建國中學

暑假地球科學讀書會

大氣動力學

Presenter: 12527 鄭竣陽

Forces

pressure gradient force, PGF
gravitational force
viscosity
friction

apparent Forces

aka pseudo force
centrifugal force
coriolis force

Pressure gradient force

assume there's an air parcel

a_x = -\frac{1}{\rho}\frac{\partial P}{\partial x\ }

a_x = -\frac{1}{\rho}\frac{\partial P}{\partial x\ }

a_y = -\frac{1}{\rho}\frac{\partial P}{\partial y\ }

a_y = -\frac{1}{\rho}\frac{\partial P}{\partial y\ }

a_z = -\frac{1}{\rho}\frac{\partial P}{\partial z\ }

a_z = -\frac{1}{\rho}\frac{\partial P}{\partial z\ }

Viscosity

x is parrallel to the line of latitude

y is parralel to the line of longitude

z is the altitude

\dot x \leftrightarrow u \\ \dot y \leftrightarrow v \\ \dot z \leftrightarrow w

\dot x \leftrightarrow u \\ \dot y \leftrightarrow v \\ \dot z \leftrightarrow w

F = \mu A \frac{\Delta u}{\Delta z}

F = \mu A \frac{\Delta u}{\Delta z}

(observed)

\tau_{z \to x} = \large \frac{F}{A} \normalsize = \mu \large \frac{\partial u}{\partial z}

\tau_{z \to x} = \large \frac{F}{A} \normalsize = \mu \large \frac{\partial u}{\partial z}

Viscosity

a_{z \to x} = \frac{(\tau_u - \tau_d)\Delta zA \\}{m}

a_{z \to x} = \frac{(\tau_u - \tau_d)\Delta zA \\}{m}

\\ = \frac{\frac{\partial}{\partial z} \tau_{z \to x} \Delta x \Delta y \Delta z}{m}

\\ = \frac{\frac{\partial}{\partial z} \tau_{z \to x} \Delta x \Delta y \Delta z}{m}

\\ = \frac{1}{\rho} \frac{\partial}{\partial z} \tau_{z \to x}

\\ = \frac{1}{\rho} \frac{\partial}{\partial z} \tau_{z \to x}

\\ = \frac{\mu}{\rho} \frac{\partial}{\partial z} \frac{\partial u}{\partial z}

\\ = \frac{\mu}{\rho} \frac{\partial}{\partial z} \frac{\partial u}{\partial z}

\\ = \nu \frac{\partial^2 u}{\partial z^2}

\\ = \nu \frac{\partial^2 u}{\partial z^2}

a_x = a_{x \to x} + a_{y \to x} + a_{z \to x}

a_x = a_{x \to x} + a_{y \to x} + a_{z \to x}

= \nu [\frac{\partial^2 u}{\partial x} + \frac{\partial^2 u}{\partial y} + \frac{\partial^2 u}{\partial z}]

= \nu [\frac{\partial^2 u}{\partial x} + \frac{\partial^2 u}{\partial y} + \frac{\partial^2 u}{\partial z}]

= \nu \nabla^2 u

= \nu \nabla^2 u

\nabla = \displaystyle \sum_{i=1}^n \vec e_i {\partial \over \partial x_i} = \left({\partial \over \partial x_1}, \ldots, {\partial \over \partial x_n} \right)

\nabla = \displaystyle \sum_{i=1}^n \vec e_i {\partial \over \partial x_i} = \left({\partial \over \partial x_1}, \ldots, {\partial \over \partial x_n} \right)

1 . 1

建國中學暑假地球科學讀書會大氣動力學 Presenter: 12527 鄭竣陽

大氣動力學 Atmospheric Dynamics

By BrineTaiwan

大氣動力學 Atmospheric Dynamics

The study of motion systems of meteorological importance, integrating observations at multiple locations and times and theories.

3 years ago
250

BrineTaiwan

歡迎來教我我想變電神

youtube.com/channel/UCCZTue2ueya6I9yAsMLJZsA

建國中學

Index

Forces

apparent Forces

whiteboard time

Pressure gradient force

Gravitational force

Viscosity

Centrifugal Force

Viscosity

大氣動力學 Atmospheric Dynamics

大氣動力學 Atmospheric Dynamics

BrineTaiwan

建國中學

大氣動力學 Atmospheric Dynamics

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