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Baroclinic Instability This article has This been published in or collective redistirbution of any portion of this article by photocopy machine, reposting, or other means is permitted only with the approval of The approval portionthe ofwith any permitted articleonly photocopy by is of machine, reposting, this means or collective or other redistirbution HANDS-ON OCEANOGRAPHY Oceanography A Tabletop Demonstration of Atmospheric Dynamics journal of The 21, Number 4, a quarterly , Volume Baroclinic Instability BY BALASUBRAMANYA T. NADIGA AND JONATHAN M. AURNOU O ceanography ceanography S ociety. ociety. PURPOSE OF ACTIVITY analysis, but the fundamental appreciation of the phenomenon C opyright 2008 by The 2008 by opyright Here we study a fundamental instability mechanism of the is well achieved in the simple setup described here. atmosphere that affects us very directly in terms of mid-latitude Students learn how a combination of rotation and buoyancy winter weather. We provide a hands-on demonstration of this (density contrasts) underlies this instability mechanism. We instability using a setup that can be put together at home and naturally anticipate that when a dam breaks, gravity causes the O ceanography ceanography O at minimal cost. Increased sophistication that can be achieved water to flow outward. Students will learn how this behavior ceanography with institutional support will aid in further quantitative fundamentally changes when the system is rotating sufficiently S fast. The experiment also ociety. S ociety. ociety. A serves as an accessible intro- ll rights reserved. S a b duction to large-scale dynam- or Th e [email protected] to: correspondence all end ics in the atmosphere. P ermission is granted to copy this article for use in teaching and research. article use for research. and this copy in teaching to granted is ermission AUDIENCE This activity can be conducted with groups ranging from middle-school science classes through graduate classes in O fluid dynamics. Components ceanography of this laboratory exercise have been used in undergradu- S ociety, ociety, ate and graduate classes on PO Figure 1. (a) The distribution of temperature in the southern-hemisphere atmosphere in winter at midlevel in geophysics and fluid dynam- Box 1931, the troposphere (temperature in degrees Celsius on the 500 millibar pressure surface at 1200 GMT on 25 August ics at the University of New 2008; map from http://www.atmo.arizona.edu). A cold air mass is shown in blue and light blue, centered over R Mexico, Albuquerque, the ockville, R Antarctica. The surrounding temperature field is shown via light green line contours. Because of rotation, the reproduction, systemmatic epublication, cold Antarctic air mass does not simply respond to gravity by settling and flowing outwards and below warmer University of California, Los lower latitude air . Instead, rotational effects give rise to an azimuthal “thermal wind flow” that circulates around Angeles, and the Los Alamos MD the cold air mass. The thermal wind can, however, become unstable and develop meanders (visible in green line 20849-1931, contours). (b) NASA image showing tropospheric clouds over Antarctica that trace out a pattern of meanders Summer School. that are qualitatively similar to those in panel a. USA . 196 Oceanography Vol.21, No.4 BACKGROUND In Earth’s atmosphere, a Nonrotating Planet Rotating Planet cold dome of air forms a) Time t = t ; Side View a) Time t = t ; Side View over the pole in winter 1 1 Rotation Axis (Figure 1a). Because cold Surrounding Initial Cold Surrounding Initial Cold air is denser than warm Warmer Air Air Mass Warmer Air Air MMass Planet's Surface Planet's Surface air, this relatively dense polar cap of air might b) Time t = t2; Side View b) Time t = t2; Side View be expected to settle, under the force of gravity, Gravitational Settling Thermal Wind Balance and spread radially out- wards to lower latitudes c) Time t = t ; Top View c) Time t = t ; Top View (e.g., Figure 2). However, 3 3 because of Earth’s rota- tion, this does not occur (Figure 3). Gravitational Baroclinic Instead, a Coriolis force Settling Instability Spiraling Eddies deflects flow to the right Cold Cold of its intended path in Air Mass Air Mass theur northernur hemisphere:r = − Ω × FurCoriolis 2 u, where Warmer Ω is the planet’s angular Warmer Air Air rotationalr velocity vec- tor and u is the fluid’s velocity vector (Holton, 1992). Thus, when a mass Figure 2. Sideview schematics of the settling of an Figure 3. Schematics of the settling of an atmospheric dome atmospheric dome of cold air on a nonrotating planet. of cold air on a rapidly rotating planet. The cold air mass of fluid attempts to settle, Time increases down the page such that t1 < t2 < t3. For does not spread out indefinitely, as in Figure 2. Instead, a the Coriolis force deflects reasons of simplicity, the boundary of the cold air mass “thermal wind” flow develops that is able to support the is shown to be smooth. In reality, the boundary tends air mass (b). This thermal wind is not stable. It breaks apart the flow (Figure 3b), that to be highly corrugated and contorted and the associ- via a process called baroclinic instability (c). Time increases is, the Coriolis force effec- ated flow turbulent. down the page such that t1 < t2 < t3. tively opposes the gravita- tional settling force. Cold, dense fluid attempting to spread outwards at the base of a cold air mass is deflected wind speeds must be in order to generate a sufficiently strong clockwise, whereas warmer air attempting to converge toward Coriolis force to balance the greater gravitational settling force. the rotation axis is deflected counterclockwise. Such a vertically For sufficiently dense air masses, the thermal wind can become sheared atmospheric flow that circulates around the edge of the “unstable”—that is, minor perturbations to the system can grow dense polar air mass is called a “thermal wind” (Holton, 1992; with time and consequently lead to major changes—through a Cushman-Roisin, 1994; Vallis, 2006). The Coriolis force associ- ated with the thermal wind largely balances the gravitational Balasubramanya (Balu) T. Nadiga ([email protected]) is settling force and thus prevents the dense column of air from Technical Staff Member, Los Alamos National Laboratory, Los settling, in contrast to the nonrotating case (compare Figures 3 Alamos, NM, USA. Jonathan M. Aurnou is Associate Professor, and 1a with Figure 2). Department of Earth and Space Sciences, University of California, The denser the polar air mass, the higher the thermal Los Angeles, CA, USA. Oceanography December 2008 197 process called baroclinic1 instability (Figures 3 and 1a; e.g., see Figure 4. Photograph of the experimental setup. A Holton, 1992; Cushman-Roisin, 1994; Vallis, 2006). This com- vinyl record player is used plex process produces a number of large-scale spiraling eddy as the rotating table. The structures that tend to propagate away from the poles and planter, with a hole cut in its bottom, accommodates toward lower latitudes. In so doing, and with the addition of the spindle of the record moist physics (physics of water vapor), they produce strong player and is centered by winter storm events such as snowstorms and blizzards. These hand along the axis of rotation. The shallow pan eddies serve to horizontally mix up the cold dome of air over is then hand centered on the pole (e.g., Figure 3b), which in effect transports heat pole- the planter. Water is used ward and makes the higher latitudes warmer. in the shallow pan as the working fluid. In this baroclinic instability process, part of the gravitational potential energy stored in the dome of cold polar air is con- verted to kinetic energy in the form of the eddies. The kinetic energy of these eddies is eventually dissipated, allowing the system to settle down to a state of lower energy (Valllis, 2006). Interestingly, the kinetic energy of the eddies is felt in the form of strong winds and gusts that accompany the wintertime (2) the rotation direction, (3) the location of the cold mass storm systems. In summary, while heavier air sinks without of fluid, and (4) the temperature difference between the cold much fanfare in a nonrotating system, the process of equilibra- fluid and the surrounding warmer fluid? tion is far more dramatic in a rotating system.2 3. In rotating experiments, is the thermal wind observable? Baroclinic instability is also an important dynamical process Does it qualitatively agree with the flow shown in Figure 3b? in the atmospheres of the giant planets and in Earth’s ocean. How does the thermal wind change if the rotation rate of the For example, intense wintertime storms can cool localized system is increased, decreased, or reversed? regions of the ocean surface. These cooling events produce 4. In comparison to nonrotating systems, does rotation tend to regions of locally cold, dense ocean water. These localized inhibit or enhance mixing? regions of dense ocean water tend to break apart via baroclinic instability processes, which disperse the cold fluid around the MATERIALS ocean basin in the form of baroclinic eddies (Marshall et al., 1. A vinyl record player (see Figure 4) 1998; Vallis, 2006; Marshall and Plumb, 2007). In other settings 2. A plastic planter relevant to the ocean, wind-driven gyres in ocean basins give 3. Two wide, flat-bottomed, shallow circular pans (e.g., found rise to western boundary currents such as the Gulf Stream and at grocery or kitchen-accessory stores) the Kuroshio current. These western boundary currents and 4. A piece of rigid, transparent acrylic sheet that can be their extensions are active sites of baroclinic instability as well placed over the shallow pan as a cover (e.g., found at home- (Vallis, 2006).
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