Physics of Atmosphere and Ocean Flashcards
fundamental forces to consider in atmospheric/ocean motions
gravitational force
pressure gradient
friction
Additional forces to consider in atmospheric/ocean motions
centrifugal
Coriolis
formula for gravitational force
F = G (m.m)/r^2
per unit mass (a) = -GM/r^2 = -g
quantitative formula for pressure gradient force
F (per kg) = -1/rho (∂P/∂x)
(in 3d ∂x, ∂y, or ∂z)
What can friction be caused by
- viscosity
- frictional drag at base of atm
- windstress on ocean
formula for centrifugal force (per unit mass)
c.f. = Ω^2 . R
Ω = angular velocity = ∆theta/∆t
R = radius = 6400km
what direction does Coriolis force act in northern and southern hemisphere
N: 90º to right
S: 90º to left
formula for Coriolis parameter
f = 2Ω.sin(theta)
equation for Coriolis acceleration
a = 2Ω.v
Where is maximum and minimum spin on the earth
max = poles
min = equator
magnitude of Coriolis force formula
mag = f.v
value for Coriolis parameter, f, at mid latitudes
10^ -4 (/s)
force balance equation in x, y, z direction
∂u/∂t = -1/rho (∂P/∂x) + fv
∂v/∂t = -1/rho (∂P/∂y) - fu
∂w/∂t = -1/rho (∂P/∂z) - g
What forces is geostrophic balance between
pressure gradient + Coriolis = 0
what is the significance of geostrophic balance
on a rotating planet, winds do not flow high->low pressure, but along constant pressure contours
equation for velocity of geostrophic winds
rearrange force balance equations for velocity in x and y directions
(p.g + Coriolis = 0)
directions of winds around pressure systems
in N:
anticlockwise around low
clockwise around high
= cyclonic
what is the effect on geostrophic wind balance of being close to the surface
additional frictional force
(moving slower = Coriolis weaker, cannot balance)
=> spiral into low pressure (ascent)
=> spiral out of high pressure (descent)
what are the forces involved in hydrostatic balance
pressure gradient force + gravity = 0
hydrostatic balance formula
∂P/∂z = -rho . g
rearrange force balance equation in z direction
how to use hydrostatic balance formula to find pressure at given point in atm
integrate between that point and infinity
= weight per unit area at that point = pressure
equation of state for ocean (what does density depend on)
rho = rho(T, S, P)
what does the TS diagram show
temperature more important for determining density at usual conditions
salinity becomes more important at polar temperatures
definition and formula for potential temperature, θ
θ = temperature a fluid parcel would be if brought adiabatically to the surface
θ = T . (Ps / P) ^ 2/7
What is thermal wind balance in words
combination of geostrophic and hydrostatic balance to show how geostrophic flow varies with height
How to find thermal wind equations
partially differentiate geostrophic velocity equations with respect to height, z, and sub in hydrostatic balance equation
example of how thermal wind balance works in oceans and atm
Gulf Stream
high temp, low density off coast
= +ve wind equation
= increase velocity of currents in y with height
Jet Stream in atm
meaning of westerly winds and easterly winds
westerly = west -> east
meaning of eastward ocean currents
eastward = west -> east
why does wind speed up as moves north from equator (westerlies)
air must conserve angular momentum = mass . velocity . radius
moving polewards = decrease r, therefore increase v
Where are the westerlies seen
almost everywhere except equator, strongest at mid latitudes - subtropical jet
how is heat transported to the poles
temperature gradient gets stronger across jet stream, strengthening it, flow becomes unstable, anomalies amplify into EDDIES
= baroclinic instability
How are the easterly trade winds formed
Air moving equator-ward at the surface in the hadley cell deflected by Coriolis force
what do eddies do in the atmosphere
eddies transport hot air northwards, and cold southwards (net flux=heat N) , by a lateral motion rather than overturning
trailing tails into tropics = move westerly momentum northwards
describe regional climate of near equatorial regions
- trade wind convergence
- rain
(tropical rainforests)
describe regional climate of subtropics
- descending air from Hadley cell
- hot and dry
(deserts)
describe the regional climate of the mid latitudes
- westerlies
- eddies dominate weather
- cyclone = wet+stormy
- anti = calm+fine
what are factors of the earth to also consider when describing general atmospheric circulation
- land/sea contrast (oceans warmer, mountains deflect wind)
- seasonal variations
what creates low pressure systems (that dominates UK weather)
contrast of hot and cold air masses
describe lifecycle of an extratropical cyclone
- warm and cold front contrast
- kink created by baroclinic instability
- cold (W) pushes under, forces warm (E) to rise
- low pressure at centre
- cold front moves faster so catches up to warm
- more catches up = wind
- caught up = cut off from rising hot air supply = occluded front => dissipates
conditions at warm and cold fronts
warm = grey skies and drizzle
cold = sudden temp drop + heavy rain
how is flow in the upper atmosphere different to surface
no friction, so not spiralling in/out of high/low therefore exist in geostrophic balance
what would happen if upper and surface highs/lows were vertically stacked
geostrophic balance in upper lows remains stable, and convergence into surface low will cause it to dissipate
why do weather systems (high/low pressure systems) tilt westwards with height
so there is a region of divergence vertically above a low pressure, allowing it to develop
(or convergence above high)
where are regions of divergence and convergence found in relation to jet stream ridges
divergence found downstream of trough
convergence upstream
how do low pressure systems intensify/weaken
upper divergence > surface convergence
= low intensify
what happens to wind as low pressure system moves over
‘veers’ - changes direction suddenly then returns
what is an anticyclone
-high pressure system
- subsiding air = few clouds
- weak pressure grad = light winds
- hot summer, cold winter
when does blocking by anticyclones occur
when a ridge in the upper atmospheric jet breaks off
=> extreme weather
what is the NAO (North Atlantic oscillation)
variable strength in the jet stream leads to different conditions
- +ve = more storms = wet winter europe
- -ve = fewer storms = cold air europe
what is ensemble weather forecasting
chaotic nature of atmosphere means small changes in initial conditions have large knock on impacts. Run many initial scenarios to see all possible states
what is ocean circulation driven by
- surface wind stress
- surface heat fluxes
- freshwater fluxes
- tidal forces
what is the gradient between warm and cold below water in oceans called
thermocline
properties of the mixed layer
- 50-100m
- stirred by wind stress + convection
- uniform T + S
(below T-S thermocline rapidly -> abyss)
Definition of transport
T = u . L . H
= speed . area
T = volume of fluid passing through an area per unit time
Units of transport
m^3 per s
sverdrups (Sv) = 10^6
what is the continuity equation
convergence in one direction must mean divergence in another
∂u/∂x + ∂v/∂y + ∂w/∂z = 0
directions of wind driven gyres across latitudes
tropics = equatorial jets
subtropics = anticyclonic
subpolar = cyclonic
What is surface wind stress and its two components
Force exerted on ocean by atmosphere per m^2
- viscous shear stress
(downward transfer of momentum) - form stress
(wind accumulate one side + accelerate)
formula for wind stress
Tau = C . rho . u(10)^2
(N/m^2)
C = drag coefficient =
rho = air density
u(10) = wind speed 10m above surface
how is the ekman layer impacted by wind stress
wind stress acts on surface but turbulence redistributes momentum over ekman layer
Formula for depth integrated ekman transport velocity
U = Tau(y) / rho . f
V = -Tau(x) / rho . f
What does the formula for ekman transport velocities tell us
- independent of ekman layer depth + structure
- net acts at 90º to wind stress (velocity spirals down with depth)
- force balance between wind stress and Coriolis force
Where and how does ekman upwellings occur
equatorial upwelling
- easterlies = ekman R in N, L in S
- divergence => upwelling
coastal upwellings
- west coasts/ east of oceans
- equator ward wind = offshore ekman transport
(California, Antarctic circumpolar)
cold nutrient rich water brought to surface
equation for circulation (around eddy)
C = (line integral) u . dl
C = 2π r. u
- for circle
equation for vorticity
vorticity = measure of spin about it axis
ε = C / A
ε = ∂v/∂x - ∂u/∂y
what is kelvins circulation theory
circulation is conserved following fluid parcel
(no viscosity and density change)
what happens to vorticity when you stretch a fluid parcel parallel to axis of spin
increase vorticity
ε (f) / ε (i) = h(f) / h(i)
same as equation for circulation conserved
what are the 2 components of absolute vorticity
planetary vorticity + relative vorticity
= f + ε
how to know when what type of vorticity dominates
Rossby number = u / f . L
> 1 = relative dominate
<1 = planetary dominate
why does an upwelling fluid column move polewards (sverdrup balance)
- fluid column stretched
- increase vorticity
- to do so, move polewards to increase f
(reverse = squashed + equator ward)
what do boundary currents do
return interior transports that flowed from subtropics towards equator back polewards, by small currents by continent boundaries where sverdrup balance breaks down (»1)
e.g. gulf stream
what factors drive ocean gyres
- meridional ekman transport (westerlies + easterlies)
- conv/div = upwelling/downwelling
- stretch/squash interior fluid columns -> vorticity conserved
- western boundary currents return
equation for heat transport from wind driven gyres
heat transport = V . rho . c . (Tn - Ts)
(difference between temp of water flowing N and S)
direction of interior sverdrup transports
subtropical = equatorward
subpolar = poleward
what is a water mass
body of water with given potential temperature and salinity.
defined by:
- formation site
- depth where settles
what processes involved in water mass formation
in mixed layer:
- cooling
- evaporation
- brine rejection in sea ice formation
where is the densest water formed
closed seas allowing extended evaporation e.g. med, nordic seas, weddell sea
where does the densest water end up and why
intermediate
- much higher density -> rapid descent -> fast mixing -> density loss
Weddell sea (least dense of dense) -> slow descent -> less mixing -> bottom water
characteristics of meridional overturning circulation (thermohaline circulation)
- upper km N
- large changes in T + S as moves
- large depth + length + heat different in layers = large heat transport
Effect of meridional overturning circulation on NW Europe (and if gone)
heat transport released to atmosphere over gulf stream = warmer than average for latitude
if off:
- widespread cooling in N hemisphere
- CO2 from N sequestered in cold water forming deep waters
How do we know there must be mechanical forcing in ocean circulation
Overturning circulation driven by surface heat transfer is likely to be weak and shallow, however it is strong and deep
what mechanical forcing creates deep overturning meridional circulation
tides
- topography on ocean floor encourages mixing
winds
- westerly winds around antarctica
= coastal upwelling
deep water formation
- N lats cold absorb more CO2 and sink
What happened to the MOC in the Younger-Dryas event
Ice sheets retreating after glaciation injected freshwater into Atlantic
= sit ontop of cold saline
= weaken MOC
How might the MOC be affected by climate change in the future
warmer atm -> hold more water
-> more precipitation at high latitudes
-> freshwater to Atlantic (sinks less)
-> weaken MOC
What creates tides
gradient of the moons gravitational field across the diameter of the earth
why are there tides twice a day
each point on earth rotates under 2 bulges with one earth rotation
What happens at the spring and neap tides
spring = solar and lunar combine
neap = act at 90º
What are ‘normal conditions’ in the context of the ENSO cycles
- warm in W pacific (indonesia)
- cold in E Pacific (S America)
- strong convection current
- upper level westerly flow, lower easterly
- Equatorial thermocline shallows to east
What is anomalously warm conditions over the Eastern pacific (S America) known as
El Niño
(less of a gradient than ususal)
What is anomalously cold conditions over the Eastern pacific (S America) known as
La Nina
(stronger gradient across pacific than normal)
What is the southern oscillation, and its effects on the pacific
- large scale fluctuations in the atmospheric pressure over the pacific
- -ve = high W, low E
- +ve = low W, high E
How is El Niño linked to the southern oscillation
there is a strong coupling,
they are opposites:
el nino = -ve
la nina = +ve
What are the characteristics and effects of an El Niño event
- weak temp and pressure gradient
- weak trade winds (easterlies) -> weak upwelling -> reduced bioactivity
moves East:
- pacific warm pool (thermocline deepen)
- atm convection (thunderstorms)
- rise in sea level
What are the characteristics of a La Niña event
- stronger Walker circulation
= stronger temp difference + winds
-> phytoplankton bloom - steep thermocline
What is ENSO
the coupled climate variability caused by strong coupling between tropical ocean and atmosphere
