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ISMAR

ISMAR. Influence of different vertical mixing schemes and wave breaking parameterization on forecasting surface velocities S. Carniel 1 , J.C. Warner 2 , R.P. Signell 2 , J. Chiggiato 3 , P.-M. Poulain 4 1 CNR-ISMAR, Venice, Italy 2 USGS, Woods Hole, USA 3 SMR-ARPA-EMR, Bologna, Italy

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ISMAR

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  1. ISMAR Influence of different vertical mixing schemes and wave breaking parameterization on forecasting surface velocities S. Carniel1, J.C. Warner2, R.P. Signell2, J. Chiggiato3, P.-M. Poulain4 1 CNR-ISMAR, Venice, Italy 2USGS, Woods Hole, USA 3 SMR-ARPA-EMR, Bologna, Italy 4 OGS, Trieste, Italy ROMS-Oct’04

  2. Motivations • Most 3D circulation models compute subgrid scale momentum and tracer mixing by means of a two equation turbulence closure scheme, TCMs (e.g Mellor-Yamada 2.5 or k-ε). • These closure schemes fail, however, in wave affected surface layers, and eddy viscosity “errors” produce unrealistic velocities.

  3. Motivations • These models are tuned to treat the sea-surface as a solid boundary and therefore, during events of strong wind, reproduce a log velocity profile in the proximity of the surface. • This is in contradiction with recent studies and measurements: during breaking wave conditions, the near-surface mixing is higher and the velocity shear lower than those modeled by usual TCMs.

  4. Current picture Air-sea interface is not rigid, therefore OML cannot be patterned after a solid boundary (e.g. law of the wall) A) Near surface region “breaking layer”, O(Z0S), all mixed; B) region adjacent to air-sea interface, O(10 Z0S), turb. diss. rate decays with a power law -4 (l.o.w.: -1). (Kantha&Clayson, 2004; Drennan, 1996; Terray 1996…) C) l.o.w. valid again at a certain distance from the surface …most of wave generated TKE dissipated in the O(SWH) Highly desirable to inlcude wave-breaking to explore near-surface distributions of T, S, velocities (S&R, oil-spill predictions, etc.)

  5. k –  p=3, m=1.5, n=-1  = cp km n k – k p=0, m=1, n=1 Two-Equations 2nd mom. TCMs Following Reynolds’ approach, 2nd moment quantities are computed as u’w’= KM (U/ Z). Thus two extra prognostic eqs. are required: 1st for the transport of the TKE, k (or q2); 2nd for the transport of turbulence length scale, . ...integrating them, the Eddy Viscosity (Diffusivity) coeff.for mometum (scalar) at (t,z) is KM (KH) k Ref:Kantha, 2004. The length scale equation in turbulence models. Nonlinear processes in Geophysics, 7, 1-12 Kolmogoroff relation ( k3/2  -1) allows the choices of several … giving the name to the 2nd mom-2 eqs TCM: k-, k-k, k- (turb. Freq. k1/2 -1)…i.e. generally km n (Generic Length Scale approach) Ref: Umlauf and Burchard, 2003. A generic length-scale equation for gephysical turbulence. J. Marine Research, 61(2), 235-265

  6. Tools – Numerical Models How: integrating Umlauf & Burchard (UB 2003) GLS method, allowing to choose among different parameterisations of vertical mixing processes, into Regional Ocean Model System (ROMS), a 3-D finite-difference hydrodynamical model (Warner et al., 2005) Where: a) idealized 20 m deep basin b) Adriatic Sea When: Febraury 2003 (bora event)

  7. Sensitivity Tests 1-D ROMS Idealized basin 20 m deep 1000x1000 m 100 stretched levels Wind stress u-direction: 1 N/m2 (approx. 20 m/s) Periodic BCs NESW …vertical resolution…

  8. TKE Surface B.C.: (Craig and Banner, 1994) 100-150 …at z=0, =f(Z0s). k=0.4, but… Z0s =f(sea state) Charnock formula (1955) fully developed sea: const Turbulence and Wave-breaking a: 1400 (CB 1994; GOTM 1999, etc.) • …Navier-Stokes eqs. describe all hydrodynamic processes, but the real world has large range of spatial/temporal scales… • D.N.S.= accurate modeling of flows where all turbulent scales are resolved. No closure assumptions required. Applied numerically to idealised, small-scale problems. Demanding very large computer resources. • L.E.S.= predict large scale turbulent structures as large energy-containing eddies, while small scales into which the KE is transferred are parameterised.

  9. Sensitivity Tests 1-D ROMS -Test 1 C&B All GLS with K-w, NO C&B GEN, NO C&B (UB 2003) GEN, CB Lsft=0.2, a=1400 A …C&B increases surface TKE

  10. Sensitivity Tests 1-D ROMS C&B All GLS with K-w, NO C&B GEN, NO C&B GEN, CB Lsft=0.2, a=1400 …C&B shows minor surface velocities A

  11. Sensitivity Tests 1-D ROMS All GLS with C&B K-w K-eps GEN Lsft=0.2, a=1400 B …all including C&B... showing differences among TCMs…

  12. Sensitivity Tests 1-D ROMS All GLS with C&B K-w K-eps GEN Lsft=0.2, a=1400 B …all including C&B.. see difference among TCMs…

  13. Sensitivity Tests 1-D ROMS All GLS with C&B K-w K-eps GEN Lsft=0.2, a=1400 B B …differences due to…

  14. Sensitivity Tests 1-D ROMS All GLS-GEN with C&B Lsft=0.2, a=1400 Lsft=0.2, a=14000 Lsft=0.4, a=1400 Lsft=0.4, a=14000 C

  15. Sensitivity Tests 1-D ROMS All GLS-GEN with C&B Lsft=0.2, a=1400 Lsft=0.2, a=14000 Lsft=0.4, a=1400 Lsft=0.4, a=14000 C

  16. Sensitivity Tests 1-D ROMS All GLS-GEN with C&B Lsft=0.2, a=1400 Lsft=0.2, a=14000 Lsft=0.4, a=1400 Lsft=0.4, a=14000 NO C&B C …value of alpha to be used?

  17. TKE Surface B.C.: (Craig and Banner, 1994) 100-150 …at z=0, =f(Z0s) Z0s =f(sea state) Charnock formula (1955) fully developed sea: const Turbulence and Wave-breaking a=1400? …in order to to have Z0s=O(SWH), use O(105) (KC 2004, Stacey 1999) • …Navier-Stokes eqs. describe all hydrodynamic processes, but the real world has large range of spatial/temporal scales… • D.N.S.= accurate modeling of flows where all turbulent scales are resolved. No closure assumptions required. Applied numerically to idealised, small-scale problems. Demanding very large computer resources. • L.E.S.= predict large scale turbulent structures as large energy-containing eddies, while small scales into which the KE is transferred are parameterised.

  18. Sensitivity Tests 1-D ROMS All GLS-GEN with C&B Lsft=0.2, a=1400 Lsft=0.4, a=100000 Lsft=0.2, a=100000 C NO C&B … …

  19. Surface Wind from LAMI model LAMI: 3-D finite-difference, non hydrostatic, 7 km resolution, Forecast output every 3 hours

  20. Surface Currents from ROMS model ROMS: 3-D primitive eqs, hydrostatic, sigma level, finite difference These are surface currents (0.5 m) from the GLS GEN (UB 2003) case

  21. 3-D ROMS in the Adriatic Bora Velocity at 5-m depth(m/s)

  22. Floaters release from ROMS model GEN, No C&B GEN, C&B Z0S= f(Charnok), L_sft=0.2, a=1400 Drifters data Floaters kept at 0.5 m… (modification to floats.in file to the trajectory type file in order to keep them at a fixed depth…)

  23. GLS as k-e vs GEN KEPS C&B Z0S= f(Charnok), L_sft=0.2, a=14000 GEN C&B Z0S= f(Charnok), L_sft=0.2, a=14000 Drifters data

  24. GLS as k-e vs GEN GEN wave-breaking Z0S= f(Charnok) L_sft=0.4, a=100000 KEPS wave-breaking Z0S= f(Charnok) L_sft=0.4, a=100000 Drifters data

  25. Message • Recently it has become possible to modify two equation turbulence models in order to account for wave-breaking effects. • When wave-effects are included, near-surface shears are significantly reduced, better matching observations, surface currents are diminished (and are virtually less sensitive to the near-surface grid resolution!) • First simulations incorporating wave-enhanced mixing point out how model results (e.g. velocities) are sensitive to how we parameterize the roughness scale.

  26. Message • How to handle the length scale near the surface (i.e what is it at z=0) is still an open issue • In real-life situations the choice of correct parameters appear to be more important than the TCM selected (at least for this data-set and within the GLS set)

  27. EOP

  28. 3-D ROMS in the Adriatic Scirocco Velocity at 5-m depth(m/s)

  29. “S3” Seasonal Evolution Forcings: Wind: 1 hour S: restoration Run P1: k- Run P2: one-eq (length scale prescribed algebraically) Run P3: GLS Run P4: k- SURFACE BOTTOM

  30. Where does turbulence come from? R.A.N.S.= (still) the most convenient way to describe complex flow situations, where all turbulent motions are parameterised by a sub-scale turbulencemodel in a statistical sense. adopting Reynolds’ approach: ... are new unknowns for which transport equations can be written but contain thirdmoment covariances… ad infinitum Equations not closed at any level! Turbulence is an unresolved problem in physics! • …Navier-Stokes eqs. describe all hydrodynamic processes, but the real world has large range of spatial/temporal scales… • D.N.S.= accurate modeling of flows where all turbulent scales are resolved. No closure assumptions required. Applied numerically to idealised, small-scale problems. Demanding very large computer resources. • L.E.S.= predict large scale turbulent structures as large energy-containing eddies, while small scales into which the KE is transferred are parameterised.

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