90253_OCEAN 3/18/04 1:45 PM Page 107 MEETING REPORTS—Thirteenth ‘Aha Huliko’a Hawaiian Winter Workshop This article has been published in Oceanography, Volume 1 Volume This articlein Oceanography, has been published 5912 LeMay Road, Rockville, MD 20851-2326, USA. Road, 5912 LeMay prohibited. Send all correspondence or Society is strictly to: [email protected], The Oceanography machine, reposting, or other means without prior authorization of portion photocopy of this articleof any by Near-Boundary Processes and Their Parameterization Peter Müller University of Hawaii • Honolulu, Hawaii USA Chris Garrett University of Victoria • Victoria, B.C. Canada We think of the ocean as being driven by a variety invited speakers. The emphasis was on the physics of 7 the regions of the ocean near the surface, the bottom, , Number of forces: tides, wind, surface buoyancy fluxes associ- ated with heating, cooling, evaporation, precipitation and the sloping sides, with full recognition that predic- tive models for ocean behavior require that the effects of 1 and ice formation, and geothermal heating. Apart from , a quarterly journal of The Oceanography Society. Copyright 2003 by The Oceanography Society. All rights reserved.Reproduction Society. The Oceanography 2003 by Copyright Society. The Oceanography journal, a quarterly of tidal forces, which act throughout the ocean, geother- small-scale, near-boundary processes be “parameter- mal plumes that rise far into the ocean interior, and ized,” i.e., represented by formulae in terms of model locations of deep convection, these driving forces com- variables rather than just expressed as numbers that municate their influence to the ocean via boundary lay- might be correct only for particular conditions. ers that are thin compared to the ocean depth. In a Large-scale numerical modelers are, of course, try- sense, therefore, the behavior of the ocean is controlled ing their best to include more appropriate parameteri- by what happens in these boundary layers. The zations into their models but they face substantial bar- response of the boundary layers to forcing sets bound- riers. Their models might not resolve the variables that ary conditions of fluid injection or removal that force a the parameterizations require. Numerical errors might response in the rest of the ocean. We are familiar, for overwhelm the physical effects. Indeed, well-known example, with the role of “Ekman suction” as the effects like numerical diffusion, numerical entrainment, means by which the wind drives ocean circulation. and spurious diapycnal mixing become aggravated Quite apart from these dynamical considerations, near boundaries when topographic and isopycnal we also recognize that gas exchange with the atmos- slopes become large and when boundary layers and phere can only influence the bulk of the ocean after it overflows become thinner than the typical vertical grid has passed through the surface boundary layer. spacing. Considerable work is underway to design Similarly, sedimentary and biochemical processes at numerical algorithms that keep these numerical effects the seafloor involve the bottom boundary layer of the in check and allow physics to rule, but these efforts ocean and only affect the ocean interior through were only reviewed in passing. exchange between it and the boundary layer. The workshop also did not deal directly with Quantifying these exchanges clearly requires a thor- important issues of sediment transport, gas transfer, or ough understanding of the nature and behavior of the biogeochemical processes, but we hope that the report boundary layer or, to be more general and avoiding for helps to establish the physical framework within which now a definition of what is meant by “boundary layer,” these issues are considered. In fact, we did not even we could refer to the “near-boundary” region. focus extensively on the details of the boundary layers Some of the influence of the driving forces is more themselves. Instead, emphasis was placed on their subtle in that it involves the radiation into the ocean interaction with the ocean interior, recognizing that this interior of internal waves that carry with them both is a two-way process: near-boundary regions influence momentum and the energy that can lead to turbulence the ocean interior but are also themselves affected by and mixing elsewhere. Quantifying these effects again the properties of the interior. requires a detailed understanding of the near-bound- The report that follows only gives a broad ary region. For example, a very simple model of the summary of the meeting and a few references. More energy flux associated with wind-driven internal details and references can be found in the workshop waves shows that it depends on the thickness of a sur- proceedings which are available from www.soest. face homogeneous layer. hawaii.edu/PubServices/AhaHulikoa.html. The Thirteenth ‘Aha Huliko’a Hawaiian Winter Workshop was convened from 21 to 24 January 2003 to General Considerations review the general theme of “Near-Boundary Processes For a model that resolved the smallest scales of and Their Parameterization,” with the support of the fluid motion, perhaps only a millimeter or so, the Office of Naval Research and the participation of 25 boundary conditions would be simple. At a solid Oceanography • Vol. 17 • No. 1/2004 107 90253_OCEAN 3/18/04 1:45 PM Page 108 At both the seafloor and the ocean surface, the stress might be distributed over a turbulent region of finite thickness. In the presence of Earth’s rotation, the response should have some of the characteristics of the classical Ekman layer. This, rather than the embedded log layer, might then be taken as the unresolved boundary layer, with the bulk of the ocean driven by Ekman convergence and divergence forcing fluid into or out of the interior. The situation becomes more complicated as soon as one adds effects such as ocean stratification. The temperature and salt transported by the Ekman flux, either at the surface or sea floor, depend on how far the Ekman layer extends beyond a mixed layer into the stratified region. An additional effect at the seafloor is that the presence of a bottom slope may cause the Ekman layer to be “arrested” by buoyancy forces, and large topographic features introduce further complica- tions. It clearly becomes difficult even to decide what one will regard as a boundary layer to be parameter- ized and what one will try to treat explicitly in a model Figure 1. A map showing the varieties of topographic for the ocean interior. terrains including abyssal plains, continental shelves The parameterization of boundary layers is further and slopes, mid-ocean ridges, seamounts, canyons etc, complicated by the presence of mesoscale eddies. If in the Pacific Ocean. Such variety continues on smaller these are also unresolved, as is still the case in climate scales not resolved by the 2' longitude and 1.36' latitude models, their effect on, and interaction with, surface resolution of the Smith and Sandwell topography (see and bottom boundary layers will need to be parame- http://www.ngdc.noaa.gov/mgg/image/seafloor.html) terized. shown here, down to the smallest scales such as sand Understanding and parameterizing near-bound- ripples. ary regions is an immense and complicated, but fasci- nating, task. The rest of this report will touch on many of the questions, particularly those addressed at the workshop. The next two sections will focus on some boundary there would be no velocity at right angles to details of the bottom and surface regions, but we then the surface, a no-slip condition for the tangential veloc- return to more general questions of parameterization ity, and flux conditions for scalars that would involve philosophy and also discuss how the community can only molecular diffusion coefficients. At the moving bridge the gap between those who delight in unravel- sea surface the situation would be more complicated, ing the detailed physics of ocean processes and those but in principle everything is defined. who revel in the grand scales of general circulation Recognizing the limitations of resolution of any models. realistic model, the next step might be the assumption that the boundary layer at the sea floor obeys the “law The Near-Bottom Region of the wall,” with a logarithmic velocity profile and a While parts of the seafloor, such as abyssal plains, 2 drag that could be expressed in magnitude as Cdu , are as flat and smooth as in a modeler’s dream, regions where u is the flow speed at some prescribed height with a significant slope and bottom roughness are and Cd a drag coefficient that depends on the bottom extensive and need to be considered (Figure 1). roughness. Assuming the logarithmic layer to be of The variety of topographies immediately raises the infinitesimal thickness, one thus has a bottom bound- question as to what topographic scales matter, for the ary condition for the rest of the ocean. To be sure, some properties of the boundary layer itself, for communica- of this might also be turbulent and require process tion with the interior, and for the radiation into the parameterization, but with much less resolution interior of momentum- and energy-carrying internal required than if the log layer were treated explicitly. waves, but there are many other issues, too. A cartoon Similarly, the surface of the ocean might be assumed to of the near-bottom region and the processes there is be forced by a wind stress expressed in terms of the given in Figure 2. wind speed at some height, though the response of the ocean just below the surface is no longer a simple log The Boundary Layer layer, but is complicated by the effects of wave break- Even over flat and smooth abyssal plains, there are ing which has a major influence on turbulence levels interesting questions that are still unsettled.