3. Ocean Circulation
Ocean currents
Surface-Current Circulations: Warm Water and Cold-Water
Which are the main cool surface currents in the North Atlantic and how do you determine their
water mass properties?
Surface currents speed and waves
The direction of waves and the
driving speed of currents depends on
the frictional forces between the
atmosphere and the hydrosphere. The
processes of energy transfer from wind
to waves and currents is complex.
The wind stress is the frictional force (τ),
wind speed is W, and c prevailing
atmospheric condition. C will increase
with increasing wind speed.
τ = cW2 (Nm-2 ; 1N = kg m s-2)
A typical surface current is ~ 3% of the
wind speed, so that 10 m/s (~20 knots)
wind speed gives rise to a surface
current by 0.3 m/s.
What are the values and units for c?
C=
Laminar and turbulent flow
Molecular viscosity:
Friction within a fluid depends on the mass x
velocity (momentum) between different
parts of the fluid. A transfer of molecules
between adjacent layers with their
associated masses and velocities is laminar.
Eddy viscosity:
If parcels of water rather than individual
molecules are moving internal friction
increases.
• Eddy viscosity is related to vertical (Az) and horizontal (Ah) mixing. Ah is normally much greater than Av.
Why?
• The oceans are many thousands of kilometres wider than they are deep and frictional coupling and eddy
viscosity dominates due to the wind stress.
• Eddies in the upper layer act as a gearing mechanism transmitting motion from the surface to the deeper
levels. Eddy viscosity depends on the water stratification: a well mixed water column is easily overturned but
a well stratified water column is stable and turbulent mixing surpressed.
• The first theory for wind driven currents was published by Ekman (1905).
Ekman motion - water mass transport
Observations:
Ice movements observed by
Nansen in the Artcic were not
parallel to the wind, but at an
angle of 20-40 degrees to the right
of it.
Theory:
Hypothetial layered ocean where
the friction of the surface layer is
transferred to its lowers surface
and then downwards to the next
layer ..
All layers are affected by the
Coriolis force.
Ekman spiral and transport
Ekman spiral: The direction of
the current deviates 450 at the
surface, and then the angle
increases with depth and the
speed decreases.
Ekman layer and transport:
The layer of the ocean under
the influence of the wind. The
transport is given in m3 s-1
Gyre development
Upwelling of water masses
driven by the coriolis force
Coriolis force = m x 2 Ω sinΦ x u
=mfu
• Coriolis parameter = f = 2 Ω sinΦ
Angular velocity of the Earth = Ω = (2Π/86160)s-1 = 7.29 x 10-5 s-1
Latitude = Φ
• Mass = m
• Speed = u
• Summary:
The mean motion of the wind driven layer is at right angles to the
wind direction.
The only forces acting on the wind driven layer are wind stress and
the Coriolis force.
The total volume of water transported at right angles to the wind
direction can be calculated by the thickness of the wind driven layer
times the velocity of this layer.
Geostrophic currents
If the sea surface piles up or bents
down water tends to flow
accordingly, there will be a
horizontal pressure gradient
force.
If the Coriolis force is balanced
by this force then the current is in
geostrophic equlibrium and we
call it a geostrophic current.
The other pressure gradient is the
hydrostatic pressure, simply the
weight of the water acting on unit
area (m2).
a)
dp = - ρ g dz ; a layer
where the total column
exists of infinite number
of layers.
b) p = - ρ g z
Horizontal pressure gradients . If the seawater density is constant then the horizontal
pressure gradient force is tan θ = ΔZ/ ΔX. The horizontal pressure gradient force is
the same at all depth in this case. The greater the seasurface slope the greater the
pressure gradient.
The previous situation with a constant density and slope angle results in isobaric
surfaces parallel to the sea-surface
A well mixed ocean shows surfaces with constant density or isopycnic surfaces.
Such conditions are called barotropic.
Lateral variations in density cause depth changes in the isobaric surface so that
isobaric and isopycnic surfaces incline which is known as baroclinic.
Geostrophic currents – horizontal pressure force
is balanced by the Coriolis force – can occur in
barotropic (homogenous) or baroclinic (lateral
density variations).
Which direction does present the
horizontal pressure gradient force and
and which the Coriolis force?
If the current is flowing into the page,
is the situation on the northern or
southern hemisphere?
The distribution of density
affects the slope:
a) Barotropic flow has
isopycnic and isobaric
surfaces and a constant
geopstrophic current at a
right angle to it.
b) Baroclinic flow shows
inclined surfaces and
with increasing depth the
slope of isobaric and
isopynic surfaces
becomes smaller; and so
does the geostrophic
current.
Does the sketch relate to the southern
or northern hemisphere?
Ocean current velocity has a profound effect
on sediment sorting, erosion, transportation,
and deposition shown by the Hjulström curve
(1925). Medium sand is easily eroded while
clays due to their cohesive strength are not.
Conventional current direction
symbols.
Geostrophic current velocities
The distribution of
density with depth can
be used to determine a
profile of geostrophic
current velocity.
a)
The geostrophic current
velocity is zero at 1000
m water depth.
b)
If the current velocity
below 1000 m is not
zero, then the velocity
has a baroclinic (lateral
variations in density)
and barotropic (sea
surface slope caused by
winds) component.
Typical density profiles
equatorial
high latitudes
tropical
Pycnoclines for different
latitudes! Note the weak
thermocline in high latitudes.
An abrupt simplified density
change is used for modelling
geostrophic currents.
Slope and water mass interfaces
Layers with different
density and and velocity
directions.
Pressure, density and
dynamic topography
Hydrostatic pressure
• Hydrostatic pressure is
p = - ρgz
g= ~10 ms-2
ρ= ~1 kg m-3
z= depth m
Pressure ~104 x depth (Nm-2) or
in Pascals (1 Pa = 1 Nm-2)
Over a large area of the ocean there is a atmospheric pressure change and this is not taken into account
in the euqation. This change contributes to a surface slope and thus to the slope of isobars with depth.
The pressure from a standard atmosphere is 1 bar or 105 Pa.
What depth of seawater would give rise to the same pressure?
Dynamic topography
• To determine geostrophic current velocities we need to quantify departures of isobaric
surfaces from the horizontal.
• Solid Earth has a gravitaional equipotential surface which has a topography.
• If there were no currents the sea surface would be coincident with an equipotential surface
• The sea surface of a motionless ocea is known as a marine geoid.
• Due to both the wind driven ocean circulation and the marine geoid, the ocean has both
kinetic and potential energy.
• Because of this relationship between isobaric slope and potential energy we use the term
dynamic height or topography.
• The units are dynamic metres and the values depend on the local value of g!
Dynamic topography
Dynamic topography of the sea
surface where dynamic metres range
from 4.4 to 6.4 metres.
Topographic map of the mean seasurface: The map is based on satellite
altimetry, where the mean ocean
surface is ~ marine geoid. It reflects
the main topography of the sea floor.
Divergences and convergences
Wind stress at the surface leads not only to horizontal but also to vertical movement of water.
Upwelling of water
Downwelling of water
Ekman pumping
In the northern hemisphere the Ekman
transport is to the right of the wind-driven
circulation causing in case of a cyclone:
• upwelling and
• raising of the thermocline.
An anticyclone causes downwelling in
the northern hemisphere.
What is the situation in the southern
hemisphere?
Subtropical gyres
Anticyclonic winds in the northern
hemisphere cause a convergence of
water and a sea-surface slope
upwards towards the centre of the
gyre.
It creates a horizonatl pressure force
outwards of the gyre.
The horizontal pressure force will be
balanced by the Coriolis force, and a
Geostrophic current will flow in the
same direction as the wind.
Now let us try to explain the subpolar gyres driven by
subpolar low pressure cells!
These are the subtropical gyres
between 10 and 40 degrees of
latitude which lie beneath the
subtropical highs. They cause a
downwelling of water and a lower
productivity.
Ekman pumping &
biological productivity
H
H
H
H
The vertical motion of water masses that occur within gyres has a profound effect on the
biological productivity. The subtropical gyres where downwelling occures are nutrient poor
and therefore have low productivity.
Ocean fronts
Divergent surface flow pattern leading
to upwelling of water.
Convergent surface flow pattern
leading to downwelling of water.
Convergence zones
Linear convergences when water mass
properties are different on either side
of the convergence zone.
Ocean eddies
Bloom of coccolithophores
Ship track
350 km
75 km
Eddies form because ocean water transport is non-linear and turbulent. The formation of
eddies may result in energy removed from the mean flow but also may interact with the main
flow injecting energy to it. They may caus upwelling and higher biological productivity.
Eddies south of Australia
Mesoscale eddies are the ocean
analogues to atmospheric weather
systems. However, while cyclones or
anticyclones may have a diameter of
~ 1000 km mesocale eddies have a
diameter of ~ 50 – 200 km.
Tasmania
The travel speed of eddies may be
~ few kilometres per day while
cyclones may travel 1000km per day.
Mesoscale eddies are an exiting and
new discovery which drive the ”ocean
weather”.
Summary:
• Frictional force caused by the wind on the sea surface is known as wind stress.
Wind stress generates motion in form of waves and currents.
• Major ”forces” acting on currents are frictional forces, eddy viscosity, Coriolis
force, horizontal pressure gradient forces, dynamic topography.
• Geostrophic currents result when the horizontal pressure gradient force is
balanced by the Coriolis force.
• Ekman showed that the mean flow of the wind driven ocean layer is 90 degrees
to the right on the northern or to the left on the southern hemisphere.
• Surface wind stress gives rise to both horizontal and vertical motion of water
masses causing upwelling or downwelling, raising or depression of the
thermocline.
• Upwelling may increase ocean biological productivity!