1. The structure of turbulence in a shallow water wind-driven shear current with Langmuir circulation Andrés E. Tejada-Martínez and Chester E. Grosch Center for Coastal Physical Oceanography Department of Earth, Ocean and Atmospheric Sciences Old Dominion University Norfolk, Virginia

2. Observed structure of Langmuir cells Courtesy of J. Smith, UCSD

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

4. The filtered Navier-Stokes equations Continuity: Momentum: SGS stress Craik-Leibovich vortex forcing

5. Subgrid-scale (SGS) stress SGS stress: Smagorinsky model for the SGS stress: Eddy viscosity: is computed dynamically using the Germano identity (Germano et al., Phys. Fluids, 1991)

6. LES of Langmuir cells in wind-driven channel Surface stress is applied such that Craik-Leibovich vortex forcing is added to the filtered momentum equations (LES equations) to account for Langmuir cells (Lc) Two simulations were performed: 1) Langmuir forcing, 2) no Langmuir forcing no-slip wall Parameters in simulation with Lc are derived from wave and wind conditions during field observations of Lc:

7. LES of Langmuir cells (mean streamwise velocity) Enhanced mixing due to Langmuir circulation tends to homogenize mean streamwise velocity

8. LES of LC (instantaneous streamwise velocity fluctuation) No Langmuir forcing With Langmuir forcing

9. LES of Langmuir cells (streamwise-time averages) No Langmuir forcing spanwise vel. fluctuations wall-normal vel. fluctuations streamwise vel. fluctuations With Langmuir forcing

10. LES of Langmuir cells (Reynolds stress components) No Langmur forcing With Langmuir forcing

11. LES of Langmuir cells (Lumley’s triangle) No Langmuir forcingWith Langmuir forcing Presence of Langmuir cells greatly affects the state of the turbulence near the bottom and near the surface Trajectory of Lumley map for case with Langmuir forcing agrees well with observed data especially near the bottom See tomorrow’s talk at 9:40am: “Characteristics of Langmuir turbulence observed in shallow water,” Judith Wells and Ann Gargett

12. Turbulent kinetic energy budget terms (near bottom) No Langmuir forcing With Langmuir forcing

13. No Langmuir forcing With Langmuir forcing Turbulent kinetic energy budget terms (near surface)

14. Final Remarks First observations and simulations of Langmuir circulation covering entire water column Secondary flow structures of simulations characteristic of Langmuir circulation agree well with observations More recent work explores effects of: 1) Reynolds number 2) domain size 3) subgrid-scale parameterization 4) grid size 5) rotation 6) stratification Reynolds stresses of simulations agree well with observations in lower region of the water column

15. Domain length dependence Extended domain spanwise vel. fluctuations wall-normal vel. fluctuations streamwise vel. fluctuations Original domain

16. Reynolds number dependence Re = 180 Re = 395

17. SGS model (parameterization) dependence Dynamic Smagorinsky Dynamic mixed

18. Grid dependence 32x64x97 48x96x145