Upload
lamtram
View
215
Download
0
Embed Size (px)
Citation preview
Lecture 15: The energetics of the ocean circulationAtmosphere, Ocean, Climate
DynamicsEESS 146B/246B
The energetics of the circulation
• Sources and sinks of the kinetic energy of the large scale circulation.
• The release of available potential energy by baroclinic instability.
• The dissipation of the large scale circulation’s kinetic energy.
Sources and sinks of kinetic energy
•Equation for the total kinetic energy:
CONVERSION OF PE TO KE
DISSIPATION
WIND-DRIVEN SOURCE/SINK OF KE
SINK OF KE VIA BOTTOM FRICTION
Wind-work on the circulation
(mW m-2)
Map of the wind-work from Wunsch JPO 1998
•Integrated over the area of the ocean, the winds input energy at a rate equal to 1 TW.
WIND-WORKwind-stress
velocity of circulation at sea surface
How much energy is in the form of APE versus KE?
L, B H
N2
Local APE and KE
•Flows with length scales larger than the Rossby radius contain more APE than KE.
Available potential energy
FRONT STATE WITH LOWEST PE
total mass of water
center of mass of water
•The available potential energy is the PE that can be converted to kinetic energy
•Eddies that form at fronts draw their kinetic energy from the APE and in doing so reduce the APE by generating a net overturning motion.
LIGHT DENSE
LIGHT
DENSE
Eddy versus mean kinetic energykinetic energy of mean circulation
kinetic energy of eddies
•One can split the circulation into a mean and eddy components:
mean, time average
eddy, time-variable
•Eddy kinetic energy tends to be greatest where the mean circulation is strongest →eddies derive their energy from the mean circulation.
Eddy versus mean kinetic energy
From Wunsch 2002
•Oceanic kinetic energy is dominated by eddies, on average by a factor of 150.•The ocean circulation is to first order turbulent and dynamic.
How do eddies drive a net transport?
•If the average of an eddy quantity is zero:
how can it generate a mean overturning circulation?
mean eddy
How eddies generate a net transport
Quantity that measures Isopycnallayer thickness
•Blue shades: thicker isopycnallayer
Thomas, Dynamics of Atm. and Ocean, (2008)
How eddies generate a net overturning
•Eddies subduct surface waters with greater isopycnal layer thickness while upwelling water from the interior with thinner isopycnal layer thickness.
•Blue shades: thicker isopycnallayer
Quantifying the eddy-induced transport
•A correlation develops between the eddy’s modification of isopycnal thickness and velocity
Net transport along an isopycnal per unit length
EDDY-INDUCED TRANSPORT
Two-dimensional turbulence: the inverse cascade
ENERGY TRANSFER
Kinetic Energy Spectrum
Figures from McWilliams, JFM, 1984.
wavenumber
Evolution of the vorticity
•In turbulence strongly constrained by rotation, smaller eddies are engulfed and merge with larger eddies.
•Energy is transferred from small to large scales, following an inverse cascade of energy.
Jovian example of a vortex merger
The Great Red Spot viewed from the Voyager 1 1979. JPL/NASA
•Fluids strongly constrained by rotation such as the atmosphere of Jupiter are characterized by mesoscale turbulence that exhibits an inverse cascade.
The energy budget of the ocean
•The inverse cascade short circuits the transfer of energy from the large-scale circulation to viscous dissipation.
•How is the kinetic energy budget for the ocean circulation closed?
•How can energy be transferred from the mesoscale to small scale turbulence where viscous dissipation can act?
LARGE-SCALE CIRCULATION
MESOSCALE EDDIES
SMALL-SCALE TURBULENCE
WIND-WORK
ENERGY SOURCE
VISCOUS DISSIPATION
ENERGY SINK
INSTABILITY
INVERSE CASCADE
ENERGY TRANSFER
?
1000-10000 km 100 km <100 m
1 mm-1 cm
1 TW
Removal of kinetic energy from the circulation by bottom friction.
•Bottom friction removes KE from bottom currents at a rate:
bottom stress near bottom velocity
•Sen et al, GRL 2008 estimate using current meter observations that bottom drag removes KE from the circulation at a rate 0.2 TW.
LARGE-SCALE CIRCULATION
MESOSCALE EDDIES
SMALL-SCALE TURBULENCE
WIND-WORK
ENERGY SOURCE
VISCOUS DISSIPATION
ENERGY SINK
INSTABILITY
INVERSE CASCADE
ENERGY TRANSFER
?
1000-10000 km 100 km <100 m
1 mm-1 cm
1 TW BOTTOM FR
ICTIO
N
0.2 TW
•Bottom friction alone cannot close the energy budget, other processes are needed to transfer energy from the mesoscale to the small scales where friction can act.
Generation of internal gravity waves by mean circulation flowing over rough topography
zona
l vel
ocity
(m/s
)
Drake Passage
Southeast Pacific
Fig. from Nikurashin and Ferrari JPO 2010