Your email. Send Cancel. Check system status. Toggle navigation Menu. Name of resource. Problem URL. Describe the connection issue. SearchWorks Catalog Stanford Libraries. Air-sea exchange : physics, chemistry and dynamics. Responsibility edited by G. Imprint Dordrecht ; Boston : Kluwer Academic, c Physical description xii, p. Series Atmospheric and oceanographic sciences library ; v.
Online Available online. Full view. Earth Sciences Library Branner. G44 Unknown. More options. Find it at other libraries via WorldCat Limited preview. Contributor Geernaert, G. Bibliography Includes bibliographical references and index. Contents Preface. Historical Perspective-- G. Theory of air-sea momentum, heat and gas fluxes-- G.
The leading edge of turbulence instrumentation-- S. Dynamical coupling of surface waves with the atmosphere-- V. Makin, V. Effect of surface gravity waves on near-surface atmospheric turbulence-- T. Hara, et al. The budget of turbulence kinetic energy in the marine atmospheric surface layer-- J. Wilczak, et al. The marine atmospheric boundary layer during swell, according to recent studies in the Baltic Sea-- A.
House ofReps , ; Ronayne ; Greenberg On October 4, , the Soviet Union surprised the world with the launch of the first spacecraft, Sputnik 1. Sputnik was such a surprise to the West that a new dimension of science policy soon afterwards emerged in, in particular, the United States. The technology leading to the Sputnik launch illustrated that the capabilities in the Soviet block were no less than those in the West, and that these capabilities had major military significance.
With the launch of Sputnik, the race for space began, and this race was supported by expanded investments in the atmospheric sciences, oceanography, and astrophysics, in most maritime industrial countries. The sea surface was the primary medium for Navy activity, and space was the preferred medium for reconnaissance and surveillance.
A new national goal in the United States emerged, Le. Air-sea interaction as a discipline grew and profi ted from this new national goal. As mentioned before, the success of air-sea interaction also benefitted from the initiatives of ReveIle, Munk, Kort, and other leading scientists of those days, in the design of the Indian Ocean Experiment and in building oceanographic research within the purview and infrastructure of the Uni ted Nations Le. During the decade after the launch of Sputnik and as a consequence of the national strategy for space, a new type of customer for air-sea interaction researchers was introduced, which would carry them into the 21st century.
Using the newly developed supercomputers of the early 's, atrnospheric and ocean models required massive amounts of data which could not be supplied by the few buoy networks and ships of opportunity. A large number of field activities was designed, with emphasis on an the worId's oceans reviewed in the next section. To support these endeavors, the use of sateIIite derived signatures as indicators of geophysical, hydrodynamic, andlor thermodynamic quantities was the most practical approach. Active microwave sensors were able to infer surface roughness parameters, which in turn relate to surface waves, wind stress, and wind vector.
Passive microwave sensors provide information on roughness, cloud and water vapor. The infrared and visual sensors were able to provide estimates of surface temperature, temperature profiles, clouds, aerosol, and ocean color related for example to water column biomass productivity and concentrations. A growing need to understand surface processes and how the surface interacts with electromagnetic interaction emerged in the years during and after the IGY.
Much effort was placed on describing surface wave spectra and turbulence in the adjacent boundary layers. For surface waves, efforts were placed on studies of wave growth e. Pierson, Moscowitz ; spectral dynamics e. Hasselmann , wave breaking Toba, Kunishi , interactions between spectra and wind turbulence Kitaigorodskii, Volkov , and relationships between spectral amplitude and windspeed Kondo et al. In addition, a major international study of fetch-limited wave growth was carried out in the North Sea, i.
Building on the expanded knowledge on surface waves from a wide variety of countries , a number of remote sensing experiments was also carried out, in order to identify relationships between radar backscatter and wind speed e. These and other efforts were used in the planning for the first sateIIite which emphasized monitoring of the ocean environment, i. The 's witnessed the first use of the sonic anemometer and dissipation techniques for estimating fluxes Weiler and Burling , and indirect methods for estimating fluxes at windspeeds up to hurricane force Hawkins, Rubsam The first evidence that flux magnitudes were intimately related to the state of the sea, e.
Kitaigorodskii, Volkov In addition, aseries of international field campaigns was carried out in the 's and 's, which had subprograms to investigate the processes which govern air-sea fluxes. The IIOE Indian Ocean Experiment , carried out in , included the first intensive measurements of simultaneous momentum, heat, and moisture fluxes using profile methods, in order to assess these fluxes in ocean dynamics Badgley et al.
Conducted in , ATEX was based on a triangle of ships drifting with the NE trades and spatial structures of the boundary layer were gathered. Air-sea fluxes were measured by the profile method and the eddy correlation technique was used on two separate buoys: a stable, wave following buoy for profiles and a servo-stabilized buoy for eddy fluxes Dunckel et al.
The neutral drag coefficient from the eddy correlation technique was found to be 1. The comparison of fluxes by the two methods revealed discrepancies that lead to a detailed investigation by Wucknitz , where he showed that the the longitudinal and lateral high frequency spectral densities which were measured had deviated substantially from the classical law; this study suggested that use of the dissipation technique required careful and critical analysis. The data analysis also revealed the importance of flow distortion as an issue to be considered, even for narrow masts.
The value of the Dalton number for water vapor exchange, i. GATE had a boundary layer subprogramme, with contributions from many nations e. Eddy correlation, profile, and dissipation techniques were used to determine the fluxes. Values of the flux coefficients corroborated earlier results within an acceptable level of statistical uncertainty, and no windspeed dependence was reported for the low to moderate windspeeds.
During the passage of cold air, it was observed that the surface layer profile up to 10m height re-established itself to a new equilibrium profile within a few minutes Hasse et al. It was also determined from GATE data that the cool skin of the ocean surface plays a significant role in determining the rate of evaporation and the Dalton number Hasse FIuxes were estimated by caIculating the one dimensional windspeed spectrum and integrating over the band passed inertial subrange and relating dissipation to stress. The data provided evidence that fluxes are cIosely related to large boundary layer scale eddies, and tbis implied a strong coupling between the surface fluxes and both surface waves and boundary layer scale turbulent motions Mitsuta Conducted in primarily north and west of ScotIand, the emphasis was on marine boundary layer dynamics.
Surface fluxes were collected only by aircraft, the most notable resuits reported by Shaw and Businger who showed that boundary layer rolls were able to systematically modulate fluxes, even in the neutral boundary layer. Seasat unfortunately suffered technical malfunctions, and only provided the scientific community with 90 days of data. The MARSEN experiment, which was originally a ground truth campaign to provide a calibration and validation of SeaSat's microwave instruments, was carried out in , in spite of the early death of SeaSat.
MARSEN included a collection of studies on wave dynamics, air-sea fluxes, and remote sensing via aircraft and ground based systems, and was carried out in the North Sea. The key air-sea interaction reSUitS of Marsen were drag coefficients which were reported to depend on sea state and wave age, and where extrapolations of the resuits suggested that shallow water waves produce higher drag than deep water waves Geernaert et al. For the decade after the demise of Seasat, the remote sensing community relied on extensive funding to study the Seasat data sets and explore newer technologies for future environmental sateIIites.
Most of the remote sensing research after Seasat relied on dedicated aircraft missions. It was not until the laie ' s when environmental sateIIite programs were reinvigorated, with the planned launch of sateIIites dedicated to specific missions within a variety of countries. The early 's saw the revival of remote sensing with the beginnings of aseries of American, European, Canadian, and Japanese sateIIites Goroch Air sea interaction research during the late 's and 's maintained its growth via a large number of field experiments and field sites, and an emphasis was placed on producing flux estimates for high windspeeds, and gathering more data on the momentum, heat and moisture exchange coefficients in order to establish more accurate parameterizations.
During the decade of the 's, the research community shifted away from profile method of estimating surface fluxes towards the direct eddy- correlation method using propellers and sonic anemometers. Results reported before using profile and other older techniques were in general characteristic of very large scatter, and the modelling and remote sensing communities had greater accuracy requirements to meet their needs.
Projects were carried out in Lake Ontario on surface exchange e. Donelan , the Bedford Tower e. While the BASS data sets resulted in a clearer understanding of the relationships between wave state, wind stress, and surface layer turbulence e. Chambers and Antonia , they also raised controversies concerning the dependence of the drag coefficient on windspeed and fetch e. Toba, et al. The first extensive set of aircraft results also emerged in the 's, e.
Byrne Ship-borne studies were also carried out in a wide number of field studies. In general, there was a common goal with the various field projects, Le. The HEXOS experiment Humidity Exchange over the Sea , conducted in , was the first comprehensive open ocean air-sea flux field project which emphasized surface exchange processes.
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Conducted on the Dutch Noordwijk platform, HEXOS contained the largest range of windspeeds where all three fluxes momentum, sensible heat, and latent heat were measured. It furthermore provided the physical basis for linking aerosol, sea spray, and sensible and latent heat fluxes under a common framework Smith et al.
The drag coefficient dependence on windspeed and sea state determined from the North Sea Tower in a parallel remote sensing experiment Geernaert et al. In parallel to the process oriented air-sea flux experiments carried out on towers, regional experiments were being conducted which included the measurement of air- sea fluxes. While the fluxes on the warm water side of the surface temperature fronts in FASINEX were expected to be higher than over the cold side, it was found that the difference in fluxes was larger than predicted given the diabatic profile coefficients reported by Businger This suggested that there was a possibility for additional processes acting on the marine surface layer which do not take place over terrestrial surfaces, such as surface wave effects.
The limitations of the results of the Kansas experiment were now suspected to be more important than previously expected for application to marine conditions, and it was suggested that an experiment similar to the Kansas Experiment should be designed for the marine domain Geernaert CODE emphasized the local ocean temperature response to wind stress patterns, and also illustrated that the stress vector direction can deviate from the wind direction due to cross-shelf pressure gradients e.
Zemba, Friehe ; Enriquez, Friehe Protection of human health, coastal marine ecosystems, and shared common resources e. Negotiations for the protection of inland seas e. Sirnilar efforts were dedicated to the Great Lakes, Chesapeake Bay, and other regional seas. Budgets of pollution loads required new research, in order to identify the air-sea gas exchange rates of key pollutant compounds with sufficient accuracy so that the impacts associated with anthropogenic sources could be identified. In addition to the pollutant gases, estimating carbon dioxide exchange with the oceans emerged as a priority issue in the development of global and climate models as weIl as in response to international agreements to reduce atmospheric ambient CO2 concentrations.
A surge of interest appeared in the 's and 's on air-sea gas and particle exchange. Gas exchange was investigated using processes involving windspeed e. Liss, Merlivat The particle flux from the ocean was also investigated, not simply in terms of physical mass exchange but also in terms oftheir bacterial content e. Blanchard The climate gases were a special focus. As a follow-on to HEXOS, and prior to the start of the marine version of the Kansas experiment see below , the ASGASEX campaign was launched as a multi-year project in to measure a variety of air-sea fluxes, including CO2, and to identify the set of governing processes.
Fluxes of momentum, heat, moisture, gases, and aerosols, subsurface bubbles, surface waves, and information on bulk boundary layer properties in both the atmosphere and ocean, were collected from the Noordwijk Platform, in the North Sea. Results from this project will be emerging over the next half decade. A key air-sea interaction question conceming the degree to which the atmospheric pathways contributed to coastal marine problems was also raised in the late 's Algal blooms and the famous "red tide" events are due, in part, to excess nutrient input to coastal seas from both atmospheric and riverine pathways.
The methods to estimate and parameterize the deposition of nutrient species e. Revelle and Suess However, the climate forcing problem became much more complex in subsequent decades. During the 's, atmospheric aerosols were argued to playa significant role in climate dynamics, and it was hypothesized that the air-sea exchange of dimethyl sulfide is a key process which participates intimately in climate dynamics Charlson et al.
Subsequent studies have shown that variations in marine biogeochemistry, and that the geographic variations in radiative forcing also are important, in terms of the direct and indirect forcing of climate see e. Seinfeld et al. This interplay has provided the basis for recent efforts to construct high spatiotemporal resolution, multi-compartment climate models, activities which continue today. Contributing to interest in climate dynamics were the scientific analyses of an event in and During these years, one of the more severe EI Nifio events was observed in the equatorial Pacific, which inflicted major economic damage worldwide.
This event was not able to be predicted at the time, but it provided the opportunity for study and planning of major research programs for the next two decades. Biological effects of the EI Nifio were postulated e. Barber, Chavez , and speculations on global and long term impacts were made, e. Because very few data sets have become available for such situations, i. The conditions encountered during SOWEX included windspeeds exceeding 20 mlsec and wave heights over 9 m Banner et al.
While the analyses initially focussed on wind- wave coupling and remote sensing, the results whieh are expected to emerge during the next half decade are anticipated to extend our understanding of high windspeed fluxes, and lead to the improved performance of future climate models. During the early 's, the massive computer power which had become available during the 's made possible the development of much higher resolution models than had been possible in the past.
At the same time, the U. There was a new customer need placed on the scientific community: the quality of remote sensing data needed to be improved and extended to much higher resolution scales than was previously possible. The shift to high resolution implied that the surface processes needed to be formulated with considerations of processes acting in the adjacent boundary layers. Existing model system were insufficient to do the job, and a high priority was placed on accuracy. Stationarity and homogeneity could no longer be assumed.
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A number of projects emerged which examined the full set of processes involved in wave propagation and in examining the nonlinear character of ocean waves and boundary layer turbulence. They were carried out in These two field experiments were succeeded by a broad project dedicated specifically to the processes which govem air-sea exchange, Le. The MBL project bridged marine boundary layer meteorology with surface wave dynamics and ocean mixed layer physics. A gas exchange component started in with funding from the National Science Foundation.
The research activities within the MBL project involved indirect contributions from a wide number of U. The key objectives of the MBL project were to understand the set of goveming processes acting on scales where waves and turbulence interact to modulate all air-sea fluxes. Momentum, heat, moisture, other trace gases, and aerosols were included in the program.
Boundary layer phenomena included both the oceanic Langmuir circulations and the atmospheric large eddy states. Due to the complexity of the problem, direct numerical simulation, large eddy simulation, and various statistical techniques were applied to a variety of data sets collected from two dedicated sets of research experiments. The first set included measurements off the Califomia coast, using FLIP, ships, and aircraft, in and ; during the same years, the second set used an offshore mast in shallow water within the inner waters of Denmark.
More recently, aseries of experiments began in and with a focus on coastal waves and air-sea interaction near Duck, North Carolina using aircraft and in-situ observations ; and with a focus on high resolution nutrient fluxes based on nested models and measurements on both fixed platforms and ferries transiting the North Sea. In addition to specific focussed efforts, preliminary results of the MBL, Duck, North Sea, and other projects are presented throughout this book. In arecent paper by Smith et al , the future of air-sea interaction was suggested to follow five themes: satellite monitoring; the coastal domain; the integration of surface and boundary layer processes; the direction of the wind and wind stress; and the interactions among swell, waves, and surface roughness.
Some of the recent findings from field measurements which lead to these themes may be found in Geemaert ; Mahrt and Gibson ; Rogers et al. Due to the model predictions that heat fluxes depend on thermodynamic interactions with sea spray aerosols Fairall et al. Many of these issues will be dealt with in chapters within this book. Tbe final chapter will highlight the uncertainty in our knowledge and identify directions for future research. Tbis chapter benefitted from input received from various authors in this book. B, Monahan, E. Smith, s. Layer Met. Badgley, F. Barger, W. Banner, M.
Overview and mean results, J. Barber, R.
Measurements of air–sea gas transfer velocities in the Baltic Sea
Science , Blanchard, O. Liss and Slinn, Reidel Pub!. Boussinesq, J. Brocks, K. Congress, proceedings, New York. Byme, H. Businger, J. Haugen, Amer. Chambers, AJ. Chan, W-T. Princeton University Press, pp. Charlson, RJ. Nature , Chamock, H. Clarke, J. Cox, C. Oeacon, E. Hili ed , The Sea, 1, Paper 4, Melboume. Deacon, E. Deacon, G. OeCosmo, J. Donelan, M. Dunckel, M. Dunne, J. Ekman, V. Elzinga, A. Books, Gothenburg, pp Enriequez, A. Erisman, J. Fairall, C. Geernaert and W. Plant, vol. Ferrell W. Journal, v. Fleagle R. Fleagle, R.
Francis, J. London, A, Frisinger, H. Howard The History ofMeteorology to , Sci. History Publications, New York, pp. Galushko, V. Galushko V. Geernert, G. Geemaert and W. Plant, vo!. Geemaert, G. Geernaert, G. Gehrke, J. Goroch, A. Plant, KJuwer Pub!. Greenberg, D. Hasse, L. Hasselmann, K. Fluid Mech. Olbers, D. A, No. Hawkins, H. Structure and budgets of the hurrricane on October 1, Hay, J. Holligan, P. Hull, L. Longman, Greens, and Col, London, pp. Jones, 1. Jones Oceanography in the Days of Sail. Hale and Iremonger, Sydney, pp.
Kerr, D. Khalsa, S. Kitaigorodskii, S. Kondo, J. Lagrange, J. Beiles Lettre Berlin, v. Large, W. Li, F. Liss, P. Buat-Menard, pp Meyrac, V. Lyman, J. Long John, U.
Naval Institute, Annapolis, pp. Melillo, J. Press, Mitsuta, Y. Monin, A. Muller-G1uwe, J. Nicholls, S. Paret, P. Press, pp. Phillips, O. Pierson, W J. Kitaigorodskii, J. Pond, S. Paquin, J. Prandtl, L. Revelle, R. Rieder, K. Rogers, D. Part gravity waves and the momentum balance, J.
Ronayne, J. Ross, D. Rossby, C. Papers Phys. Seinfeld, J. Shaw, W. Shaw, D. Sheppard, P. Smith, R. Smith, S. Song, Z. Guo, R. Chen, and L. Starr, V. McGraw Hili, New York, pp. Takenaka, Y. Taylor, G. London, Sero A, , I. Toba, Y. Van Dorn, W. GfIlttingen, Math. Volkov, Y. I, Gidrometeoizdat, Leningrad.
Wanninkhof, R. Webster, P. Weiler, H. Wenk, E. Witting, R. Wucknitz J. Zemba, J. Chapter 2. Air-sea fluxes are governed by processes acting on the interface from both above and below, as weIl interfacial processes which influence vertical exchange. The atmospheric process which governs most air-sea exchanges is turbulent transport throughout the depth of the atmospheric boundary layer ABL. The oceanic boundary layer influences many of the surface fluxes, via for example mixing associated with Langmuir circulations Le's and the bubble distributions within the water column.
In addition, biochemical processes acting on plantkonic matter, fungi, and bacteria, all exhibit an interplay with surface proceses in particular in surface films , and this interplay governs air-sea exchange via both surface diffusion and wave breaking events. The two houndary layers adjacent to the air-sea interface are governed by a set of common physical and dynamical characteristics. Often capped hy an overlying inversion, the atmospheric boundary layer has a depth which can range from tens of meters during strongly stahle flow to several kilometers during convective conditions.
The ocean mixed layer OML is order of m deep, depending on stratification, wind stress, and the strength of the underlying thermocline. When normalized by 25 G. Both boundary layers contain coherent motions, or circulations. The ABL often contains eddies which are elongated with the wind, which form cloud streets; and the oceanic Langmuir circulations exhibit the same type of behavior though with smaller dimensions.
Because these circulations act as mechanisms for inducing spatial patterns of flux at the surface, their presence must be quantified, predicted, and assessed, in reference to all fluxes of interest. There is also sirnilarity with the decrease of turbulence levels as one goes away from the interface into the atmosphere or ocean.
For example, when normalized by the buoyancy flux, turbulent kinetic energy TKE levels within both boundary layers exhibit nearly the same similarity when plotted against the ratio of zIH, where z is distance away from the interface, and His the distance, respectively, to the top of the ABL or bottom of the OBL see e. Kraus, Businger Surface waves exert an influence on profiles of turbulence and fluxes in the adjacent boundary layers, extending to distances between 2 to 5 times the wave height into both the ABL and OML. In the ABL, this depth of influence is insignficant with respect to the full depth of the ABL, but in the ocean the depth of influence can at times encompass the entire depth of the OBL.
The ABL has complicated feedbacks associated with thermodynamic processes, e. The OBL can be strongly influenced by shallow bottom topography, and in addition the role of internal waves complicates the OBL dynamics. In most part, the ABL forces the air-sea interface, which in turn drives the air-sea fluxes. For moderate to high windspeeds, the surface exchanges of momentum, heat, moisture, and aerosols are governed by atmospheric and surface processes alone.
However, for many of the gas fluxes, e. Bubbles are also a key mechanism for temperature flux. Langmuir circulations can be blamed for creating and distributing bubbles, and these motions must therefore be considered as important processes when parameterizing specific classes of fluxes. Traditional theory, however, has in general ignored all processes except for those in the atmospheric SUrface layer and at the interface, the result being that present air-sea flux parameterizations models are lirnited in accuracy and quality.
Because the theory of air-sea exchange is rather exhaustive and lengthy, this chapter will provide only abrief overview, with special focus on the set of governing equations, assumptions invoked, the sirnilarity hypotheses, and the uncertainty in the parameterizations presently used.
The reader is referred to Kraus and Businger , Stull , and Panofsky and Dutton for a more complete treatment of the derivations. In most cases, later chapters in this volume will address those additional processes not presently considered and explore improved parameterizations due to multi-process approaches. Turbulence is characterized as random, highly irregular motions. In the ABL and OBL, the motions are often described in terms of a spectrum of eddies, each able to transfer momentum, heat, andlor mass with varying degrees of efficiency.
The eddies contain a high degree of vorticity, and their interactions with the mean flow produce a highly inhomogeneous distribution of vorticity which depends in most part on the shear ofthe flow. The kinetic energy associated with turbulent motions is quickly transformed into internal heat energy due to molecular viscosity. Since the sink of kinetic energy is associated with the dissipation of the smallest possible turbulent eddies order of 1 mm size , the source of energy is via the larger eddies. This mismatch of scales leads to the "energy cascade", where energy is transferred through the spectrum of eddies towards the smallest scales.
For the smaller scales of the spectrum, Taylor's hypothesis is often invoked in order to relate the eddie's wavenumber, k. Because equation is not necessarily valid for all eddy sizes, this forces us to examine the nature of the spectrum of turbulent eddies, and identify characteristic features of spectra and cospectra. The most important part of the spectrum to be discussed here is the high frequency part, known as the inertial subrange.
In this subrange, the turbulent eddies intimately participate in transferring energy to higher frequencies, and one may assume that the spectral density, S k. The inertial subrange for the atmosphere may be written as:. The lowest frequency applicable to the scaling in is both height and windspeed dependent, and a practicallower limit in Hz, is 1. The largest sale eddies within the boundary layer may have a size which is controlled by convective activity within the boundary layer and the height to the inversion or depth to the thermocline.
These large eddies are often coherent and elongated with the flow. However, due to their sometimes coherent nature, the largest eddies may at times carry no flux to the surface and at other times dominate the flux. Important characteristics of turbulent flows are the degrees to which the turbulence is time-independent stationary and horizontally homogeneous. One can define an autocovariance function, R.. In , r is the separation distance between measurements of w. With , one obtains an integral scale, I.
Studies of the size of the integral scale have been carried out using tower data e. Kaimal et al. Lenschow, Stankov Results of these studies lead to expressions for the required averaging length or time associated with error variance in flux measurements, Je. Following Lenschow , and relevant to the surface layer defined below , one obtains:. For a windspeed of 10 mlsec, a 40 minute averaging time to yield the same standard error would be required. These error constraints will be dealt with in later chapters. In the atmosphere, fluxes of momentum and heat tend to decrease monotonica11y with height throughout the depth of the boundary layer.
It is therefore practical to define a shaw layer near the surface, where the flux has not deviated significantly from its surface value. The reader is reminded that the term "constant flux layer" should never mean that the fluxes are actua11y constant with height, but rather that the similarity within this layer considers the flux to be approximately constant with height. Above the surface layer, the mean quantities change very little with height, since the larger turbulent eddies act to mix boundary layer properties quite efficiently.
This overlying layer, called the mixed layer, is capped by an inversion which can extend 's of meters above the ABL. Similarity in the mixed layer and inversion are quite different from the surface layer and will not be dealt with here. The reader is referred to Stu11 for a review. Tbe stress tensor is defined as:. Assuming incompressibility and invoking tbe Boussinesq approximation Panofsky and Dutton, , one may now write:. Letting mecbanical equilibrium represent a reference state Lumley and Panofsky, , simplifies to:. In , we have assumed that the term representing mechanical-to-energy production can be neglected, and that there is no condensation or evaporation.
Equations for scalars which may involve source or sink terms may be written in analogy to as:. In , the first term on the r. Substitution into , , and yields the following:. Tbe first term on the r.
Tbe second term represents shear production. Tbe third term is the flux divergence of TKE, while the following term is the divergence of pressure flux. Tbe fifth term on the r. Equations for other higher order moments have been derived and reported elsewhere. Tbe reader is referred to Sorbjan for a complete treatment. Most equations in the previous two sections cannot readily be solved, due either to the presence of highly nonlinear terms or the requirement for enormous in-situ data bases.
For practical reasons, insight is needed concerning the higher order terms, with the goal to produce a closed set of equations which can be easily solved. Tbe surface layer has been best described by the similarity theory proposed by Monin and Obukhov , hereinafter referred to as MOS theory. It is furthermore assumed that the surface layer is a constant flux layer. In the original MOS theory, density variations are attributed only to temperature, with no influence of humidity.
We discuss the corrections to MOS, which take humidity into account, in section 2. With the use of Buckingham's TI theorem Buckingham , combinations involving N variables and n fundamental units leads to N-n independent dimensionless groups TI's. Inspection of these parameters shows that there are three fundamental units length, time, and temperature. We may therefore expect independent dimensionless TI's. Following Shaw , the two dimensionless groups are:. Tbe von Karman constant has been introduced in and for convenience in order to adjust the height z to the turbulent mixing length.
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Tbrough years of debate, k now has a well-accepted value of 0. Rewriting in its flux form, and combining with , it is easy to see that the momentum flux may now be written as:. While analogous to the molecular viscosity of non-turbulent flows, the eddy viscosity in becomes a dynamic property of the atmospheric flow field. The Obukhov length was originally defined such that density variations were due alone to temperature fluxes. Over the ocean, the heat flux depends on both the temperature and water vapor see e. Geernaert, Larsen To account for this, the Obukhov length must be defined in terms of the virtual temperature, T which is y'.
Over tbe open ocean, tbe stratifications are typically near neutral for windspeeds above 5 mlsec. However, in coastal regions, strong non-neutral conditions can occur during offsbore flow. In eitber case, tbe stability functions in , and 2- 30 , must be weIl specified. To-date, tbe stability functions for gases bave not yet been determined.
To overcome this, it is common practice to assume tbat for all gases, tbe stability function for beat may be applied. Tbe validity of tbis assumption still needs to be verified. See Geemaert or Kraus and Businger for a summary of their functional forms for use over the ocean during moderately unstable through stably stratified conditions. Dry fluxes in contrast to wet deposition between the atmosphere and ocean depend on a wide set of processes: turbulent transport in the adjacent boundary layers associated with shear in the local sense, and gustiness in the larger sense ; surface wave slope and pressure flux; wave breaking events; chemical reactions involving surfactants; laminar sublayer diffusion; sea spray scavenging and reactions with water immediately over waves; and biological interactions at or near the interface.
Characterizing the fluxes in terms of parameterizations would require a fuH understanding of these processes. Such an understanding, unfortunately, has been difficult to achieve, in most part since the nonlinearities are highly complex and sampling has been difficult to carry out near the ocean surface. It has therefore been practical to simplify the problem of estimating fluxes by focussing on the processes which are expected to dominate.
For momentum, heat, and moisture, turbulent transport in the atmospheric boundary layer has been considered to be the overwhelmingly dominant process to parameterize, given that one can assume that in the lowest part of the surface layer one can invoke the constant flux layer assumption. By considering turbulent transport alone, missing information on the remaining processes provides the uncertainty in the flux estimates. One can tackle the problem of parameterizing the turbulent processes by extending Monin-Obukhov similarity theory.
The quantities Co, CH' and CE' are respectively the drag coefficient, Stanton number, and Dalton number, which in turn are defined to be:. In - , the flux coefficients are functions of three independent parameters, Le. Such an approach is practical, as varying stratifications or roughness over the ocean would only become corrections to the reference values.
The neutral coefficients for momentum, heat, and water vapor have been investigated in a number of field campaigns during the past five decades. In most part, the early measurements were obtained by the "profile" method, and subsequent studies have employed more direct methods, Le.
These methods and the assumptions behind them will be described herein. Other methods have been used which will not be summarized here, e. This method is based on rewriting the logarithmic profiles eq. Plots associated with neutral stratifications yield a measure of the roughness lengths. The application of this method requires a guarantee that the profile truly is logarithmic and that the surface wave motions do not introduce deviations in the logarithmic wind profile. In addition, because the bulk parameters reach statistical averages quickly, averaging times may be short, e.
For momentum, must be treated in its vector form and account for both the downwind and crosswind velocity components:. According to Wyngaard , recommended averaging times exceed one hour for low windspeeds but may be reduced to rninutes at windspeeds over 20 mlsec. In the case of trace gas exchange, equation must involve corrections, if the gases are sampled in terms of rnixing ratio. Webb et al. It follows that zero vertical mass flux must correspond to a net upward vertical velocity.
Wyngaard simplified Webb's results and derived the following expression applicable only to trace gas fluxes measured in terms of rnixing ratios:. The air density is Pa' and Pe is the rnixing ratio of the trace gas of interest. For regions such as the tropics where water vapor and heat fluxes can be substantial, the Webb corrections in can be quite large. Fairall, Larsen Recalling eq. The tenn R is generally small unless there are unusual pressure gradients associated with mesoscale circulations or surface waves Geernaert et al.
The dissipation method is applied with the same constraints of homogeneity and stationarity as for the eddy correlation method, where R can generally be ignored, resulting in:. The dissipation rate may be detennined by measuring the turbulence spectrum within the inertial subrange eq. The bulk exchange coefficients have been measured in the field using the three techniques described above as weIl as other indirect methods. The reader is referred to Table as an illustration of some of the studies during recent years.
When exarnining the drag coefficients compiled from different regional experiments, the large differences of their mean values for neutral conditions has suggested that the surface wave field is a secondary controlling factor in the drag coefficient's magnitude. Larger drag coefficients have appeared to be associated with lower wave age, which in turn is associated with either short fetch andlor shallow water waves Iones, Toba This trend in drag coefficients appears to be for conditions when no swell are present.
On the other hand, when swell are present, the dependence of the drag coefficient on wave age loses it statistical reliability. Tbe drag coefficient is nonnally reported in tenns of a windspeed dependence, mainly for practical application. However, the inconsistency of units between Co and windspeed has inspired many experimentalists to explore nondimensional relationships between zo and wave state, in order to explain why CD increases with windspeed.
On the other hand, the statistical scatter in measurements of the Stanton and Dalton numbers has, in general, prevented any significant dependence on windspeed or any other parameter to be determined. We will touch this issue in the next section. Modellers during the past decade have placed requirements on the air-sea flux cornmunity to produce much better parameterizations of the flux coefficients, which involve less scatter and uncertainty than is presently reported. Tbis implies that atmospheric turbulence alone is insufficient in explaining the air-sea exchange rates within the desired accuracy requirements andlor that the reference flux coefficients need to be defined with a nonnalized roughness scale, e.
It is weIl recognized that the flux coefficients involve specification of a roughness length for momentum, heat, andlor gas. While these roughness lengths were defined based on the need to integrate , , and , it has been widely assumed that one can relate the z. Tbis assumption is intuitively reasonable, insofar that the magnitudes of the roughness lengths are on the order of 0. Due to the complexity of modelling wave-turbulence interactions in the sublayer, statistical models which relate tbe rougbness to various sets of wave and surface parameters bave been developed.
However, since wave state also depends on windspeed, using wave state as a proxy for windspeed via the roughness length was desired. Charnock was among the earliest to establish a relationship to demonstrate the anticipated increase of CD with windspeed. In subsequent decades, a wide range of a's has been reported, with values ranging from.
The scatter in the Chamock coefficient reported by experimentalists inspired researchers to explore the use of specific scaling parameters of the wave spectrum, and use of such scales to parameterize the Charnock coefficient.
Air-Sea Exchange of Gases and Particles - P S Liss, W G N Slinn - Häftad () | Bokus
Building on the early theories which relate wave drag to the slope of roughness elements, Hsu suggested that one could write. Following the approach of using wave scales, other approaches emerged. Using arguments that wave growth is related to wave age and in an attempt to account for surface motions induced by wave orbital velocities, a hypothesis emerged that the Charnock coefficient should be related to wave age. This hypothesis was also based on statistical evidence that young seas were associated with higher drag coefficients than older seas Geemaert et al.
The following formulation emerged:. These constants have been measured by many experimentalists, e. In the formulations represented by or , the data used to determine the magnitudes of the respective coefficients contained little or no swell.
Data sets which contained large swell corresponded to much larger scatter in z" and CD' thus making it nearly impossible to derive statistically significant formulations based on wave state see e. Yelland, Taylor Considering the case of "no swell", one can now extend the earlier approach of defining a normalized drag coefficient which incIudes a reference roughness. Recalling that the neutral drag coefficient already contains a reference height and stability, we introduce here a reference roughness length. Using to illustrate the additional reference state, we now have:.
The reader is reminded that is based on the assumption that swell are NOT present. Combining with , one obtains. There are other models of the roughness length which incorporate different variations based on wave state e. However, due to the complications introduced by swell interaction with the local wave spectrum, there is no real consensus on a simple form. There is no doubt that further research in fluid dynamics will be needed to assess the dynarnical interaction between turbulence and waves in reaching closure.
In addition to the effects of surface waves and outer layer influences via gustiness on the drag coefficient, the assumption in MOS theory that the surface stress is in the same direction as the surface layer wind is not always valid. Evidence during a number of field campaigns e. Geemaert ; Geemaert et al. The relationship to wave direction has been the easiest to tackle from a conceptual point of view e. On the other hand, the outer layer influences caused by horizontal pressure gradients Zemba, Friehe and thermal advection Geemaert have lacked supporting observations and the reasons for the departures of stress directions from wind directions remain at the hypothesis stage.
There is no closure on this issue. The low windspeed regime has required that one also incorporates gustiness as an additional process in producing air-sea momentum exchange. This lower limit is more relevant to unstable stratitications Godfrey, Beljaars ; Grachev et al. Given this, the current approach is to incorporate a gustiness factor, G, in the bulk aerodynamic relation for momentum, e. In general, very little systematic dependence on windspeed or wave state has been detected with any statistical significance in most data bases. The only exception to this is the analysis of RASEX data by Mahrt, et al , where a slight increase of CH was observed with windpeed, and CH was observed to decrease with increasing wave age.
This is a similar trend as has been observed for the drag coefficient. Heat exchange coefficients have also been modelIed using two approaches: surface renewal theory; and thermodynamics involving temperature, humidity, and sea spray. Only the first approach will be described here.