An asymptotically reduced model of turbulent Langmuir circulation

References

• Bhaskaran , R and Leibovich , S . 2002 . Eulerian and Lagrangian Langmuir circulation patterns . Phys. Fluids , 14 : 2557 – 2571 .
   Google Scholar
• Chini , GP . 2008 . Strongly nonlinear Langmuir circulation and Rayleigh–Bénard convection . J. Fluid Mech. , 614 : 39 – 65 .
   Web of Science ®Google Scholar
• Chini , GP and Leibovich , S . 2003 . Resonant Langmuir circulation–internal wave interaction. Part 1. Internal wave reflection . J. Fluid Mech. , 495 : 35 – 55 .
   Google Scholar
• Chini , GP and Leibovich , S . 2005 . Resonant Langmuir circulation–internal wave interaction. Part 2. Langmuir circulation instability . J. Fluid Mech. , 524 : 99 – 120 .
   Google Scholar
• Clever , RM and Busse , FH . 1974 . Transition to time-dependent convection . J. Fluid Mech. , 65 : 625 – 645 .
   Web of Science ®Google Scholar
• Cox , SM . 1997 . Onset of Langmuir circulation when shear flow and Stokes drift are not parallel . Fluid Dynamics Research , 19 : 149 – 167 .
   Google Scholar
• Cox , SM and Leibovich , S . 1993 . Langmuir circulations in a surface layer bounded by a strong thermocline . J. Phys. Oceanogr. , 23 : 1330 – 1345 .
   Web of Science ®Google Scholar
• Cox , SM and Leibovich , S . 1994 . Large-scale Langmuir circulation and double-diffusive convection: Evolution equations and flow transitions . J. Fluid Mech. , 276 : 189 – 210 .
   Google Scholar
• Cox , SM and Leibovich , S . 1997 . Large-scale three-dimensional Langmuir circulation . Phys. Fluids , 9 : 2851 – 2863 .
   Google Scholar
• Cox , SM , Leibovich , S , Moroz , I and Tandon , A . 1992a . Hopf bifurcations in Langmuir circulations . Physica D , 59 : 226 – 254 .
   Google Scholar
• Cox , SM , Leibovich , S , Moroz , I and Tandon , A . 1992b . Nonlinear dynamics in Langmuir circulations with O(2) symmetry . J. Fluid Mech. , 241 : 669 – 704 .
   Web of Science ®Google Scholar
• Craik , ADD . 1977 . The generation of Langmuir circulations by an instability mechanism . J. Fluid Mech. , 81 : 209 – 223 .
   Web of Science ®Google Scholar
• Craik , ADD and Leibovich , S . 1976 . A rational model for Langmuir circulations . J. Fluid Mech. , 73 : 401 – 426 .
   Web of Science ®Google Scholar
• Gnanadesikan , A and Weller , R . 1995 . Structure and instability of the Ekman spiral in the presence of surface gravity waves . J. Phys. Oceanogr. , 25 : 3148 – 3171 .
   Web of Science ®Google Scholar
• Herbert , T . 1983 . Secondary instability of plane channel flow to subharmonic three-dimensional disturbances . Phys. Fluids , 26 : 871 – 874 .
   Web of Science ®Google Scholar
• Herbert , T . 1988 . Secondary instability of boundary layers . Ann. Rev. Fluid Mech. , 20 : 487 – 526 .
   Web of Science ®Google Scholar
• Hou , TY , Yang , DP and Ran , H . 2005 . Multiscale analysis in the Lagrangian formulation for the 2D incompressible Euler equation . Discr. Continuous Dyn. Sys. , 13 : 1153 – 1186 .
   Google Scholar
• Hou , TY , Yang , DP and Ran , H . 2007 . Multiscale analysis and computation for the 3D incompressible Navier–Stokes equations . SIAM Multiscale Model. Simulation , 6 : 1317 – 1346 .
   Google Scholar
• Hou , TY , Yang , DP and Wang , K . 2004 . Homogenization of the incompressible Euler equation . J. Comp. Math. , 22 : 220 – 229 .
   Google Scholar
• Julien , K , Knobloch , E , Milliff , R and Werne , J . 2006 . Generalized quasi-geostrophy for spatially anisotropic rotationally constrained flows . J. Fluid Mech. , 555 : 233 – 274 .
   Web of Science ®Google Scholar
• Julien , K , Knobloch , E and Werne , J . 1998 . A new class of equations for rotationally-constrained flows . Theoret. Comput. Fluid Dynamics , 11 : 251 – 261 .
   Web of Science ®Google Scholar
• Kelly , RE . 1967 . On the stability of an inviscid shear layer which is periodic in space and time . J. Fluid Mech. , 27 : 657 – 689 .
   Web of Science ®Google Scholar
• Leibovich , S . 1977 . On the evolution of the system of wind drift currents and Langmuir circulations in the ocean. Part 1. Theory and averaged current . J. Fluid Mech. , 79 : 715 – 743 .
   Web of Science ®Google Scholar
• Leibovich , S . 1983 . The form and dynamics of Langmuir circulations . Ann. Rev. Fluid Mech. , 15 : 391 – 427 .
   Web of Science ®Google Scholar
• Leibovich , S . 1985 . Oscillatory and competing instabilities in a nonlinear model for Langmuir circulations . Phys. Fluids , 28 : 2050 – 2061 .
   Google Scholar
• Leibovich , S , Lele , SK and Moroz , I . 1989 . Nonlinear dynamics in Langmuir circulations and in thermosolutal convection . J. Fluid Mech. , 198 : 471 – 511 .
   Web of Science ®Google Scholar
• Leibovich , S and Tandon , A . 1993 . Three-dimensional Langmuir circulation instability in a stratified layer . J. Geophys. Res. , 98 : 16501 – 16507 .
   Web of Science ®Google Scholar
• Li , M and Garrett , C . 1993 . Cell merging and the jet/downwelling ratio in Langmuir circulation . J. Mar. Res. , 51 : 737 – 769 .
   Web of Science ®Google Scholar
• Li , M and Garrett , C . 1997 . Mixed layer deepening due to Langmuir circulation . J. Phys. Oceanogr. , 27 : 121 – 132 .
   Google Scholar
• Li , M , Garrett , C and Skyllingstad , E . 2005 . A regime diagram for classifying turbulent large eddies in the upper ocean . Deep-Sea Res. I , 52 : 259 – 278 .
   Google Scholar
• Marmorino , GO , Smith , GB and Lindemann , GJ . 2005 . Infrared imagery of large-aspect-ratio Langmuir circulation . Continental Shelf Research , 25 : 1 – 6 .
   Web of Science ®Google Scholar
• McWilliams , JC and Sullivan , PP . 2000 . Vertical mixing by Langmuir circulations . Spill Sci. Tech. Bull. , 6 : 225 – 237 .
   Google Scholar
• McWilliams , JC , Sullivan , PP and Moeng , C . 1997 . Langmuir turbulence in the ocean . J. Fluid Mech. , 334 : 1 – 30 .
   Web of Science ®Google Scholar
• Orszag , SA and Patera , AT . 1983 . Secondary instability of wall-bounded shear flows . J. Fluid Mech. , 128 : 347 – 385 .
   Web of Science ®Google Scholar
• Poje , AC and Lumley , JL . 1995 . A model for large-scale structures in turbulent shear flows . J. Fluid Mech. , 285 : 349 – 369 .
   Google Scholar
• Skyllingstad , ED and Denbo , DW . 1995 . An ocean large-eddy simulation of Langmuir circulations and convection in the surface mixed layer . J. Geophys. Res. , 100 : 8501 – 8522 .
   Web of Science ®Google Scholar
• Sprague , M , Julien , K , Knobloch , E and Werne , J . 2006 . Numerical simulation of an asymptotically reduced system for rotationally constrained convection . J. Fluid Mech. , 551 : 141 – 174 .
   Web of Science ®Google Scholar
• Szeri , A . 1996 . Langmuir circulations in Rodeo Lagoon . Mon. Weather Rev. , 124 : 341 – 342 .
   Web of Science ®Google Scholar
• Tandon , A and Leibovich , S . 1995a . Secondary instabilities in Langmuir circulations . J. Phys. Oceanogr. , 25 : 1206 – 1217 .
   Google Scholar
• Tandon , A and Leibovich , S . 1995b . Simulations of three-dimensional Langmuir circulation in water of constant density . J. Geophys. Res. , 100 : 22,613 – 22,623 .
   Google Scholar
• Teixeira , MAC and Belcher , SE . 2002 . On the distortion of turbulence by a progressive surface wave . J. Fluid Mech. , 458 : 229 – 267 .
   Google Scholar
• Tejada-Martinez , AE and Grosch , CE . 2007 . Langmuir turbulence in shallow water. Part 2. Large-eddy simulation . J. Fluid Mech. , 576 : 63 – 108 .
   Google Scholar
• Thorpe , SA . 2004 . Langmuir circulation . Ann. Rev. Fluid Mech. , 36 : 55 – 79 .
   Web of Science ®Google Scholar
• Trefethen , LN . 2000 . Spectral Methods in Matlab , SIAM : Philadelphia .
   Google Scholar
• Waleffe , F . 1997 . On a self-sustaining process in shear flows . Phys. Fluids , 9 : 883 – 900 .
   Web of Science ®Google Scholar