Surface Gravity Waves And Coupled Marine Boundary Layers

Transcription

1 Surace Gravity Waves And Coupled Marine Boundary Layers Peter P.Sullivan National Center or Atmospheric Research Boulder, CO Phone:(303) ax:(303) James C. McWilliams Department o Atmospheric Sciences and Institute o Geophysics and Planetary Physics, UCLA Los Angeles, CA Phone:(310) ax:(310) jcm@atmos.ucla.edu Chin-Hoh Moeng National Center or Atmospheric Research Boulder, CO Phone:(303) ax:(303) moeng@ncar.ucar.edu Award #: N C tech/ocean/ino/dri00/cblast00.htm LONG-TERM GOALS The long term objective o our research is to advance the understanding o air-sea interaction and the coupling between the atmospheric and oceanic boundary layers (the ABL and OBL) mediated by the surace gravity wave ield, in order ultimately to develop better parameterizations o the boundary layers and surace luxes or coupled, large-scale numerical models. Turbulenceresolving, large-eddy and direct numerical simulations (LES and DNS) are the main tools to be used to investigate interactions among the ABL, OBL, and the air-sea interace. Using numerically generated databases, we intend to investigate: (1) vertical heat and momentum luxes carried by wave-correlated winds and currents; (2) enhanced small-scale, turbulent energy, mixing, and dissipation due both to enhanced wave-correlated wind and current shears and to wave breaking; and (3) wave-averaged inluences due to mean Lagrangian currents (Stokes drit) that give rise to coherent Langmuir circulations in the ocean. These mechanisms will be considered or a variety o surace wave states. Finally, we intend to make an eort to connect our simulation results with the proposed Coupled Boundary Layers Air-Sea Transer (CBLAST) ield campaigns. OBJECTIVES Our recent research eorts have ocused on the interaction between an imposed surace gravity wave and stratiied turbulence in the ABL. O particular importance is the dependence o the orm stress (drag) on stratiication over a range o wave age c/u, where c is the wave phase speed and u is the riction velocity. APPROACH We are investigating interactions among the ABL, OBL, and the connecting air-sea interace using both LES and DNS. The premise behind this approach is that the undamental processes that lead to air-sea coupling will maniest themselves in three-dimensional, time-dependent simulations. Hence, the creation o suicient numerical databases will allow or the interpretation o air-sea

2 Report Documentation Page Form Approved OMB No Public reporting burden or the collection o inormation is estimated to average 1 hour per response, including the time or reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection o inormation. Send comments regarding this burden estimate or any other aspect o this collection o inormation, including suggestions or reducing this burden, to Washington Headquarters Services, Directorate or Inormation Operations and Reports, 1215 Jeerson Davis Highway, Suite 1204, Arlington VA Respondents should be aware that notwithstanding any other provision o law, no person shall be subject to a penalty or ailing to comply with a collection o inormation i it does not display a currently valid OMB control number. 1. REPORT DATE SEP REPORT TYPE 3. DATES COVERED to TITLE AND SUBTITLE Surace Gravity Waves And Coupled Marine Boundary Layers 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) National Center or Atmospheric Research,,Boulder,CO, PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR S ACRONYM(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved or public release; distribution unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT 11. SPONSOR/MONITOR S REPORT NUMBER(S) 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT a. REPORT unclassiied b. ABSTRACT unclassiied c. THIS PAGE unclassiied Same as Report (SAR) 18. NUMBER OF PAGES 7 19a. NAME OF RESPONSIBLE PERSON Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18

3 interaction. The LES code adopted or our work evolves rom the eorts o Moeng (1984), Sullivan et al.(1994), Sullivan et al.(1996), and McWilliams et al.(1997). The spatial discretization in our LES is pseudospectral in horizontal directions and inite dierence in the vertical, with third order Runge-Kutta time stepping. A novel nesting procedure allows or ine nested meshes to be embedded within an outer coarse grid. A recently developed DNS code that accommodates a temporally and spatially varying lower boundary (Sullivan et al.2000) is also being extensively used. DNS has served a dual role in our research; it provides a clean ramework or testing LES developments and the DNS results have provided insight into low over moving surace gravity waves. WORK COMPLETED Several tasks relevant to the current project were completed and or initiated during the past iscal year. To date we have concentrated our eort on examining the coupling mechanisms among surace gravity wave ields and stratiied atmospheric turbulence, developing a ramework or posing LES o the ABL and OBL with wave eects, enhancing a large scale ocean parameterization, and developing eicient computer codes. Highlights rom the irst three eorts are described urther in the next section. The development o eicient computer codes is one o the technical aspects that must be addressed in order or our research to be successul. In anticipation o the large numbers o gridpoints required or our simulations, we undertook a code conversion project to move our existing lat LES code (i.e., the LES code with no surace geometry) rom a shared memory (Cray vector supercomputer) environment to a distributed memory massively parallel (e.g., IBM SP3 supercomputer) environment. We have rewritten our simulation codes to use both the Message Passing Interace (MPI) and OpenMP programming libraries. Initial tests o the new codes indicate that they scale well, i.e., the wall clock time decreases linearly as the number o MPI processes increases. To date, we have eiciently used as many as 100 processes on the IBM SP3 or problems with gridpoints. RESULTS In the past year, we published an archival manuscript (Sullivan et al.2000) and two meeting papers ( Sullivan et al.1999; Sullivan & McWilliams 2000) describing the technical developments and analysis o DNS o stratiied turbulent low over a series o moving waves as depicted in Figure 1. The low considered is a three-dimensional, turbulent, Couette low over a series o heated (or cooled) two-dimensional, monochromatic, deep-water gravity waves with orbital velocities given by irst-order wave theory. The external orcing o the low occurs through a constant velocity U o and a thermal gradient θ = θ L θ u. Both unstable θ L > θ u (hot waves) and stable θ L < θ u (cold waves) stratiication are considered. Despite the relative simplicity o this model low, the presence o a moving wavy lower boundary is suiciently complicating that a new numerical method had to be developed to simulate turbulent low in this geometry. The new algorithm is a mixed pseudospectral inite-dierence scheme that utilizes a surace itted grid, a conormal mapping between physical and computational space, and a co-located grid architecture or all variables. Our new DNS code was used to model stratiied turbulent low over a monochromatic water wave with varying waveslope ak and wave age c/u at a bulk Reynolds number Re = U o h/ν = 8000 with Rayleigh number Ra = gβ θh 3 /να = [6, 2, 0, 2]10 6, and Prandtl number P r = ν/α = 1. In this initial investigation, DNS as opposed to LES was used because o the absence o a complicating SGS model that includes wave eects and the simplicity o the surace boundary conditions. Results rom these DNSs show that the level o stratiication inluences the lowields above moving water waves. The magnitude o the surace orm stress can vary by as much as a actor o 3 depending on the level o stratiication and the wave age. We ound a good collapse o the surace drag

4 θ u Lx U o a θ L h z y λ Ly x Figure 1: Sketch o 3D stratiied Couette low driven by velocity U o over a moving wavy boundary o wavelength λ (wavenumber k = 2π/λ), phase speed c, amplitude a, and waveslope ak = a2π/λ in a domain o size (L x, L y, h) = (6, 5, 1)λ (see Sullivan et al.2000). The Boussinesq luid has temperature, density, viscosity, and thermal conductivity (θ, ρ, ν, α), respectively. Surace temperatures o the wave and upper boundary are θ L and θ u, and the riction velocity u is based on the constant stress τ = ρu 2. Here the coeicient o thermal expansion β = 1/θ o where θ o is a reerence temperature. variation, over a wide range o stratiication (unstable, neutral, stable), using the riction velocity u to normalize the drag and wave age (see igure 3). A good correlation between the position o the critical layer (see Figure 2) and the drag level was observed; as z cr D p. In McWilliams & Sullivan (2000a) an overview o the eect o surace waves on winds and currents in marine boundary layers is presented. This work also develops a ramework or posing ABL and OBL LES problems with wavy boundaries which will be evaluated as part o our uture research. In the ABL, two workable avenues can be considered: an equilibrium situation where the input to LES is the empirically determined relationship between C D and wind speed U 10 or various wave ages, or the alternative is to modiy the conventional LES drag law or wave eects. The ormer approach has the advantage that direct measurements o the total surace drag enter into LES, but the method is not easily generalized to include wind-wave disequilibrium, stratiication, and other eects since the available measurement database does not span a broad range o low conditions. The second approach is the method most oten used in second-order closure modeling in low over stationary hills and uses a drag-law imposed at the wavy surace or the unresolved surace roughness. In the OBL, the coupling between waves and turbulent motions is stronger than in the atmosphere because o wave breaking and the ormation o Langmuir circulations. Plunging breakers are carried into the interior o the OBL and their inertia also disturbs the near-surace currents over a much larger distance. An option or OBL LES is then to use the Craik-Leibovich wave-averaged dynamical equations but with a modiied SGS turbulent kinetic energy (TKE) model to incorporate non-conservative wave-breaking inluences. An important goal o CBLAST research is to distill rom the large body o physical evidence relatively simple parameterization schemes that can then be used in large scale models. In a recent work, McWilliams & Sullivan (2000b) analyzed LES cases with surace-wave-averaged dynamical equations. These results show that the eect o Langmuir circulations is to make the vertical mixing substantially more eicient or both material properties and momentum. We also provide a new conirmation that our previously proposed K-Proile Parameterization (KPP) model (Large et al.1995) accurately characterizes the turbulent transport in a weakly convective, wind-driven

5 D p /u * Ra = 6 x 10 6 Ra = 2 x 10 6 Ra = 0 Ra = -2 x Figure 2: Phase averaged streamlines over stationary and moving waves with ak = 0.1, Ra = 0 in surace itted coordinates: upper, c/u = 0; upper middle, c/u = 3.9; lower middle, c/u = 7.8; lower, c/u = The dotted line corresponds to the height o the critical layer z cr where u + u w = 0. Here u and u w are the mean and phase averaged components o the horizontal velocity (see Sullivan et al.2000). Figure 3: Surace orm stress, normalized by u 2, or several values o wave age c/u with varying Ra or unstable, neutral, and stable stratiication (Sullivan & McWilliams 2000). The nondimensionalization is such that the stratiication is unstable or Ra > 0 and stable or Ra < 0. boundary layer with stable interior stratiication. McWilliams & Sullivan (2000b) generalized KPP or the regime o weakly convective Langmuir turbulence by modiying two o its rules: (1) an increasing value or the turbulent velocity scale, or decreasing Langmuir number La and (2) a decreasing value o the non-gradient lux coeicient. These modiications make the KPP turbulent lux proiles match reasonably well those in the LES case with Langmuir circulations present, especially so or material properties, and even more especially so or density and scalars with sources at the surace. IMPACT/APPLICATIONS These results conirm that turbulence resolving simulations can provide insight about the complex low near the air-sea interace. The newly developed simulations codes that include a time dependent moving lower boundary provide low details very near the air-water interace that are diicult to achieve with measurements and thus provide additional insight into air-sea coupling mechanisms. TRANSITIONS & RELATED PROJECTS

6 These numerical results can potentially be used to help guide and interpret uture low-wind CBLAST ield campaigns, where stratiication is expected to be important. The Geophysical Turbulence Program at NCAR hosted a workshop or approximately 50 researchers and students on Turbulence and the Air-Sea Interace rom August, A link to the meeting abstracts can be ound by browsing the web page at REFERENCES Large, W.G., J.C. McWilliams, & S.C. Doney, 1995: Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization. Rev. Geophys. 32, McWilliams, J.C. & P.P. Sullivan, 2000a: Surace-wave eects on marine boundary layers. In: The Fluid Dynamics o the Environment: A Symposium Honoring Sidney Leibovich, J. Lumley, ed., Springer-Verlag, in press. McWilliams, J.C. & P.P. Sullivan, 2000b: Vertical mixing by Langmuir circulations. Spill Science and Technology, in press. McWilliams, J.C., P.P. Sullivan, & C-H. Moeng, 1997: Langmuir turbulence in the ocean. J. Fluid Mechanics, 334, Moeng, C.-H., 1984: A large-eddy-simulation model or the study o planetary boundary-layer turbulence. J. Atmos. Sci., 41, Sullivan, P.P., J.C. McWilliams, & C.-H. Moeng, 1994: A subgrid-scale model or large-eddy simulation o planetary boundary-layer lows. Boundary-Layer Meteorology, 71, Sullivan, P.P., J.C. McWilliams, & C.-H. Moeng, 1996: A grid nesting method or large-eddy simulation o planetary boundary-layer lows. Boundary-Layer Meteorology, 80, Sullivan, P.P. & J.C. McWilliams, 2000: Simulations o stratiied turbulent low over moving waves. Preprints 14th Symposium on Boundary Layer and Turbulence, Aspen, CO., Sullivan, P.P., J.C. McWilliams, & C-H. Moeng, 2000: Simulation o turbulent low over idealized water waves. Journal o Fluid Mechanics, 404, Sullivan, P.P., J.C. McWilliams, & C-H. Moeng, 1999: Direct numerical simulations o turbulent low over moving sinusoidal boundaries. Preprints, International symposium on turbulence and shear low phenomena. Santa Barbara, CA. PUBLICATIONS Dubrulle, B., J-P. Laval, & P.P. Sullivan, 1999: A new dynamical subgrid model or the planetary surace layer. I. Analytical results. Journal o the Atmospheric Sciences, submitted. Davis, K.J, N. Gamage, C.R. Hagelberg, C. Kiemle, D.H. Lenschow, & P.P. Sullivan, 2000: An objective method or deriving atmospheric structure rom airborne lidar observations. Journal o Oceanic and Atmospheric Technology, in press.

7 McWilliams, J.C., C-H. Moeng, & P.P. Sullivan, 1999: Turbulent luxes and coherent structures in marine boundary layers: Investigations by large-eddy simulation. In: Air-Sea Exchange: Physics, Chemistry, Dynamics, and Statistics, G. Geernaert, ed. Kluwer Publishers. Sullivan, P.P., E.G. Patton, & C.-H. Moeng, 2000: Large-eddy simulation o a coupled pbl/land surace system. Preprints 14th Symposium on Boundary Layer and Turbulence, Aspen, CO., Patton, E.G., P.P. Sullivan, & K.J. Davis, 2000: On the inluence o a orest canopy on top-down and bottom-up diusion in the planetary boundary layer. Preprints 14th Symposium on Boundary Layer and Turbulence, Aspen, CO., Weil, J.C., P.P. Sullivan, & C.-H. Moeng, 2000: Lagrangian modeling o mean and luctuating concentrations rom sources in the convective boundary layer. Preprints 14th Symposium on Boundary Layer and Turbulence, Aspen, CO. Muschinski, A., P.P. Sullivan, & V.I.Tatarskii, 2000: Using Large-Eddy Simulation (LES) to quantiy the systematic dierence between wind-proiler Doppler velocity and radial wind velocity, 5th Int. Symp. on Tropospheric Proiling, Adelaide, Australia. Weil, J.C., P.P. Sullivan, & C.-H. Moeng, 2000: Lagrangian modeling o dispersion in the convective boundary layer over a range o stability. Preprints 11th Joint Conerence on the Applications o Air Pollution Meteorology with the AWMA, Amer. Meteor. Soc., Boston,