A Model for the Simulation of Turbulent Boundary Layers in an Incompressible Stratified Flow

Journal of Computational Physics

Volumn 144, Issue 2, 1998, Pages 550-602

  Slinn, Donald N ^a   Riley, J J ^a  

^a University of Washington   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATMOSPHERIC THERMODYNAMICS; BOUNDARY LAYER FLOW; BOUNDARY LAYERS; POTENTIAL ENERGY; TURBULENCE; TURBULENT FLOW;

FOURTH-ORDER; INTERNAL WAVES; LARGE-EDDY SIMULATIONS; LARGE-SCALE FLOWS; MONOCHROMATIC WAVE; NUMERICAL FEATURES; PHYSICAL FEATURES; STRATIFIED FLOWS; STRATIFIED FLUID; TURBULENT BOUNDARY LAYERS;

LARGE EDDY SIMULATION;

EID: 0000198511     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1997.5983     Document Type: Article

References (60)

1. Adam Y. Highly accurate compact implicit methods and boundary conditions. J. Comput. Phys. 24:1977;10.
2. Anderson D. A., Tannehill J. C., Pletcher R. H. Computational Fluid Mechanics and Heat Transfer. 1984.
3. Bell J. B., Colella P., Glaz H. M. A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 85:1989;257.
4. Bender C. M., Orszag S. A. Advanced Mathematical Methods for Scientists and Engineers. 1978.
5. Cacchione D., Wunsch C. Experimental study of internal waves over a slope. J. Fluid Mech. 66:1974;223.
6. Canuto C., Hussaini M. Y., Quarteroni A., Zang T. A. Spectral Methods in Fluid Dynamics. 1988.
7. Chorin A. J. Numerical solution of the Navier-Stokes equations. Math. Comp. 22:1968;745.
8. Chorin A. J. Book review, computational methods for fluid flow. Bull. Amer. Math. Soc. 5:1984;87.
9. Davies H. C. A lateral boundary formulation for multi-level prediction models. Quart. J. R. Meteorol. Soc. 102:1976;405.
10. Davies H. C. Limitations of some common lateral boundary schemes used in regional NWP models. Monthly Weather Rev. 111:1983;1002.
11. Durran D. R., Klemp J. P. A compressible model for the simulation of moist mountain waves. Monthly Weather Rev. 111:1983;2341.
12. Durran D. R. Computational Fluid Dynamics for Atmospheric Modeling. 1992.
13. Durran D. R. The third-order Adams-Bashforth method: An attractive alternative to leapfrog time differencing. Monthly Weather Rev. 119:1991;702.
14. Durran D. R., Brown R., Slinn D. N., Yang M. J. Towards more accurate wave-permeable boundary conditions. Monthly Weather Rev. 121:1993;604.
15. Eriksen C. C. Internal wave reflection and mixing at Fieberling Guyot. J. Geophys. Res. Oceans. 1998.
16. Fletcher C. A. J. Computational Techniques for Fluid Dynamics. Vol. II. Specific Techniques for Different Flow Categories. 1991.
17. Fortin M., Peyret R., Temam R. Calcul des ecoulements d'un fluide visqueux incompressible. Lecture Notes in Physics. 8:1971;337.
18. Fovell R., Durran D., Holton J. R. Numerical simulations of convectively generated stratospheric gravity waves. J. Atmospheric Sci. 49:1992;1427.
19. Garrett C. The role of secondary circulation in boundary mixing. J. Geophys. Res. 95:1990;3181.
20. Garrett C. Marginal mixing theories. Atmosphere-Ocean. 29:1991a;313.
21. Garrett C. Dynamics of Oceanic Internal Gravity Waves. 1991b;433.
22. Gear C. W., Watanabe D. S. Stability and convergence of variable order multistep methods. SIAM J. Numer. Anal. 11:1974;1044.
23. Gear C. W. Numerical Initial Value Problems in Ordinary Differential Equations. 1971.
24. Gresho P. M. On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 1. Theory. Int. J. Numer. Methods Fluids. 11:1990;587.
25. Gresho P. M. Incompressible fluid dynamics: Some fundamental formulation issues. Ann. Rev. Fluid Mech. 23:1991;413.
26. Gresho P. M., Sani R. L. On pressure boundary conditions for the incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids. 7:1987;1111.
27. Hirsh R. S. Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique. J. Comput. Phys. 19:1975;90.
28. Ivey G. N., Nokes R. I. Vertical mixing due to the breaking of critical internal waves on sloping boundaries. J. Fluid Mech. 204:1989;479.
29. Karniadakis G. E., Israeli M., Orszag S. A. High-order splitting methods for the incompressible Navier-Stokes equation. J. Comput. Phys. 97:1991;414.
30. Kim J., Moin P. Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59:1985;308.
31. Klemp J. B., Lilly D. K. Numerical simulation of hydrostatic mountain waves. J. Atmospheric Sci. 35:1978;78.
32. Kreiss H. O. Math. Comp. 26:1972;605.
33. Lele S. K. Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103:1992;16.
34. Lesieur M. Turbulence in Fluids: Stochastic and Numerical Modelling. 1987.
35. Maxey M. R., Riley J. J. Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids. 26:1983;883.
36. Orszag S. A., Israeli M., Deville M. O. Boundary conditions for incompressible flows. J. Sci. Comput. 1:1986;75.
37. Peyret R., Taylor T. D. Computational Methods for Fluid Flow. 1983.
38. Phillips O. M. The Dynamics of the Upper Ocean. 1977.
39. Phillips, O. M. On flows induced by diffusion in a stably stratified fluid, Deep-Sea Res. 17, 435.
40. Pond S., Pickard G. L. Introductory Dynamical Oceanography. 1983.
41. Rai M. M., Moin P. Direct simulations of turbulent flow using finite-difference schemes. J. Comput. Phys. 96:1991;15.
42. Rai M. M., Moin P. Direct numerical simulation of transition and turbulence in a spatially evolving boundary layer. J. Comput. Phys. 109:1993;169.
43. Roberts J. Internal Gravity Waves in the Ocean. 1975.
44. Shih T. M., Tan C. H., Hwang B. C. Effects of grid staggering on numerical schemes. Int. J. Numer. Methods Fluids. 9:1989;193.
45. Slinn D. N. Numerical Simulation of Turbulent Mixing Caused by Internal Wave Reflection from Sloping Boundaries. 1995.
46. Slinn D. N., Riley J. J. Turbulent dynamics of a critically reflecting internal gravity wave. Theoret. Comput. Fluid Dynam. 1998a.
47. Slinn D. N., Riley J. J. Internal wave reflection from sloping boundaries. J. Fluid Mech. 1998b.
48. Slinn D. N., Riley J. J. Turbulent mixing in the oceanic boundary layer caused by internal wave reflection from sloping terrain. Dynam. Atmospheres Oceans. 24:1996;51.
49. Spalart P. R., Moser R. D., Rogers M. M. Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96:1991;297.
50. Squires K. D., Eaton J. K. Particle response and turbulence modification in isotropic turbulence. Phys. Fluids A. 2:1990;1191.
51. Taylor J. R. Turbulence and mixing in the boundary layer generated by shoaling internal waves. Dynam. Atmospheres Oceans. 19:1993;233.
52. Temam R. Arch. Rational Mech. Anal. 32:1969;377.
53. Temperton C. Self-sorting mixed-radix fast Fourier transforms. J. Comput. Phys. 52:1983;1.
54. Thomas L. H. Elliptic Problems in Linear Difference Equations over a Network. 1949.
55. Thorpe S. A., Haines A. P. On the reflection of a train of finite-amplitude internal waves from a uniform slope. J. Fluid Mech. 178:1987;279.
56. Thorpe S. A. Thermal fronts caused by internal gravity waves reflecting from a slope. J. Phys. Ocean. 22:1992;105-108.
57. Winters K. B. Intensification and Instability of Internal Gravity Waves at Caustics and Critical Levels. 1989.
58. Winters K. B., Riley J. J. Instability of internal waves near a critical level. Dynam. Atmospheres Oceans. 16:1992;249.
59. Winters K. B., Lombard P. N., Riley J. J., D'Asaro E. A. Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 289:1995;115.
60. Wunsch C. On oceanic boundary mixing. Deep-Sea Res. 17:1970;293.