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3A.2 IMPACTS OF BREAKING AND LANGMUIR CIRCULATIONS ON THE MIXED LAYER IN HIGH

1 2 3 Peter P. Sullivan ∗, James C. McWilliams , and W. Kendall Melville 1National Center for Atmospheric Research, Boulder, CO 2Department of Atmospheric and Oceanic Sciences, UCLA, Los Angeles, CA 3Scripps Institution of , University of , San Diego, La Jolla, CA

1. INTRODUCTION for the interaction between and resolved vor- ticity (us ζζζ) as first suggested by the Craik-Leibovich Breaking waves are the signature feature of the ocean asymptotic× analysis. These LES however still omit the surface layer in high conditions. Dynamically, intermittency of the surface stress associated with wave breaking is important since it is believed to be breaking. the primary path for stress transfer between a wind- We are interested in investigating the combined and in- generated wave field and the underlying oceanic currents teracting influences of Stokes drift and intermittent stress (Melville, 1996). Wave breaking is triggered in the open transmission, caused by wave breaking, on the mixed ocean by wave-wave, wave-, and wind-wave in- layer. Our modeling approach is of modest complex- teractions (Melville, 1996), but even in equilibrium con- ity compared to a full microphysical simulation of air ditions it is highly intermittent in space and time. For and and incorporates the following essential ele- example, Melville and Matusov (2002) find that the per- ments: (1) a Stokes drift profile, us(z), developed from centage of surface area that is actively entraining air in- the Pierson-Moskowitz equilibrium wave as creases with cubed, and for wind speeds less function of the U10 winds; and, (2) a stochastic model 1 than 15ms− is O(1%). It increases to about 8% for wind for breaking waves developed from laboratory (Melville 1 speeds of 20ms− . Wave breaking events occur over et al., 2002) and field measurements (Melville and Ma- a spectrum of ranging from centimeters or tusov, 2002). In our model, the wave breaking field is less to tens or hundreds of meters (plunging breakers in assumed to be a collection of horizontal impulses (i.e., high ; see review by Melville, 1996) with the asso- body ) A(x,t) that have similar 3D space and time ciated time scale of active breaking approximately pro- dependencies. Restricted to the x direction, portional to the period of the (Melville − and Matusov, 2002). Further, wave breaking co-exists c A = kb T (α)X (β)Y (δ)Z(γ), (1) and interacts with Langmuir circulations, which are gen- T erated by vortex forces associated with the wave Stokes where (T ,X ,Y ,Z) are space-time shape functions that drift. Hence, a model of ocean currents under high wind describe the evolution of a breaking event. All breakers conditions needs to consider the wave field. are assumed to be self similar and separable in dimen- sionless time and space coordinates α = (t to)/T,β = − 2. MODELING WAVE INFLUENCES (x xo)/c(t to),δ = 2(y yo)/λ and γ = z/χc(t to). − − − − (to,xo,yo,zo = 0) is the onset time and position of the Ocean mixed layer models that utilize ensemble aver- chosen breaker and (c,λ,T) are its phase speed, wave- aged closures ignore the wave field and drive length, and period. The wave characteristics (c,λ,T) are the underlying currents by a mean surface related to each other through the deep water linear dis- τττ which spatially and temporally filters out the events persion relation c2 = gλ/2π with T = λ/c. The constant h i (e.g., wind gusts and breaking waves) responsible for ac- 0 < χ < 1, which is just the aspect ratio of the depth to tual stress transfer from winds to waves to currents. The length of the breaker, controls the depth penetration of wave field is however critical to mixed layer dynamics the breaker forcing. and is included to a certain degree in most large- The breakers are randomly located at the surface of simulation (LES) models (e.g., Skyllingstad and Denbo the water, but their number at any time t is constrained 1995; McWilliams et al. 1997). LES models account to match the observed white cap coverage for a given U10. The phase speed c is drawn from an exponential ∗corresponding author address: Peter P. Sullivan, National Center for Atmospheric Research, P. O. Box 3000, Boulder, CO 80307-3000; distribution that matches observations and the breakers email: [email protected] are oriented at random angles π/2 < θ < π/2 about the − 0 0

z/h -0.25

z/h -0.25

-0.5 -0.5 0 10 20 0 10 0 2 4 2 2 2 2 2 2 0 10 20 30 /u* /u* /u*

/u* Figure 2: Vertical variance profiles normalized by u2 for Figure 1: Vertical current profiles normalized by u for the same cases as in figure 1. ∗ DNS driven by: constant stress ; 100% breaking∗ ; 4 5 constant stress plus Stokes forcing N; and 100% break- ing plus Stokes forcing H. h is the height of the compu- tational domain. where the mean current shear is near zero. Langmuir circulations are disrupted by breaking, but the combined influences of breaking and Stokes forcing leads to the highest amount of turbulent kinetic energy. Analysis of x axis. At present, observations are uncertain as to the the DNS profiles shows how the effective surface rough- − exact partitioning of the forcing between wind stress and ness zo increases with wind speed and scales with the breaking. We thus introduce the modeling constant kb breaker field. LES and comparison with hurri- so as to examine regimes spanning zero and full stress cane observations will be discussed. intermittency (i.e., 0 to 100% breaking). The final in- Acknowledgments: NCAR is sponsored by the Na- gredient of our stochastic model adds a work to tional Science Foundation. PPS and WKM are supported the parameterization for the subgrid-scale turbulent ki- by ONR (CBLAST) and NSF (). netic energy to account for fine scale breaker processes. Further details are provided in Sullivan et al. (2004). REFERENCES

McWilliams, J. C., P. P. Sullivan, and C.-H. Moeng, 3. SIMULATION RESULTS 1997: Langmuir turbulence in the ocean, J. Fluid Mech., 334, 1–30. The above modeling components have been evaluated in direct numerical simulations (DNSs) and are presently Melville, W. K., 1996: The role of wave breaking in air- being implemented in an ocean boundary layer LES interaction, Ann. Rev. Fluid Mech., 28, 279–321. code. The DNS are performed with 200 200 96 grid- points and utilize a monochromatic Stokes× profile× and Melville, W. K. and P. Matusov, 2002: Distribution of a single breaker phase speed. Various combinations of breaking waves at the ocean surface, Nature, 417, 58– upper surface forcing have been considered: results for 63. neutrally stratified flow driven by constant stress or 100% Melville, W. K., F. Veron, and C. J. White, 2002: The ve- breaking waves with and without Stokes forcing are pre- locity field under breaking waves: Coherent structures sented. We find that a small amount of active breaking, and turbulence, J. Fluid Mech., 454, 203–233. less than 2%, significantly alters the instantaneous flow as well as the ensemble statistics. The impor- Skyllingstad, E. D. and D. W. Denbo, 1995: An ocean tance of intermittent breaking and Stokes forcing to the large-eddy simulation of Langmuir circulations and near surface currents and velocity variances is illustrated convection in the surface mixed layer, J. Geophys. in figures 1 and 2. Model breakers are effective agents Res., 100, 8501–8522. in energizing the surface region of ocean mixed layers and can adequately drive ocean currents in the absence Sullivan, P. P., J. C. McWilliams, and W. K. Melville, of any other mechanism of momentum transfer from the 2004: The oceanic boundary layer driven by wave winds. The greatest mixing occurs with 100% break- breaking with stochastic variability. I: Direct numer- ing co-existing with Langmuir circulations: a situation ical simulations, J. Fluid Mech., in press.