• Baumert, H., , and H. Peters, 2000: Second-moment closures and length scales for weakly stratified turbulent shear flows. J. Geophys. Res, 105 , 64536468.

    • Search Google Scholar
    • Export Citation
  • Bryan, K., 1969: A numerical model for the study of the world ocean. J. Comput. Phys, 4 , 347376.

  • Burchard, H., 2001: Note on the q2 l equation by Mellor and Yamada (1982). J. Phys. Oceanogr., 31, 1377–1387.

  • Burchard, H., , and H. Baumert, 1995: On the performance of a mixed-layer model based on the kϵ turbulence closure. J. Geophys. Res, 100 , 85238540.

    • Search Google Scholar
    • Export Citation
  • Burchard, H., , and O. Petersen, 1999: Models of turbulence in the marine environment—A comparative study of two-equation turbulence models. J. Mar. Syst, 21 , 2953.

    • Search Google Scholar
    • Export Citation
  • Burchard, H., , O. Petersen, , and T. P. Rippeth, 1998: Comparing the performance of the Mellor–Yamada and the kϵ two-equation turbulence models. J. Geophys. Res, 103 , 10 54310 554.

    • Search Google Scholar
    • Export Citation
  • Burchard, H., , K. Bolding, , and M. R. Villarreal, 1999: GOTM—A general ocean turbulence model. Theory, applications and test cases. European Commission Rep. EUR 18745 EN, 103 pp.

    • Search Google Scholar
    • Export Citation
  • Businger, J. A., , J. C. Wyngaard, , Y. Izumi, , and E. F. Bradley, 1971: Flux profile relationships in the atmospheric surface layer. J. Atmos. Sci, 28 , 181189.

    • Search Google Scholar
    • Export Citation
  • Canuto, V. M., 1994: Large eddy simulation of turbulence: A subgrid model including shear, vorticity, rotation and buoyancy. Astrophys. J, 428 , 729752.

    • Search Google Scholar
    • Export Citation
  • Canuto, V. M., , F. Minotti, , C. Ronchi, , M. Ypma, , and O. Zeman, 1994: Second-order closure PBL model with new third-order moments: Comparison with LES data. J. Atmos. Sci, 51 , 16051618.

    • Search Google Scholar
    • Export Citation
  • Canuto, V. M., , A. Howard, , Y. Cheng, , and M. S. Dubovikov, 2001: Ocean turbulence. Part I: One-point closure model momentum and heat vertical diffusivities. J. Phys. Oceanogr., 31, 1413–1426.

    • Search Google Scholar
    • Export Citation
  • Craig, P. D., , and M. L. Banner, 1994: Modeling wave-enhanced turbulence in the ocean surface layer. J. Phys. Oceanogr, 24 , 25462559.

  • D'Alessio, S. J. D., , K. Abdella, , and N. A. McFarlane, 1998: A new second-order turbulence closure scheme for modeling the oceanic mixed layer. J. Phys. Oceanogr, 28 , 16241641.

    • Search Google Scholar
    • Export Citation
  • Deleersnijder, E., , and P. Luyten, 1994: On the practical advantages of the quasi-equilibrium version of the Mellor and Yamada level 2.5 turbulence closure applied to marine modelling. Appl. Math. Model, 18 , 281287.

    • Search Google Scholar
    • Export Citation
  • Denman, K. L., 1973: A time-dependent model of the upper ocean. J. Phys. Oceanogr, 3 , 173184.

  • Galperin, B., , L. H. Kantha, , S. Hassid, , and A. Rosati, 1988: A quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci, 45 , 5562.

    • Search Google Scholar
    • Export Citation
  • Haidvogel, D. B., , and A. Beckmann, 1999: Numerical Ocean Circulation Modelling. Series on Environmental Science and Management, Vol. 2, Imperial College Press, 318 pp.

    • Search Google Scholar
    • Export Citation
  • Hossain, M. S., 1980: Mathematische Modellierung von turbulenten Auftriebsströmungen. Ph.D. dissertation, University of Karlsruhe, Karlsruhe, Germany, 145 pp.

    • Search Google Scholar
    • Export Citation
  • Kantha, L. H., , and C. A. Clayson, 1994: An improved mixed layer model for geophysical applications. J. Geophys. Res, 99, , 25 23525 266.

    • Search Google Scholar
    • Export Citation
  • Kato, H., , and O. M. Phillips, 1969: On the penetration of a turbulent layer into stratified fluid. J. Fluid Mech, 37 , 643655.

  • Kolmogorov, A. N., 1942: The equations of turbulent motion on an incompressible fluid. Izv. Akad. Nauk. USSR, Ser. Fiz., VI (1–2), 56–58.

    • Search Google Scholar
    • Export Citation
  • Large, W. G., , and P. R. Gent, 1999: Validation of vertical mixing in an equatorial ocean model using large eddy simulations and observations. J. Phys. Oceanogr, 29 , 449464.

    • Search Google Scholar
    • Export Citation
  • Large, W. G., , J. C. McWilliams, , and S. C. Doney, 1994: Oceanic vertical mixing: A review and a model with nonlocal boundary layer parameterization. Rev. Geophys, 32 , 363403.

    • Search Google Scholar
    • Export Citation
  • Launder, B. E., 1975: On the effect of a gravitational field on the turbulent transport of heat and momentum. J. Fluid Mech, 67 , 569581.

    • Search Google Scholar
    • Export Citation
  • Launder, B. E., , and D. Spalding, 1972: Mathematical Models of Turbulence. Academic Press, 169 pp.

  • Launder, B. E., , G. J. Reece, , and W. Rodi, 1975: Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech, 68 , 537566.

    • Search Google Scholar
    • Export Citation
  • Lesieur, M., 1997: Turbulence in Fluids. 3d ed. Kluwer Academic, 515 pp.

  • Martin, P. J., 1985: Simulation of the mixed layer at OWS November and Papa with several models. J. Geophys. Res, 90 , 903916.

  • Mellor, G. L., 1989: Retrospect on oceanic boundary layer modeling and second moment closure. Parameterization of Small-Scale Processes: Proc ‘Aha Huliko’ a Hawaiian Winter Workshop, Manoa, HI, University of Hawaii, 251–271.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., 2001: One-dimensional, ocean surface layer modeling: A problem and a solution. J. Phys. Oceanogr, 31 , 790803.

  • Mellor, G. L., , and T. Yamada, 1974: A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci, 31 , 17911806.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., , and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys, 20 , 851875.

    • Search Google Scholar
    • Export Citation
  • Mironov, D. V., , V. M. Gryanik, , C-H. Moeng, , D. J. Olbers, , and T. H. Warncke, 2000: Vertical turbulence structure and second-moment budgets in convection with rotation: A large-eddy simulation study. Quart. J. Roy. Meteor. Soc, 126 , 477515.

    • Search Google Scholar
    • Export Citation
  • Moeng, C-H., , and P. P. Sullivan, 1994: A comparison of shear and buoyancy-driven planetary boundary layer flow. J. Atmos. Sci, 51 , 9991022.

    • Search Google Scholar
    • Export Citation
  • Monin, A. S., , and A. M. Obukhov, 1954: Basic laws of turbulent mixing in the ground layer of the atmosphere. Akad. Nauk SSSR Geofiz. Inst. Tr, 151 , 163187.

    • Search Google Scholar
    • Export Citation
  • Prandtl, L., 1945: Über ein neues Formelsystem für die ausgebildete Turbulenz. Nachr. Akad. Wiss., Goettingen, Math.-Phys. Kl.,, p. 6.

    • Search Google Scholar
    • Export Citation
  • Price, J. F., 1979: On the scaling of stress-driven entrainment experiments. J. Fluid Mech, 90 , 509529.

  • Rodi, W., 1976: A new algebraic relation for calculating the Reynolds stresses. Z. Angew. Math. Mech, 56 , T219T221.

  • Rodi, W., 1980: Turbulence models and their application in hydraulics. International Association for Hydraulic Research, Delft, Netherlands, 104 pp.

    • Search Google Scholar
    • Export Citation
  • Rodi, W., 1987: Examples of calculation methods for flow and mixing in stratified flows. J. Geophys. Res, 92 , 53055328.

  • Rohr, J. J., 1985: An experimental study of evolving turbulence in uniform mean shear flow with and without stable stratification. Ph.D. dissertation, University of San Diego, 271 pp.

    • Search Google Scholar
    • Export Citation
  • Rosati, A., , and K. Miyakoda, 1988: A general circulation model for upper ocean simulation. J. Phys. Oceanogr, 18 , 16011626.

  • Rotta, J. C., 1951: Statistische Theorie nichthomogener Turbulenz. Z. Phys, 129 , 547572.

  • Roussenov, V., , E. Stanev, , V. Artale, , and N. Pinardi, 1995: A seasonal model of the Mediterranean Sea general circulation. J. Geophys. Res, 100 , 13 51513 538.

    • Search Google Scholar
    • Export Citation
  • Sander, J., 1998: Dynamic equations and turbulent closures in geophysics. Continuum Mech. Thermodyn, 10 , 128.

  • Schumann, U., , and T. Gerz, 1995: Turbulent mixing in stably stratified shear flows. J. Appl. Meteor, 34 , 3348.

  • Shih, T. S., , and A. Shabbir, 1992: Advances in modeling the pressure correlation terms in the second moment equations. Studies in Turbulence, T. B. Gatsky, S. Sarkar, and C. G. Speziale, Eds., Springer-Verlag, 91–128.

    • Search Google Scholar
    • Export Citation
  • Taylor, G. I., 1935: Statistical theory of turbulence, Parts i–iv. Proc. Roy. Soc. London, 151A , 421478.

  • Willis, G. E., , and J. W. Deardorff, 1974: A laboratory model of the unstable planetary boundary layer. J. Atmos. Sci, 31 , 12971307.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 318 318 18
PDF Downloads 167 167 15

Comparative Analysis of Four Second-Moment Turbulence Closure Models for the Oceanic Mixed Layer

View More View Less
  • 1 Institut für Meereskunde, Universität Hamburg, Hamburg, Germany
  • | 2 Space Applications Institute, CEC—Joint Research Centre, Ispra, Italy
© Get Permissions Rent on DeepDyve
Restricted access

Abstract

In this comparative study, four different algebraic second-moment turbulence closure models are investigated in detail. These closure schemes differ in the number of terms considered for the closure of the pressure–strain correlations. These four turbulence closures result in the eddy-diffusivity principle such that the closure assumptions are contained in dimensionless so-called stability functions. Their performance in terms of Prandtl number, Monin–Obukhov similarity theory, and length scale ratios are first tested against data for simple flows. The turbulence closure is then completed by means of a kϵ two-equation model, but other models such as the two-equation model by Mellor and Yamada could also be used. The concept of the steady-state Richardson number for homogeneous shear layers is exploited for calibrating the sensitivity of the four models to shear and stable stratification. Idealized simulations of mixed layer entrainment into stably stratified flow due to surface stress and due to free convection are carried out. For the latter experiment, comparison to recent large eddy simulation data is made. Finally, the well-known temperature profile data at OWS Papa are simulated for an annual cycle. The main result of this paper is that the overall performance of the new second-moment closure model by Canuto et al.—expressed as nondimensional stability functions—is superior compared to the others in terms of physical soundness, predictability, computational economy, and numerical robustness.

Corresponding author address: Dr. Hans Burchard, Institut für Meereskunde, Universität Hamburg, Troplowitzstrasse 7, 22529 Hamburg, Germany.Email: hans@gotm.net

Abstract

In this comparative study, four different algebraic second-moment turbulence closure models are investigated in detail. These closure schemes differ in the number of terms considered for the closure of the pressure–strain correlations. These four turbulence closures result in the eddy-diffusivity principle such that the closure assumptions are contained in dimensionless so-called stability functions. Their performance in terms of Prandtl number, Monin–Obukhov similarity theory, and length scale ratios are first tested against data for simple flows. The turbulence closure is then completed by means of a kϵ two-equation model, but other models such as the two-equation model by Mellor and Yamada could also be used. The concept of the steady-state Richardson number for homogeneous shear layers is exploited for calibrating the sensitivity of the four models to shear and stable stratification. Idealized simulations of mixed layer entrainment into stably stratified flow due to surface stress and due to free convection are carried out. For the latter experiment, comparison to recent large eddy simulation data is made. Finally, the well-known temperature profile data at OWS Papa are simulated for an annual cycle. The main result of this paper is that the overall performance of the new second-moment closure model by Canuto et al.—expressed as nondimensional stability functions—is superior compared to the others in terms of physical soundness, predictability, computational economy, and numerical robustness.

Corresponding author address: Dr. Hans Burchard, Institut für Meereskunde, Universität Hamburg, Troplowitzstrasse 7, 22529 Hamburg, Germany.Email: hans@gotm.net

Save