Meteorology Flashcards
How far does the troposphere extend and why is it significant?
11km, it is where weather occurs
What characterises a region of convergent flow?
Air flows in toward a central point at ground level and rises before diverging near the upper limit
What characterises a region of divergent flow?
Air flows together high in the troposphere and descends before parting near the ground
What force causes wind flow to deviate from a straight path?
Coriolis force
What is a typical size and speed of a depression?
4000km diameter
15-25 m/s
Which type of front causes severe weather?
Cold front
What is the lapse rate?
Decrease in temperature with height
What is the equation for the polytropic law?
p=k * rho^n
What is the equation of state?
p=rho * R * T
What does adiabatic mean?
No transfer of heat or mass outside the system
What is the density ratio?
rho2/rho1 = (p1/p2)^(gamma-n/gamma*n)
What is n in these equations? What is its equation?
Polytropic index
n = g/(g-RL) where L is lapse rate
What is assumed for Earth-fixed motion?
Linear acceleration di V/dt = 0
Rotational acceleration di Omega/dt = 0
What is the pressure gradient force?
-delta p/rho
What are the forces denoted by Ff and g respectively?
Friction force
Gravity force
What is the equation for coriolis force relative to motion?
-2 * Omega * Vm
Gravity force is not used directly in acceleration calculations, what is used instead?
Effective gravity force
g - Omega(Omega * r)
What are the unit vectors s, n and k?
s is along the particle path
n is normal to the path
k is vertically up from the Earth’s surface
How is coriolis force different to the other involved forces when resolving into s and n?
Coriolis force only has an n component, all others have both
What is the coriolis parameter f?
2 * Omega * sin phi
What are the conditions for geostrophic wind?
Negligible friction
Negligible curvature
Pressure gradient and coriolis force are balanced
What is the equation for geostrophic wind speed?
Vg = -1/(f*rho) * dp/dn
How do you begin the derivation of gradient wind speed?
(dv/dt)s = 0
(dv/dt)n = v^2/r
If centripetal acceleration is positive, what is the direction of circulation?
Anti-clockwise
What direction is cyclonic flow in the northern hemisphere?
Anti-clockwise
What is the equation for solutions of gradient wind speed?
Vgr = -fr/2 * (1+- sqrt(1+ 4Vg/fr))
For a regular low in the northern hemisphere (acw circulation) which solution for Vgr is used?
The negative
What is the Rossby number?
Ratio of centrifugal to coriolis actions
Ro = v/f*r
What does it mean when the Rossby number is large?
Coriolis force can be neglected
What is cyclostrophic wind speed? What is the equation?
Gradient wind speed neglecting coriolis force
Vc = sqrt(-r/rho * dp/dn)
What is the radius of maximum winds in relation to the fitting factors A and B?
Rw = A^(1/B)
What is the name of the height, delta, at which wind speed becomes equal to gradient wind speed?
Boundary layer depth
What is the equation for maximum shear stress at the ground surface?
Tao 0 = rho * u^2
Where u is friction velocity
What is z0?
Roughness length, used to scale relative height z
What is the function g(x) which relates x = z/z0 to y = Vz/u*?
2.5ln(x) + (34.5fz)/u*
For what heights is the mean velocity equation using z0 applicable?
Up to 300m
Below 30m the 34.5fz/u* part is neglected
What is the power law Vz/Vr?
Vz/Vr = (z-d/r-d)^alpha
Where d is the zero level, r is reference height and alpha is tabulated based on terrain
How is turbulent wind speed quantified?
A sum of mean and fluctuating components
How is turbulence intensity found?
Standard deviation of wind speed divided by mean wind speed
What is the gust factor Ktao?
Peak wind speed (V^)/ mean wind speed (V-)
What is the autocovariance function used for?
Measuring the persistence of turbulent eddies
What is the autocovariance function Cuu(Tao)?
The time-averaged product of velocity and times t and t+tao
What is the autocorrelation function rhouu?
rhouu(tao) = Cuu(tao)/variance
What is the equation for time period of turbulence?
The integral of autocorrelation by tao
Similarly to time based covariance and correlation equations, what else can be represented in this way?
Velocity measured simultaneously at two different points in SPACE
How is the Power Spectral Density equation Suu defined?
Variance = integral of Suu over frequency range n
What is the PSD function used for?
Finding the frequency distribution of kinetic energy of fluctuations
What are the 3 types of anemometer?
Pressure
Rotation
Research (Hot wire/sonic)
What are advantages and disadvantages of pressure anemometers?
+ Robust, low maintenance
+ Quick response to fluctuation
- Many factors affecting calibration
- Poor accuracy at high yaw
What are advantages of rotation anemometers?
+ Calibration unaffected by temperature, humidity etc
+ Linear response
+ Robust
+ Omnidirectional
What are disadvantages of rotation anemometers?
- Slow response at low wind speeds
- Cannot record wind direction
- Differently calibrated for smooth and turbulent flow
- Overspeeding possible
What are generally the main advantage and disadvantage of research anemometers?
Very accurate
Very expensive
What distribution is commonly used to approximate cumulative probability of wind speeds in storm conditions?
Weibull distribution
What is the notation Px signifying? What about Pxn?
Px is the probability that the extreme value is less than x in any one year
Pxn is the probability x is not exceeded in n years
How do you create a quadratic in the gradient wind speed derivation?
Substitute in the equation for geostrophic wind speed
In what direction does coriolis force act relative to wind motion as viewed from above?
To the right of wind direction in the Northern Hemisphere, to the left in the Southern Hemisphere
Why is (dV/dt)s = 0 in gradient wind?
Flow is steady so there is no streamwise acceleration
How do you convert bar to Pascals?
Divide by 1e-5
What is the equation for peak wind speed in a hurricane?
sqrt(B/rho*e (pn -pc))
What is typically assumed of Omega if no information about rotational acceleration is given?
Omega = 2pi/86400
Where 86400 is the number of seconds in a day
What is true in adiabatic conditions?
n = gamma
