Dynamics Final

Front 1

typical horizontal length scales of atmospheric motion

Back 1

little eddies: 0.01-0.1 m
dust devils: 1-10m
tornadoes: 10-1000 m
cumulonimbus: 1000-10^4 m
fronts: 10^4-10^5 m
H/L pressure systems: 10^6 m
planetary waves: 10^7 m

Front 2

(1+x)^n

Back 2

1 + nx

Front 3

cosx taylor series approx

Back 3

1 + x^2/2!

Front 4

sinx taylor series approx

Back 4

x

Front 5

eulers formula

Back 5

cosx + isinx

Front 6

newtons 2nd law

Back 6

F = ma

Front 7

body force

Back 7

force on object is proportional to mass of object

force due to action at a distance

gravity

Front 8

surface force

Back 8

force on object is proportional to surface area of object

force due to contact of object with its surroundings

force exerted on surface of fluid elements by outside fluid

pressure force, friction

Front 9

pressure gradient force was derived by...

what is it proportional to?

Back 9

considering the net pressure force acting on a blob of air

proportional to gradient of p not to p itself

Front 10

gravitational force is proportional to what?

Back 10

inversely proportional to the square of the distance between the masses

Front 11

viscous force is related to what?

Back 11

spatial changes in the velocity field

Front 12

physical basis for friction force on air?

Back 12

random migration of air molecules

Front 13

non inertial reference frame

Back 13

reference frame that speeds up or rotates .... accelerating

Front 14

inertial reference frame

Back 14

non accelerating

Front 15

centrifugal and coriolis forces are both what?

Back 15

apparent forces

Front 16

gravity force combines what 2 forces?

Back 16

gravitational and centrifugal

Front 17

u velocity comp is along what and increases in what direction

Back 17

along latitude

u>0 toward east
u<0 toward west

Front 18

v velocity comp is along what and increases in what direction

Back 18

along meridian

v>0 toward north
v<0 toward south

Front 19

z velocity comp is along what and increases in what direction

Back 19

vertical

w>0 up
w<0 down

Front 20

hydrostatic eq is an exact eq for .... and a good approx for ...

Back 20

exact: resting atmosphere

approx: real moving atmosphere

Front 21

pressure drops off [faster or slower] with height in a cold atmosphere

Back 21

faster

Front 22

which has a larger density? cold air or warm air?

Back 22

cold air

Front 23

scale height for an isothermal eq

Back 23

H=RT/g

Front 24

lagrangian

Back 24

following air parcel motion

Front 25

eulerian

Back 25

fixed point in space

Front 26

vector eq of motion in a rotating reference frame includes what forces?

Back 26

acceleration = pgf + coriolis + gravity + friction

Front 27

spherical coords set up

Back 27

lambda=longitude
phi=latitude
z= vertical coord

Front 28

from scale analysis Du/Dt and Dv/Dt are approx what?

Back 28

U^2 / L

Front 29

geostropic balance has what 2 forces?

Back 29

pgf and coriolis

diagnostic relation btwn pressure gradient and velocity

Front 30

geostropic wind characteristics

Back 30

wind vector is parallel to isobars

with geos wind at your back, low pressure is to your left

proportional to magnitude of pressure gradient

Front 31

rossby number

Back 31

Ro = U/fL

ratio of accel to coriolis force in horiz eq of motion

Front 32

if Ro>0

if Ro<0

Back 32

Ro>0: accel is more important than coriolis

Ro<0 accel is less important than coriolis

Front 33

spherical coord equations of motion are nonlinear with ...

Back 33

1. curvature terms
2. thermal effects
3. nonlinear inertia terms

Front 34

scale analysis: L

Back 34

1000 km

Front 35

scale analysis: H

Back 35

10 km

Front 36

scale analysis: U

Back 36

10 m/s

Front 37

scale analysis: W

Back 37

0.01 m/s

Front 38

scale analysis: dp/rho horizontal

Back 38

1000 m^2/s^s

Front 39

scale analysis: dp/rho vertical

Back 39

10^5 m^2/s^2

Front 40

scale analysis: T horiz

Back 40

L/U

10^5 sec

Front 41

scale analysis: T vert

Back 41

H/W

10^6 sec

Front 42

we can neglect what terms for synoptic scale flows

Back 42

curvature terms

Front 43

dominant balance in vertical is what?

Back 43

hydrostatic balance

even though atmosphere is not at rest hydrostatic balance is a good approx

Front 44

the difference between the true density and the mean density is defined to be what?

Back 44

perturbation density

Front 45

synoptic flows are horizontally what?

Back 45

horizontally non-divergent

horiz area of parcels is conserved

Front 46

what is a trajectory?

Back 46

curve traced out by the tip of the position vector of an air parcel as it moves around

lagrangian

Front 47

what is a streamline?

Back 47

curve that is everywhere tangent to the local velocity at a given time.

eulerian

Front 48

when to trajectories and streamlines coincide?

Back 48

in steady state flows

Front 49

natural coords set up

Back 49

s: in t hat
n: in n hat
z: in k hat

n hat is perpendicular and to the left of parcel motion (t hat)

Front 50

sign of R in natural coords

Back 50

R is positive when n hat points toward the center (curves left)

R is negative when n hat points away from the center (curves right)

R is small where curvature is large

Front 51

tangential comp of eq of motion contains what terms?

Back 51

speed accel = - pgf in direction of motion

Front 52

normal comp of eq of motion contains what terms?

Back 52

0 = - centrifugal - coriolis - normal comp pgf

Front 53

geostophic flow characteristics

Back 53

parallel to isobars
isobars are straight

balance between pgf and coriolis

Front 54

inertial flow characteristics

Back 54

balance between centrifugal and coriolis

horizontal pgf is negligible

Front 55

orbital period of air parcel is...

Back 55

1/2 day / sin(phi)

Front 56

cyclostrophic balance

Back 56

centrifugal and pgf

no coriolis

Front 57

gradient wind characteristics

Back 57

wind is parallel to isobars

isobars can be curved

no change in p along trajectory

dp/ds = 0

centrifugal + coriolis + pgf

Front 58

for gradient wind and dp/dn >0 what solution(s) to you get?

Back 58

anomalous low

Front 59

for gradient wind and dp/dn <0 what solution(s) to you get?

Back 59

regular low, regular high and anomalous high

Front 60

why can't we have a cyclonic high?

Back 60

in cyclonic high, centrifugal, coriolis, and pgf all act in the same direction and this is not physically possible because they must all sum to zero

Front 61

subgeostrophic vs supergeostrophic?

Back 61

gradient wind is subgeostrophic in cyclonically curved flow in northern hemi (LOW)

gradient wind is supergeostrophic in anti cyclonically curved flow in northern hemi (HIGH)

Front 62

thermal wind characteristics

Back 62

V thermal = V geo upper - V geo lower

parallel to mean isotherms

cold air is to the left of V thermal

Front 63

vertical changes in the geos wind are associated with

Back 63

horizontal changes in temperature

Front 64

veering

Back 64

clockwise turning
warm air advection

Front 65

backing

Back 65

counter clockwise turning
cold air advection

Front 66

barotropic condition

Back 66

rho = rho(P)

dVg/dP= 0

Front 67

baroclinic condition

Back 67

rho = rho(P, T)

dVg/dP is not = 0

Front 68

air parcels moving in geostrophic wind cannot change their...

Back 68

horizontal area

Front 69

vorticity is a measure of

Back 69

twice the local angular velocity

Front 70

constant wind has what vortiicy?

Back 70

no vorticity

Front 71

cylindrical coords set up

Back 71

u --> v_r r hat
v --> v_theta theta hat
w --> w k hat

Front 72

solid body vortex

Back 72

U = Kr theta hat

vert vort is twice angular velocity of the vortex = 2K

circulation = 2KA

Front 73

circulation

Back 73

evaluated counterclockwise

line integral of u dot dl

Front 74

stokes theorem

Back 74

line integral of u dot dl = double integral n hat dot (grad cross u) dA

Front 75

stokes theorem "rules"

Back 75

1. curve doesn't have to be flat
2. true for any vector field u
3. vector u must be continuous
4. if u is velocity then grad cross u is vorticity

Front 76

express relative vertical vorticity in a special natural coordinate system defined by...

Back 76

streamlines rather than trajectories

= V/Rs - dV/dn

Front 77

T/F

there is no vertical vorticity in a jet stream

Back 77

true

Front 78

right hand rule for shear vorticity

Back 78

align fingers with u, curl toward smaller speeds... thumb points in direction of shear vorticity

Front 79

T/F

curvature vorticity is negative in cyclonic vortex

Back 79

false

positive curvature vorticity

Front 80

right hand rule for curvature vorticity

Back 80

curl fingers along streamline pointing in the direction of the flow... thumb indicates direction of curvature vorticity

Front 81

vorticity in a vr vortex

Back 81

v theta = A/r

rel vert vort = 0

Front 82

absolute vert vort is...

Back 82

rel vert vort + earth vort (f)

Front 83

vertical vorticity term: local derivative

Back 83

if positive, then increase

if negative, then decrease

Front 84

vertical vorticity term: advection

Back 84

SW of low: negative

SE of low: positive

Front 85

vertical vorticity term: tilting

Back 85

tilt up: positive

tilt down: negative

for easterly wind, N has positive tilting and S has negative tilting

Front 86

vertical vorticity term: baroclinic

Back 86

if barotropic flow: term goes to 0

Front 87

vertical vorticity term: stretching

Back 87

positive vert vort and negative horizontal divergence causes positive

Front 88

vertical vorticity term: earth vorticity advection

Back 88

positive with northerly wind
negative with southerly wind

Front 89

vertical vorticity term: diffusion of vorticity

Back 89

molecular diffusion acts to smooth out large gradients of vert vort

smooths out peaks

Front 90

flows where baroclinic vorticity generation are important

Back 90

bbq
cigarettes
convective clouds, squall lines, supercells
leading edge of cold fronts and thunderstorm outflows
atom bomb blasts

Front 91

theory for tornado genesis

Back 91

1. horiz vort gets generated baroclinically at leading edge of thunderstorm outflow
2. horiz vort gets tilted into the vertical by an updraft
3. vert vort gets stretched in a convergent updraft --> get tornado