
特征比 惯性力／浮力 浮力／耗散力 惯性力／粘滞力 静力稳定度／(切变) 相对于旋转坐标惯性力／科氏 力 对流加速度／相对于一个固定 观测者的局地加速度
(hurricanes), jet streaks, polar lows
Meso-b (20 -200, 2 h - 1 d), e.g , squall lines, MCCs,
mountain waves, lee cyclones, sea breezes, meso-lows/meso-highs, high
and low-level jet streaks
Meso-g (2 - 20 , > 2 h),
fronts, micro-downbursts, tornadoes e.g , thunderstorms, gust
实 用 （ 几 何 ） 分 类
天气尺度 中间尺度 次天气尺度
图1.3 Ⅰ.Orlanski的尺度划分(右)及几种主要的尺度定义的对照 (Orlanski，1975)
图1.2 按拉格朗日罗斯贝数作出的尺度分类（Emanuel,1986）
§1.2 中尺度大气运动的基本特征
尺度 ２~２，０００千米 散度、涡度、垂直速度 地转偏向力、浮力的作用 质量场和风场的适应过程
Divergence ,vorticity and vertical motion
Meso a
Horizontal scale L Divergence D and vorticity Vertical motion W
102 s 1
minutes Cloud-scale
StratificationRotationgravity(buoyancy) inertial wave waves
Restoring force
Four-fold division of atmospheric circulations
FN
Ro= |du/dt |/ |fu | =|u (U/ x)|/ |fu | = U/fL Baroclinic, barotropic, Kelvin-Helmholtz, Symmetric and convective instability
Ri T Ro synoptic scale 100 L/U 0.1 mesoscale 1-10 1/f 1.0 small scale <1 1/N >1
理论分类
统计理论 动力学理论
图1.1 自由大气(实线)和近地面(虚线)的东西风分量的平均动能功率谱分析(Vinnichenko,1970)
动力学分类
c) 动力学定义
c = w/k, k = 2p/L, w= 2p/T 大气中三种基本频率: Brunt-Vä isä lä频率: N2=(g/Q)( Q/z) 惯性频率: f = 2 Wsinf 行星频率: P=(Ub)1/2
Type of motion
Baroclinic waves Slantwise convection Cumulus convection
Vertical Horizontal scale scale f2Uz/(Nb2) fUz/(Nb)
D D UzD/f D h
Time scale 2pN/(fUz)
du / dt fv dv / dt fu
104 s 1
hours Geostrophic flow
Planetary
d ( f ) / dt 0
106 s 1
days Planetary scale The earth curvature – Rossby waves
f -1 N-1 h/U2
Rossby number
1/Ri1/2 2p 2pN/f 2pU2/(hf)
PBL turbulence h
(AfterK.A.Emanuel,1986).
Mesoscale system may be defined as that with a state ratio L/D=Uz /f and temporal scale f -1 定义2 具有状态比L/D=Uz/f,时间尺度T=f-1的运动称为中 尺度运动
Two primary restoring forces governing the response are N (gravitational) and f (rotational). If the gravitational response is strong, the atmosphere will generate a gravity wave.
Meso b
Meso g
103 10-5 10-1
102 10-4 100
101 (Km) 10-3(s-1) 101(ms-1)
I w
0
p0
dF
g
p0
d p.
d p d t.
W
t2
t1
0
w
dF
g
Coriolis force and buoyancy force
Macro (大)Scale Meso (中)Scale Micro (小)Scale
mesoscale
300-600 km (100 to 1000 km), 12hrs
定义1 “中尺度”是指比常规探空网的时空尺度小，但比单 个积云的时空尺度大得多的一种尺度
实用（几何）分类
Orlanski (1975),
来源网站 | 查看原图
Meso-a : (200-2000,1 –5 d), e.g , frontal cyclones, typhoon
> = <
Ｔ’
１
Ｔ０
Ｔ’
０
赤道
Ｔ－１
Ｔ’－
１
Brunt-Vä isä lä
Wave equation Frequency Period scale Physicsimplication
dw / dt ( ' / 0 ) g d ' / dt w 0 / z
Inertial
On the other hand, if the inertial forces dominate, the result is geostrophic adjustment. The atmospheric response is dependent upon the scale of the disturbance.
大气运动系统的尺度划分的基本方法
经验、实用（几何）、理论 中尺度系统的定义
Based on his research on radar storm-echoes collected at the MIT Weather Radar Research Project, Ligda (1951) made the foresighted statement,” It is anticipated that radar will provide useful information concerning the structure and behavior of that portion of the atmosphere which is not covered by either micro- or synoptic meteorological studies. We have already observed with radar that precipitation formations which are undoubtedly of significance occur on a scale too gross to
注：ν为运动粘滞性
量纲参数(表中均为常用符号)(阿特金森，1987)
q F 2N 2 S 4
N2, f, P(b), U/ Ri=N2/(U/ Z)2
ห้องสมุดไป่ตู้
z
F 2 f ( f v / x), S 2 fv / z g / 0 Q x , N 2 g / 0 Q x
§1.1 大气运动系统的尺度划分
Richardson (1922): “big whirls have little whirls which feed on their velocity and little whirls have lesser whirls and so on to viscosity.”
(After from T.T. Fujita: Review of the history of mesoscale meteorology and forecasting)
Ligda (1951) : the
phenomena that are too large to be observed by in-situ sensors at a single station, but too small to be resolved by the conventional upperair network.
be observed from a single station, yet too small to appear even on sectional synoptic charts. Phenomena of this size might will be designated as “mesometeorological”.
Ro=V/fL Ri=N2/Uz2
0.1 100
1.0 1.0
>1.0 <1.0
Typical mesoscale is the scale, which is large enough so that the static equilibrium is kept ,while is small enough so that the motion is ageostrophic. (Pielke,R.A.1984) 定义3 典型中尺度指这样的尺度: 其水平尺度足够大以至 于可适用静力平衡关系；水平尺度足够小以至于地转风关系 不成立。
中尺度气象学
Mesoscale Meteorology
（2）
寿绍文 南京信息工程大学大气科学学院 201４.0９
第一章 中尺度运动的特征 及方程组
§1.1 §1.2 §1.3 §1.4 大气运动系统的尺度划分 中尺度大气运动的基本特征 包辛尼斯克(Boussinesq)近似方程组 滞弹性(Anelastic )近似方程组
Small scale
L 2pU / N
f FN
Mesoscale
PF f
Synoptic scale
FP
Planetary scale
2pU / N L 2pU / f
L 2p (U / b )1/ 2
2pU / f L 2p (U / b )1/ 2
Mesoscale refers to as the scale of flow with a frequency larger than f but smaller than N. Buoyancy and rotation are the two fundamental variables describing the mesoscale circulation.
Adjustment of the pressure and wind fields
Large scale : wind field adjusted pressure field
Meso scale: pressure field adjusted wind field
( E / P) geo LR / L2 , ( E / P) geo ( E / P) geo
2 2
2
LR gH / f
Rossby radius of deformation
1/ 2
g RN / L RN HN / f , N z 2 2 V N 2 2 RN / L2 R synoptic o Ri B 2 Ri 100 2 2 V f L Ro 0.1 z
参数 弗劳德数Fr 雷利数Ra 雷诺数Re 里查森数Ri 罗斯贝数Ro 斯特劳哈尔 数St
形式 Ｕ２/ｇＬ(Δ ρ ／ρ ) ｇＬ(Δ ρ ／ρ )ａν ＵＬ／ν (Δ ρ ／ρ )／Ｌ(u ／ｚ)２ Ｕ／Ω Ｌ Ｕ／ｆＬ
特征比 惯性力／浮力 浮力／耗散力 惯性力／粘滞力 静力稳定度／(切变) 相对于旋转坐标惯性力／科氏 力 对流加速度／相对于一个固定 观测者的局地加速度
(hurricanes), jet streaks, polar lows
Meso-b (20 -200, 2 h - 1 d), e.g , squall lines, MCCs,
mountain waves, lee cyclones, sea breezes, meso-lows/meso-highs, high
and low-level jet streaks
Meso-g (2 - 20 , > 2 h),
fronts, micro-downbursts, tornadoes e.g , thunderstorms, gust
实 用 （ 几 何 ） 分 类
天气尺度 中间尺度 次天气尺度
图1.3 Ⅰ.Orlanski的尺度划分(右)及几种主要的尺度定义的对照 (Orlanski，1975)
图1.2 按拉格朗日罗斯贝数作出的尺度分类（Emanuel,1986）
§1.2 中尺度大气运动的基本特征
尺度 ２~２，０００千米 散度、涡度、垂直速度 地转偏向力、浮力的作用 质量场和风场的适应过程
Divergence ,vorticity and vertical motion
Meso a
Horizontal scale L Divergence D and vorticity Vertical motion W
102 s 1
minutes Cloud-scale
StratificationRotationgravity(buoyancy) inertial wave waves
Restoring force
Four-fold division of atmospheric circulations
FN
Ro= |du/dt |/ |fu | =|u (U/ x)|/ |fu | = U/fL Baroclinic, barotropic, Kelvin-Helmholtz, Symmetric and convective instability
Ri T Ro synoptic scale 100 L/U 0.1 mesoscale 1-10 1/f 1.0 small scale <1 1/N >1
理论分类
统计理论 动力学理论
图1.1 自由大气(实线)和近地面(虚线)的东西风分量的平均动能功率谱分析(Vinnichenko,1970)
动力学分类
c) 动力学定义
c = w/k, k = 2p/L, w= 2p/T 大气中三种基本频率: Brunt-Vä isä lä频率: N2=(g/Q)( Q/z) 惯性频率: f = 2 Wsinf 行星频率: P=(Ub)1/2
Type of motion
Baroclinic waves Slantwise convection Cumulus convection
Vertical Horizontal scale scale f2Uz/(Nb2) fUz/(Nb)
D D UzD/f D h
Time scale 2pN/(fUz)
du / dt fv dv / dt fu
104 s 1
hours Geostrophic flow
Planetary
d ( f ) / dt 0
106 s 1
days Planetary scale The earth curvature – Rossby waves
f -1 N-1 h/U2
Rossby number
1/Ri1/2 2p 2pN/f 2pU2/(hf)
PBL turbulence h
(AfterK.A.Emanuel,1986).
Mesoscale system may be defined as that with a state ratio L/D=Uz /f and temporal scale f -1 定义2 具有状态比L/D=Uz/f,时间尺度T=f-1的运动称为中 尺度运动
Two primary restoring forces governing the response are N (gravitational) and f (rotational). If the gravitational response is strong, the atmosphere will generate a gravity wave.
Meso b
Meso g
103 10-5 10-1
102 10-4 100
101 (Km) 10-3(s-1) 101(ms-1)
I w
0
p0
dF
g
p0
d p.
d p d t.
W
t2
t1
0
w
dF
g
Coriolis force and buoyancy force
Macro (大)Scale Meso (中)Scale Micro (小)Scale
mesoscale
300-600 km (100 to 1000 km), 12hrs
定义1 “中尺度”是指比常规探空网的时空尺度小，但比单 个积云的时空尺度大得多的一种尺度
实用（几何）分类
Orlanski (1975),
来源网站 | 查看原图
Meso-a : (200-2000,1 –5 d), e.g , frontal cyclones, typhoon