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JANUARY 1997 NOTES AND CORRESPONDENCE 203

The Damping Effect of Bottom Topography on Internal Decadal-Scale Oscillations of the

MICHAEL WINTON Geophysical Laboratory/NOAA, Princeton, New Jersey

26 April 1996 and 5 July 1996

ABSTRACT By comparing the response of ¯at and bowl-shaped basins to ®xed heat ¯uxes of various magnitudes, it is determined that coastal topography has a considerable damping in¯uence upon internal decadal oscillations of the thermohaline circulation. It is proposed that this is because the adjustment of baroclinic currents to the no-normal-¯ow boundary condition at weakly strati®ed coasts is aided in the topography case by the generation of substantial barotropic ¯ow.

1. Introduction play of heat and salt). The ®xed ¯ux experiment is a simpli®cation of the original mixed boundary conditions Analysis of the Comprehensive ± experiment that retains the timescale of the original vari- Data Set has revealed interdecadal variations of North ability as well as the prominence of slow boundary- Atlantic surface seemingly unforced propagating disturbances (Greatbatch and Peterson by contemporaneous atmospheric anomalies (Kushnir 1994). An interdecadal mode of variability involving 1996, hereafter GP). The former experiment is obtained the thermohaline circulation has also been found in a from the latter by ®xing the heat as well as the salt ¯ux. coupled ocean±atmosphere simulation (Delworth et al. Assuming a linear equation of state (its nonlinearity is 1993). Ocean-only models forced with mixed boundary not important here), the problem can be recast in terms conditions (Weaver and Sarachik 1991; Yin and Sara- of a single variable. chik 1995) and ®xed ¯ux boundary conditions (Chen The original explanation for the ®xed ¯ux variability and Ghil 1995; Greatbatch and Zhang 1995; Huang and was that it was a sort of ``lurching'' phenomenon (Chen Chou 1994) also exhibit robust decadal-scale variability and Ghil 1995; Greatbatch and Zhang 1994; Huang and related to the thermohaline circulation. Chou 1994): When a dense anomaly is in the sinking Since the goal of the modeling activity is to under- region, it accelerates the overturning, casting up a buoy- stand nature, connections must be made between the ant anomaly, which subsequently retards the overturning modeled and natural variability. The mechanism of the to the point where the ®xed buoyancy ¯uxes convert it variability is key to making this connection. The ocean- to a dense anomaly once again. This meridional-plane only experiments, because of their relative simplicity, argument is not supported, however, by meridional- should be useful for isolating the mechanism. Then, if plane frictional models, which do not produce oscilla- the same mechanism is active in nature, these experi- tions even with very large ®xed ¯ux forcing (Winton ments may help distinguish variability that is inherently 1996). These two-dimensional models do reproduce the oceanic from that which is forced by the atmosphere or millennial and centennial variabilities also found in inherently coupled. three-dimensional models. The recent ®nding of the internal decadal-scale vari- Experiments with rotating models indicate that con- ability in models forced only with ®xed buoyancy ¯uxes vective adjustment and ␤ are not critical to the vari- allows for the possibility that this kind of variability is ability. Work with various f-plane con®gurations sug- not truly thermohaline (i.e., does not involve the inter- gests that forcing of thermal currents normal to weakly strati®ed coasts is the essential element needed to produce the oscillation (Winton 1996). Caution is warranted here because the adjustment of these currents Corresponding author address: Dr. Michael Winton, GFDL/ NOAA, Princeton University, P.O. Box 308, Princeton, NJ 08542. to the no-normal-¯ow boundary condition gives rise to E-mail: [email protected] peculiar features in the ¯at-bottom model solutions that

Unauthenticated | Downloaded 09/30/21 10:38 PM UTC 204 JOURNAL OF PHYSICAL VOLUME 27 are not observed in the actual ocean, including large of dense and of buoyant water adjacent to high-latitude coasts. This thermally indirect circulation is an attempt by the model to adjust to the no-normal-¯ow boundary condition by distorting the strati®cation so as to build up a gradient normal to the coast. Since the models make their own deep water, the strati®cation vanishes at high latitudes and FIG. 1. Basin geometry for the BOWL experiments. BOX experi- the adjustment becomes problematic. ments have the same perimeter but a ¯at bottom at 4000 m. If the mechanism for the variability does, in fact, involve the adjustment of currents to the no-normal-¯ow boundary condition in weakly strati®ed regions, it should be sensitive to the inclusion of coastal a zero net heat ¯ux. The standard MOM 2 equation of topography, which fundamentally alters this adjustment. state was replaced with the linear form: This has been found to be the case in mixed boundary ␳(T) ϭϪ2ϫ10Ϫ4T. (3) condition experiments. Moore and Reason (1993) and Weaver et al. (1994) found that their models oscillated The model is formulated with two bottom topog- with ¯at bottoms but were steady when topography was raphies: 1) a ¯at bottom (the ``BOX'' experiments) and included. In this paper we seek to reproduce this sen- 2) a bottom with sloping walls along the western, east- ern, and northern boundaries (the ``BOWL'' experi- sitivity in ®xed-¯ux experiments and understand it in ments). Figure 1 shows the bottom topography for the terms of the oscillation mechanism offered by Winton BOWL experiments. The slope takes nearly 20Њ to (1996). reach bottom. This is considerably more gentle than The next section presents the model to be used in this the typical continental slope but compares to the grad- study. Following that, a comparison of the circulation ual upward slope encountered by the North Atlantic in ¯at and bowl-shaped basins is made with emphasis Current as it ¯ows northward toward Iceland and upon the coastal adjustment. In section 4 the suscepti- Greenland. The goal here is to investigate the quali- bility to oscillation of the two geometries is compared. tative effect of sidewall topography, and for that pur- Section 5 presents the conclusions. pose a slope that is well resolved by the coarse model grid was chosen. 2. The model 3. Circulation with and without bottom The ocean model used in this study is the GFDL topography MOM 2 primitive equation model (Pacanowski 1995). The model is con®gured with 3Њ by 3Њ horizontal res- First, we examine the steady states produced by forc- olution and 15 vertical levels. The basin is a sector ing the two models by restoring surface temperatures extending from 6Њ to 66ЊN and is 66Њ wide in the zonal to the reference pro®le (1). The solutions are remarkably direction. Conventional values are chosen for the dif- different in many respects. Figure 2 shows the surface fusivities and viscosities: The diffusivities are 10Ϫ4 m2 pressure for the two solutions. Since there is no wind sϪ1 (vertical) and 103 m2 sϪ1 (horizontal), and the vis- forcing, the contours are very nearly streamlines of the cosities are 2 ϫ 10Ϫ3 m2 sϪ1 (vertical) and 105 m2 sϪ1 surface ¯ow. The ¯ow is particularly different in the (horizontal). No wind stress or haline forcings are ap- high latitude part of the basin. The BOX geometry has plied to the models. Two kinds of thermal boundary a broad east bearing jet fed by upwelling along the conditions are employed: restoring and ¯ux. The re- western boundary and feeding intense downwelling on storing nudges the top 52-m grid layer to the the eastern boundary. In the BOWL geometry, the ¯ow pro®le forms a cyclonic gyre. The downwelling in the east is much reduced and the upwelling in the west is elimi- 66 Ϫ ␾ nated north of 40 N. The BOWL circulation western Tref(␾) ϭ 20 ϫ (1) Њ 60 separates from the coast in an intense on a 50-day timescale (␾ is latitude in degrees). Under jet near 35ЊN. the ¯ux forcing, a ®xed heat ¯ux Figure 3 shows the meridional overturning stream- function for the two geometries. The BOX overturning ␾ Ϫ 6 ␾ Ϫ 6 has a maximum streamfunction of 18 Sv (Sv ϵ 106 m3 Ϫ1 F(␾) ϭ Fo cos ␲ Ϫ cos ␲ (2) s ). At high latitudes, this is primarily the projection 60 60 ΂΃onto the meridional plane of the quasi-zonal circulation is applied to the top grid layer. The overbar denotes shown in Fig. 2. The BOWL geometry has only 6 Sv averaging over the area of the basinÐthis term ensures of overturning, and the node is positioned at the base

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FIG. 3. Zonally integrated circulations for the BOX and BOWL ge- ometries (units are 106 m3 sϪ1).

clinic and surface height is just a rescaled mirror image of the interface heightÐthe free surface does not help FIG. 2. Surface pressure for the BOX and BOWL geometries ex- to bring the cross-shore ¯ow to zero because its gradient pressed in equivalent surface height (10Ϫ2 m). Bottom topography also parallels the coast. If there is bottom topography greatly reduces the alongshore pressure gradients at high latitude. with a cross-shore slope, the cross-shore component of the bottom ¯ow directly modulates the free surface of the rather than at middepth as in the BOX case. Figure 4 shows the barotropic streamfunction for the BOWL geometry. The BOX geometry circulation is al- most purely baroclinic, so its barotropic streamfunction is not shown. Since the momentum terms are negligible, bottom pressure torque is responsible for the gyre ¯ows seen in the ®gure. With bottom topography, the high-latitude thermohaline circulation is more in the horizontal plane than in the meridional planeÐthere are 14 Sv of barotropic ¯ow and only 6 Sv of meridional ¯ow. It is apparent from the changes in circulation that the adjustment of the high-latitude baroclinic jet to the no- normal-¯ow boundary condition is eased by the pres- ence of topography. Why should this be so? Imagine the adjustment of a rotating two-layer ¯uid with a free surface to a boundary parallel to the interface height FIG. 4. Vertically integrated circulation for the BOWL geometry gradient. If the bottom is ¯at, the ¯ow is nearly baro- (units are 106 m3 sϪ1).

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TABLE 1. Potential to kinetic energy conversion (10Ϫ6gcmϪ1 sϪ3). Geometry Baroclinic Barotropic Total Bowl 0.5 1.9 2.4 Box 1 0 1 height through net divergence. The free surface and the interface height become decoupled and the former can be distorted so as to build up a cross- shore . In the rigid-lid models, of course, there is no defor- mation of the upper surface. Instead, energy that would have gone into free surface deformation is converted directly from potential to kinetic energy of the baro- tropic mode through bottom pressure torque. Table 1 shows the difference in potential to kinetic energy path- ways for the BOX and BOWL geometries. In the BOX geometry all of the energy goes into the baroclinic mode. In the BOWL geometry the conversion into the barotropic mode is almost four times that going into the baroclinic mode, and the total energy conversion is 2.4 times greater. The kinetic energy of the BOWL circu- lation is almost twice that of the BOX circulation (0.57 erg cmϪ3 vs 0.31 erg cmϪ3). The cyclonic subpolar circulation of Fig. 4 corre- sponds to a feature of the North Atlantic Circulation deduced from and wind stress data. Great- batch et al. (1991) solve the barotropic equa- tion using climatological data and ®nd 30 Sv of cyclonic bottom torque driven circulation in this region (their FIG. 5. Kinetic energy of the BOX and BOWL geometries under ®xed heat ¯uxes of various magnitudes (units are 10Ϫ1 kg mϪ1 sϪ2). Fig. 6). Thus, the inclusion of coastal topography adds a realistic feature to the circulation and removes some unrealistic features (large vertical velocities on the boundary). and also with the ¯uxes doubled, tripled, and quadru- pled. The BOX geometry solution is oscillatory for all of the forcing levels. As the forcing becomes stronger, 4. The effect of bottom topography upon the oscillations increase in frequency and amplitude. variability The BOWL geometry solution is steady for the standard, Now we switch from the restoring boundary condition doubled, and tripled forcing. The BOWL oscillation in- of the last section to the ®xed-¯ux form (2) in order to duced with quadrupled forcing is much smaller in am- determine the susceptibility to oscillation of the BOX plitude than the BOX oscillation under that forcing or and BOWL basins. The ®xed-¯ux boundary condition even the BOX oscillation under the standard forcing. is not used because it is a better representation than the Whether the measure of susceptibility to oscillation is restoring boundary condition of surface forcing in the the critical forcing level required to induce oscillation actual ocean (it is not). Rather, it is used here because or the amplitude of oscillation at a ®xed level of forcing, 1) it allows us to make a fair side by side comparison the BOWL is substantially less oscillatory than the of the models by applying the same ¯uxes to both and BOX. 2) it is a nondamping boundary condition that allows In addition to having a smaller amplitude, the BOWL the models maximum freedom to develop internal vari- oscillation is qualitatively different than the BOX os- ability. cillations. The most prominent aspect of the BOX os- In spite of the striking differences between the BOX cillations is the growth and decay of disturbances that and BOWL circulations described in the last section, propagate cyclonically around the basin [see Winton they transport nearly the same amount of heat poleward, (1996) and GP, for further description]. The BOWL os- 15 about 0.2 PW (1 PW ϭ 10 W). In (2) Fo is adjusted cillation involves a slight expansion and contraction to to put this amount of heat into the basin at low latitude the west of the convecting region at 55ЊN in the core and take it out at high latitude. Figure 5 shows the result of the subpolar gyre (Fig. 6). It is perhaps not so sur- of forcing both geometries with this boundary condition prising that a stagnant region in the ¯ow develops time

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the model than the generation of horizontal ¯ow by bottom pressure torque.

5. Conclusions The experiments of the last section indicate that ¯at-bottom models may overestimate the internal de- cadal-scale variability of the actual thermohaline cir- culation. This is because their variability arises out of the considerable dif®culty they have adjusting bar- oclinic currents to the no-normal-¯ow boundary con- dition at weakly strati®ed coasts. The adjustment is made easier by the presence of coastal topography, FIG. 6. Extreme phases of the BOWL oscillation cycle. The con- vecting region at 55ЊN in the core of the subpolar gyre (unshaded) which decouples the free surface from the baroclinity is expanded slightly to the west in the left panel. Velocity units are or, in terms of the rigid-lid problem, allows conver- 10Ϫ2 msϪ1. sion of directly into the barotropic mode. This conversion pathway dominates the con- version into baroclinic kinetic energy in the basin with coastal topography. Since the barotropic mode is triv- dependence to balance the imposed surface ¯ux when ially adjusted to the no-normal-¯ow boundary con- it reaches a suf®cient magnitude. Since the meridional dition through lid pressure adjustment, the problem scale of the variability is a single grid cell, an accurate is greatly reduced. parameterization for subgrid-scale horizontal mixing Winton (1996) argued that the propagating anom- would be needed to assess its realism. alies of the ¯at-bottom model oscillations are formed These results might support a claim that the bottom in the northeast corner (the boundary between strat- pressure torque, found in the last section to be such an i®ed and unstrati®ed ¯uid) by a thermally indirect important driver of the horizontal circulation in the circulation that intensi®ed the baroclinity of the on- BOWL basin, has a suppressive effect upon the oscil- shore jet. It is consistent with this mechanism that the lations. An alternative hypothesis, however, might em- oscillations are greatly inhibited in the BOWL cir- phasize the thermodynamic effect of bottom topography culation, which does not have either the onshore jet over this dynamic effect. Since the bottom shoals to the or signi®cant thermally indirect circulation at high north in the BOWL basin, thermal wind currents normal latitudes. Furthermore, that the mixed boundary con- to the coast may be weaker, reducing the forcing of dition models (Moore and Reason 1993; Weaver et coastal anomalies. To help distinguish the dynamic and al. 1994) exhibit the same sensitivity to topography thermodynamic effects two of the experiments were re- as the ®xed ¯ux boundary condition model used here peated in a ``modi®ed BOWL'' basin. This basin has the argues for a single mechanism underlying the internal same meridional bottom slope as found at the middle decadal variabilities of both. longitude of the full BOWL basin but no bottom slope in the zonal direction. Thus, the ®xed ¯ux forcing does not directly generate bottom pressure torque in this basin Acknowledgments. The idea for this paper grew out although there will in general be some generation of of preliminary experiments performed by Steve Grif®es. torque by currents that are not aligned with the forcing. The author is grateful to Ron Pacanowski for help using Thus, the modi®ed BOWL basin emphasizes the ther- the GFDL MOM 2.0 code. Steve Grif®es and Anand modynamic effect of the bottom topography at the ex- Gnanadesikan are thanked for reviews of an early ver- pense of the dynamic effect. sion of the manuscript. The ®nal version bene®tted from When the modi®ed BOWL basin was forced with F helpful reviews by Stefan Rahmstorf and an anonymous o reviewer. ϭ 0.2 PW (corresponding to the bottom panel in Fig. 5), the solution became steady after a period of damping oscillations. Increasing Fo to 0.4 PW produced self-sus- REFERENCES taining oscillations, considerably larger in amplitude than those of the BOX basin under the same forcing. Chen, F., and M. Ghil, 1995: Interdecadal variability of the ther- The modi®ed BOWL experiments had some bottom mohaline circulation and high latitude surface ¯uxes. J. Phys. pressure torque-driven barotropic ¯ow, although less Oceanogr., 25, 2547±2568. than in the full BOWL geometry. Although it is im- Delworth, T., S. Manabe, and R. J. Stouffer, 1993: Interdecadal vari- ability of the thermohaline circulation in a coupled ocean±at- possible to distinguish the thermodynamic and dynamic mosphere model. J. , 6, 1993±2011. effects completely, these experiments suggest that the Greatbatch, R. J., and S. Zhang, 1995: An interdecadal oscillation in thermodynamic effect of the bottom shoaling to the an idealized ocean basin forced by constant heat ¯ux. J. Climate, north has a lesser impact upon the oscillatory nature of 8, 81±91.

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