Laboratory Experiments With Abrupt Thermohaline Transitions and Oscillations - Modeling Atmospheric and Oceanic Flows - page 249

13
Laboratory Experiments With Abrupt Thermohaline
Transitions and Oscillations

John A. Whitehead

13.1. INTRODUCTION example, ocean estuary mathematical box models have

demonstrated abrupt thermohaline transitions [ Hearn and
Sidhu , 1999; Bulgakov and Skiba , 2003]. In actuality, no
direct observations of abrupt thermohaline transitions in
estuaries exist. Finally, abrupt transitions are also mathe-
matically predicted for wind-forced convection [ Stommel
and Rooth , 1968] and in basins forced by surface stress
alone [ Ierley and Sheremet , 1995; Jiang et al. , 1995].
Mathematical box models and numerical simulations
both have drawbacks. Although numerous box experi-
ments readily produce abrupt thermohaline transitions,
they are always subject to the criticism that they restrict
the number of degrees of freedom that the flows can
adopt. Mathematical box models cannot account for the
large number of degrees of freedom that actual flows can
include, making abrupt thermohaline transitions more
prevalent than actually exist. Even though numerical
models show that the abrupt thermohaline transitions do
not vanish, a more convincing way to illustrate whether
or not abrupt thermohaline transitions actually exist in
a physical system is by developing controlled laboratory
experiments.
Abrupt transitions in fluid mechanics are common-
place. For example, the sudden stall of an airplane wing
along with all the dangers it produces to pilots and pas-
sengers, has been continually in the minds of aviators since
the early part of the twentieth century. Generally, abrupt
transitions occur within a finite range of the parameters
that govern the flow. The flow in this range can have either
one of two modes. Each mode is locally stable and the
flow can be made to abruptly jump back and forth from
one mode to another. Therefore, the transitions are said
to have hysteresis , since the flow is determined by history,
as well as by the governing parameters. Hysteresis is obvi-
ously a significant challenge to climate modeling if it exists
(just as in airplane design). Depending on details of the

Climate records indicate that ancient ocean tempera-
tures occasionally change by many degrees within cli-
matologically “fast” times (order of 50 years). Some of
these are attributed to abrupt transitions of the thermoha-
line circulation regime [ Broecker et al. , 1985; Boyle , 1990;
Keigwin and Jones , 1994; Keigwin et al. , 1994; Bard
et al. , 1996; Broecker , 1997; Stocker and Wright , 1991;
Stocker , 2000; Burns et al. , 2003; Weart , 2003; and many
others]. In addition, some numerical ocean circulation
models produces abrupt transitions. The changes involve
both salinity and temperature (henceforth always called
thermohaline) changes [ Bryan , 1986; Cessi , 1994; Rahm-
storf , 1995; Manabe and Stouffer , 1995; Whitehead , 1998;
Rahmstorf and Ganopolski , 1999, Weaver et al. , 1999].
The dynamics of such abrupt transitions is formulated
in a pioneering mathematical box model study [ Stom-
mel , 1961]. This model has two well-mixed chambers of
water connected side by side with one tube at the top
and a second at the bottom. Both temperature and salin-
ity diffuse through sidewalls to the chambers at different
rates. Positive temperature and salinity diffuse into one
chamber, and negative values diffuse in the other. The
resulting flow has a range of the governing parameters
in which there are two possible states, one with temper-
ature dominance and the other with salinity dominance,
each with a different flow rate and direction. Subsequent
mathematical box models (reviewed by Marotzke [1994]
and Whitehead [1995]) illuminate additional aspects that
help us to understand how the abrupt thermohaline
transitions arise and what their context might be. For

Department of Physical Oceanography, Woods Hole
Oceanographic Institution, Woods Hole, Massachusetts, United
States of America.