Large-eddy simulation of Langmuir circulation in shallow water

1. Large-eddy simulation of Langmuir circulation in shallow water Andrés Tejada-Martínez and Chester Grosch Center for Coastal Physical Oceanography Old Dominion University Norfolk, Virginia American Physical Society/Division of Fluid Dynamics 22 November, 2005

2. Observed structure of Langmuir circulations (LC) Courtesy of J. Smith, Scripps Traditionally observed in surface mixed layer of deep ocean Recently observed in shallow water in southern coast of New Jersey (Gargett et al., Science, 2004).

3. Spatially filtered Craik-Leibovich equations Craik-Leibovich vortex forcing • Continuity: • Momentum: SGS stress Generalized pressure, J. C. McWilliams, et al., JFM, 1997

4. Problem domain and boundary conditions Wind stress Impermeable rigid lid No-slip bottom Observed Langmuir cell size: 3H-6H • Surface stress is applied such that with In observations Re=O(50,000-100,000) • Periodic boundary conditions are set in horizontal directions • Parameters in simulation with LC are representative of observations: intermediate depth waves

5. Instantaneous downwind velocity fluctuation With Langmuir forcing Langmuir streak No Langmuir forcing Couette streaks

6. Mean fluctuations: With Langmuir forcing (Langmuir cell) No Langmuir forcing (Couette cells)

7. Mean downwind velocity Flow with LC in a downwell in an upwell Flow without LC

8. Reynolds stresses: Flow with LC Flow without LC

9. Depth trajectories of Lumley invariants Flow with LC Flow without LC bottom middle top Observations

10. Effect of wavelength on turbulence structure Flow with LC, λ=4H/3 Flow with LC, λ=6H Flow without LC Flow with LC, λ=4H/3 bottom middle top

11. Summary and Conclusions -Near bottom intensification of positive downwind velocity fluctuations. • Large-scale Langmuir turbulence features were reproduced in LES • Turbulent structure near bottom also agrees well with observations • Future plans -Surface intensification of crosswind velocity fluctuations -Downwelling limbs narrower than upwelling limbs -Structure of Langmuir turbulence very different from shear turbulence -Near bottom structure of Langmuir turbulence affected by surface waves (long or short) -Only C-L mechanism with intermediate waves reproduced near bottom structure -Effects of rotation,stratification,andcurrents other than wind-driven -Interaction with internal waves and convection -Parameterizations of Langmuir turbulence for large-scale models

12. Thank you! Questions? Negatively buoyant algae aligned in rows by Langmuir circulations off the coast of the Bahamas (courtesy of D. Zimmerman, ODU)

13. Mean fluctuations: Re = 180 Re = 395

14. Observations of LC off the New Jersey coast Gargett et.al. Science, 2004

15. Turbulent kinetic energy Flow with LC Flow without LC

16. Summary of observations in shallow water • Near-bottom intensification of pos. downwind (x1) velocity fluctuations • Surface intensification of crosswind (x2) velocity fluctuations • Regions of downwelling and positive x1-velocity fluctuations coincide • Magnitude of vertical fluctuations in downwelling region greater than in upwelling region • Ratio between crosswind lengths of upwells and downwells: • Surface waves characteristics: R = (crosswind length of upwell) / (crosswind length of downwell) = 1.1 – 1.3 λ = 6H = 6x15m = 90m (intermediate depth waves) Wave Height = 1.2m

17. Negatively buoyant algae aligned in rows by Langmuir circulations off the coast of the Bahamas (courtesy of D. Zimmerman, ODU)