1. Wind: Small scale and Local Systems (part I)
Physics of the Atmosphere: 2nd & 3rd week
Chapter 11

2. Tradictional classification of scales

4. Microscale

5. Mesoscale

6. Microscale: The Force of the Wind
The red car is pushed leftwards by the ground wind. The force is proportional to the square of the velocity:

7. Microscale: LIFT Force
The Lift is a force perpendicular to the velocity of the air relative to the wing:
Non-propeled flyers need vertical winds to compensate velocity loss due to Drag.

8. Understanding Microscale: Fluid Mechanics
The Bernoulli Equation:
Centrifugal force:

9. Force on a aerofoil: Lift &Drag

10. Friction: Boundary Layer (BL)
Inside a BL, inertia and friction forces coexist and are of the same order of magnitude.

11. Boundary Layer Evolution
In the atmosphere, BL is usually turbulent. Vertical diffusion depends on vertical density profile.

12. Atmospheric Boundary Layer

13. Atmospheric Inversion
It almost always refers to a "temperature inversion", i.e. an increase in temperature with height, or to the layer ("inversion layer") within which such an increase occurs.[1]

14. Boundary Layer Separation
Friction can only stop the flow. It can’t reverse it.
Negative pressure gradient (left side) pushes the flow forward. It will not reverse it.
A positive pressure gradient (right side) can reverse the flow. The first fluid to inverse the velocity is the fluid with lower velocity (lower inertia) close to the wall.

15. Main Forces in each scale
Pressure + Coriolis. They almost balance. This allows easy calculation of the geostrophic wind.
Temporal inertia + Coriolis+pressure + friction
Convective inertia + pressure + friction

16. Friction. How does it occur

17. Diffusion
Figures below represent 2 material systems, one fully white and the other fully Black separated by a diaphragm. The top figures represent the molecules (microscopic view) and the figures below the macroscopic view. When the diaphragm is removed the molecules from both systems start to mix and we start to see a grey zone between the two systems (b) at the end everything will be grey (c). During situation (b) we there is a diffusive flux of black molecules crossing the diaphragm section. This flux cannot be advective because velocity is null.
(a)
(b)
(c)

18. Ver texto sobre propriedades dos fluidos e do campo de velocidades
Diffusivity
When the diaphragm is removed molecules move randomly. The net flux is the diffusive flux.
The flux of molecules in each sense is proportional to the concentration and to the individual random velocity:
But,
Diffusivity is the product of the displacement length and the molecule velocity. This velocityis in fact the difference between the molecule velocity and the average velocity of the molecules accounted for in the advective term.
Ver texto sobre propriedades dos fluidos e do campo de velocidades

19. Diffusivity Diffusivity is definide as:
is the molecule velocity part not resolved (or included) in our velocity definition. In a laminar flow is the brownian velocity while in a turbulent flow is the turbulent velocity, a macroscopic velocity that we can see in the tubulent eddies.
is the lenght of the displacement of a molecule before being disturbed by another molecule (or of a portion of fluid in a turbulent flow). When the molecule hits another molecule it gets a new velocity.
Diffusivity dimensions are:

20. Diffusive Flux Is the flux due to difusivity and property gradient:
The sense of the diffusive flux is opposit to the sense of the gradient.
Diffusive flux is nul if there is no gradient.

21. What about momentum? Flow with velocity gradient.
If a portion of fluid (e.g. molecule) descends from the higher speed for smaller, will increase the speed in that area. In this case an equal share of fluid will rise and will reduce the speed up.
In the presence of random velocity gradient from faster speeds, fluid drag the slower. According to the law of Newton, an acceleration match a force, which in this case is a force of friction.
The momentum diffusivity is called viscosity, which can also be seen as the relationship between the tension (friction) and the rate of deformation of a fluid element (velocity gradient).

22. Deiffusive flux of momentum: Shear Stress
τ(y+Δy)
τ(y)
Random movement not represented by the speed generates a transfer of momentum that is felt as a force.
This force increases with the velocity gradient and with the amount of mass it is necessary to accelerate and the rate at which the mass moves between the two layers.
In this equation the units of dynamic viscosity are (force/area)/second = >N/m2/s,
Poiseuille no SI) and the units of the cinematic viscosity are m2/s

23. Turbulent diffusivity/viscosity
The need is the same as the molecular diffusivity: in turbulent flows there are random eddies that we can not describe/measure. The random velocity associated to them originates fast mixing.
Mathematically the effect of those eddies is represented by a turbulent diffusion, where diffusivity is also
But now, the length is the size of the eddies and the velocity is their displacement velocity.

24. Atmospheric stability and diffusion
Why is vertical diffusion enhanced by atmospheric instability?

25. Unstable
Stable
Thermal instability mixes air vertically and thus also transports momentum, reducing velocity gradient

26. Air pockets: BL separation

27. Idem

28. Shelterbelt

29. Wave generation

30. Pedaling in the wind

31. Wind Power
What is the maximum energy that a 80 m diameter turbine can extract from wind when air velocity is 3 knots?

32. Summary
Atmospheric processes can be grouped into 3 scale ranges: microscale, mesoscale and macroscale. The latter is usually subdivided into synoptic and global scales.
At microscale (up to tens of meters) the most important processes are convective acceleration, pressure and friction. At this scale the flow fits in the range of aerodynamics, i.e. is the flow around man-made constructions.
At mesoscale (tens of kilometers) the most important processes are temporal acceleration, Coriolis and pressure, although friction can also play some role. At this scale heat exchange/temperature play a major role. The flow across mountains and the sea breeze are examples of mesoscale flows. Processes responsible for cloud formation and for rain happen on this scale.
The synoptic scale is the one usually represented into meteorological charts (thousands of kilometers). At this scale pressure and Coriolis are the most important driving forces and thus the flow is mostly geostrophic. The global scale describes the flow over the whole world. Meteorological forecasting requires the simulation of this scale.