Wind - Meteorology: Lab - Lecture Notes | ESCI 241, Study notes of Meteorology

Download Wind - Meteorology: Lab - Lecture Notes | ESCI 241 and more Study notes Meteorology in PDF only on Docsity! ESCI 241 – Meteorology Lesson 11 – Wind Dr. DeCaria Reading: Meteorology Today, Chapter 9 COORDINATES AND VELOCITY
In meteorology we use the following coordinate system: ο The x-coordinate increases eastward ο The y-coordinate increases northward ο The z-coordinate increases upward
The velocity components along each coordinate direction are defined as ο u ≡ dx/dt ; u is the speed in the eastward direction (zonal velocity) ο v ≡ dy/dt ; v is the speed in the northward direction (meridional velocity) ο w ≡ dx/dt ; w is the speed in the upward direction (vertical velocity) GRADIENT
The two-dimensional gradient (or del) operator is defined as ˆ ˆi j x y ∂ ∂ ∇ ≡ + ∂ ∂ .
The gradient of a scalar field (such as pressure) is a vector pointing in the direction of maximum increase in the field. It is defined as ˆ ˆ p p p i j x y ∂ ∂ ∇ ≡ + ∂ ∂ .
If a contour of the scalar field is plotted (such as isotherms or isobars) the gradient at a given point is a vector that is oriented at 90° to the contours and pointed toward higher values. ο The example below shows the direction of the pressure gradient at several points. 2 ο Since the gradient is a vector, it has components in the x- and y-directions. The table below shows the sign of the components of the pressure gradient at the five points from the example above. Point ∂p/∂x ∂p/∂y A 0 − B + + C − − D − + E 0 0 ο If it isn’t apparent to you why at point A the x-derivative is zero, imagine that you are walking from west to east across point A and are carrying a barometer (or barograph). The pressure trace would look something like the following figure. 5 CORIOLIS FORCE (CF)
This force is an apparent force that results from using a rotating coordinate system.
The Coriolis force acts horizontally at 90° to the right or left of motion (depending on which direction the coordinate system is rotating). ο Note: There is a vertical component to the Coriolis force, but it is very small and can normally be ignored.
In vector form the Coriolis acceleration is 2CORa V= − Ω×


, where Ω
is the angular velocity of the Earth’s rotation.
At a point on the surface of the Earth, the horizontal components of acceleration due to the Coriolis force are 2 sin ; 2 sin CORx CORy a v a uφ φ= Ω = − Ω , (Note: There actually is a Coriolis acceleration due to the vertical motion also, but it is small in comparison the that due to the horizontal motion. This is discussed in more advance courses. If you want to learn more about Coriolis acceleration, go to this link.)
We define the Coriolis parameter as φsin2Ω≡f , so the components of the Coriolis acceleration are then ; CORx CORy a f v a f u= = − .
In vector form, the horizontal Coriolis acceleration on the Earth is ˆ COR a k f V= − ×

. 6 GEOSTROPHIC BALANCE
If the pressure gradient force and the Coriolis force are the only two forces we are concerned with, then the total acceleration of the air is just the sum of the pressure gradient and Coriolis accelerations, Vfkpa

×−∇−= ˆ 1 ρ
In component form this is fu y p afv x p a yx − ∂ ∂ −=+ ∂ ∂ −= ρρ 1 ; 1 .
If the Coriolis force exactly balances the pressure gradient force then the net acceleration is zero, and we have what is known as geostrophic balance, and the wind in such balance is called the geostrophic wind.
The components of the geostrophic wind are x p f v y p f u gg ∂ ∂ = ∂ ∂ −= ρρ 1 ; 1 .
In vector form the geostrophic wind is pk f Vg ∇×= ˆ1 ρ
.
Properties of the geostrophic wind are: ο The geostrophic wind blows parallel to the isobars with lower pressure to the left. ο The greater the pressure gradient, the stronger the geostrophic wind. ο A given pressure gradient will give a stronger geostrophic wind at lower latitudes (because f gets smaller at lower latitudes).
To a first approximation the winds in the atmosphere can be considered to be in geostrophic balance. Therefore, we can look at a weather map and can judge what the wind flow is from the pattern of the isobars. ο BUYS BALLOTT’S LAW – In the northern hemisphere, if you stand with your back to the wind, low pressure will be to your left.
The speed of the geostrophic wind can be approximated by n p f Vg ∆ ∆ ≅ ρ 1 7 where ∆p is the difference in pressure between adjacent isobars (in Pascals, not millibars), and ∆n is the horizontal distance between the two adjacent isobars. DEVIATIONS FROM GEOSTROPHIC BALANCE
If we are dealing with winds well away from the surface of the earth, and flowing in a straight line, then we can assume that they are close to geostrophic. If friction is present, or if the flow is curved, then geostrophic balance no longer applies.
Friction (FR) – Friction always acts to slow the air down, so it is always acting opposite to the direction of motion. ο Friction is only important within a few kilometers of the earth’s surface (in what is known as the planetary boundary layer). Above the planetary boundary layer we can assume that there is no friction. ο If friction is present, the wind can no longer be in geostrophic balance. ο Friction results in a slowing of the wind. This causes the wind to blow slightly across the isobars toward lower pressure.
Curved flow (the gradient wind). ο If the flow is curved, then the wind is accelerating (since its direction is changing). Therefore, the forces on the air are no longer in balance. Whether the flow is curved to the left or right determines which force is stronger than the other. ο If the flow is curved to the left (cyclonic flow) then the pressure gradient force must be stronger than the Coriolis force. ο If the flow is curved to the right (anticyclonic flow) then the pressure gradient force must be weaker than the Coriolis force. ο The geostrophic wind, adjusted for curvature, is known as the gradient wind. ο The gradient wind will be weaker than the geostrophic wind (subgeostrophic) in cyclonically curved flow, and stronger than the geostrophic wind (supergeostrophic) in anticyclonically curved flow.