5.2.1 Scales of mixing and stirring
One of the intriguing concepts in physical
oceanography is the cascade of energy and scalar
variance from global scales, at which the ocean is
forced, to sub-centimetre scales, where molecular
dissipation reigns. Between these exist a variety of
dynamical regimes governing flows that both
transport energy through physical space and eventually flux it to smaller scales. A beautiful and
often vexing aspect of fluid dynamics involves the
relationships between these disparate scales of
motion. Simple scaling arguments even suggest
that microstructure controls the intensity of the
global-scale thermohaline circulation. This chapter
will focus on the tail of the ocean energy cascade:
the stirring role of mesoscale eddies and smallerscale motions and the mixing by turbulence and
double diffusion. A background theme will be how
stirring and mixing impact the general circulation:
the principal focus of the World Ocean Circulation
Experiment (WOCE). Basic to our presentation
will be the differentiation between mixing and
stirring. The former we define as the irreversible
action of molecular viscosity, heat conduction and
solvent diffusion responsible for the destruction of
velocity and water property gradients. Owing to
seawater’s relatively small coefficient of molecular
viscosity (:O(10
96 m
2 s
91 )), the frictional dissipation of kinetic energy in the ocean interior is
only effective at centimetre scale. Interactions and
instabilities of larger-scale motions act to flux
kinetic energy to sub-metre scales where viscous
dissipation acts. Similarly, with the molecular diffusivity of heat, D T , of order 10
97 m
2 s
91 and that
for salt, D S (and most other solutes), of order
10
99 m
2 s
91
, it is only by successive straining of
scalar property distributions (stirring) by mesoscale
flows, internal waves and ultimately, turbulent
eddies that water property gradients at millimetre
scale are enhanced to where molecular diffusion is
effective. Importantly, the sub-metre sized motions
responsible for the actual mixing clearly lie well
beyond the reach of global- or even basin-scale
numerical simulations. Indeed, not even mesoscale
eddies are resolved in today’s climate simulations.
Therefore, in addition to summarizing recent experimental findings and ideas, we will also address
the parameterization question of how to express
stirring and mixing in terms of larger-scale (modelresolved) motions.
To place our story in context, we will begin by
reviewing in Section 5.2.2 some of the scaling
arguments that relate mixing to the ocean’s
general circulation. Though developed for highly
idealized domains, the scaling (supported by
numerical simulations) suggests a dynamical connection between the mean global-scale overturning
circulation and mixing supported by turbulent
eddies: a horizontal length scale range of order
10
9
. Our background discussion continues with a
summary of indirect estimates of diapycnal ocean
mixing inferred from large-scale circulation studies, water property distributions and simple ocean
dynamics. Subsequent sections highlight some of
the physical processes involved in the energy cascade between the gyre and dissipation scales.
Mesoscale eddies near the Rossby radius of deformation are the principal stirring agents within the
5.2
Mixing and Stirring in the Ocean Interior
John M.Toole and Trevor J. McDougall
337
OCEAN CIRCULATION AND CLIMATE
Copyright © 2001 Academic Press
ISBN 0-12-641351-7
All rights of reproduction in any form reserved
CHAPTER
One of the intriguing concepts in physical
oceanography is the cascade of energy and scalar
variance from global scales, at which the ocean is
forced, to sub-centimetre scales, where molecular
dissipation reigns. Between these exist a variety of
dynamical regimes governing flows that both
transport energy through physical space and eventually flux it to smaller scales. A beautiful and
often vexing aspect of fluid dynamics involves the
relationships between these disparate scales of
motion. Simple scaling arguments even suggest
that microstructure controls the intensity of the
global-scale thermohaline circulation. This chapter
will focus on the tail of the ocean energy cascade:
the stirring role of mesoscale eddies and smallerscale motions and the mixing by turbulence and
double diffusion. A background theme will be how
stirring and mixing impact the general circulation:
the principal focus of the World Ocean Circulation
Experiment (WOCE). Basic to our presentation
will be the differentiation between mixing and
stirring. The former we define as the irreversible
action of molecular viscosity, heat conduction and
solvent diffusion responsible for the destruction of
velocity and water property gradients. Owing to
seawater’s relatively small coefficient of molecular
viscosity (:O(10
96 m
2 s
91 )), the frictional dissipation of kinetic energy in the ocean interior is
only effective at centimetre scale. Interactions and
instabilities of larger-scale motions act to flux
kinetic energy to sub-metre scales where viscous
dissipation acts. Similarly, with the molecular diffusivity of heat, D T , of order 10
97 m
2 s
91 and that
for salt, D S (and most other solutes), of order
10
99 m
2 s
91
, it is only by successive straining of
scalar property distributions (stirring) by mesoscale
flows, internal waves and ultimately, turbulent
eddies that water property gradients at millimetre
scale are enhanced to where molecular diffusion is
effective. Importantly, the sub-metre sized motions
responsible for the actual mixing clearly lie well
beyond the reach of global- or even basin-scale
numerical simulations. Indeed, not even mesoscale
eddies are resolved in today’s climate simulations.
Therefore, in addition to summarizing recent experimental findings and ideas, we will also address
the parameterization question of how to express
stirring and mixing in terms of larger-scale (modelresolved) motions.
To place our story in context, we will begin by
reviewing in Section 5.2.2 some of the scaling
arguments that relate mixing to the ocean’s
general circulation. Though developed for highly
idealized domains, the scaling (supported by
numerical simulations) suggests a dynamical connection between the mean global-scale overturning
circulation and mixing supported by turbulent
eddies: a horizontal length scale range of order
10
9
. Our background discussion continues with a
summary of indirect estimates of diapycnal ocean
mixing inferred from large-scale circulation studies, water property distributions and simple ocean
dynamics. Subsequent sections highlight some of
the physical processes involved in the energy cascade between the gyre and dissipation scales.
Mesoscale eddies near the Rossby radius of deformation are the principal stirring agents within the
5.2
Mixing and Stirring in the Ocean Interior
John M.Toole and Trevor J. McDougall
337
OCEAN CIRCULATION AND CLIMATE
Copyright © 2001 Academic Press
ISBN 0-12-641351-7
All rights of reproduction in any form reserved
CHAPTER