Will we ever simulate, via nonhydrostatic LES, real estuarine and coastal problems?

1. Will we ever simulate, via nonhydrostatic LES, real estuarine and coastal problems? Oliver Fringer Bob and Norma Street Environmental Fluid Mechanics Laboratory Dept. of Civil and Environmental Engineering Stanford University Support: NSF, ONR, Stanford Woods Institute NSF Workshop on Estuarine and Coastal Modeling June 18-21, 2018

2. Outline • Where should we focus our efforts related to improved parameterizations? • What aspects of numerical methods related to coastal modeling can be improved?  • How can in-situ and remote-sensing measurements be used, and improved, to benefit coastal modeling? • How can coastal modeling better leverage HPC resources?

3. FilteredNavier-Stokes equation LES: RANS: (e.g. GOTM)

4. DNS in estuaries and coasts? • DNS assumes ALL scales are resolved, even in the viscous sublayer. Thus DNS is possible, in principle, if the flow is hydraulically smooth • Hydraulically smooth: Grain size ~400 mm (medium sand) • True in much of the coastal ocean, but DNS would not be possible where the grain size is hydraulically rough or where bioturbation/vegetation require a statistical description of the roughness. P. Y. Julien (2010)

5. LES/DES in estuaries? LES is more realistic than DNS, and can be employed for smooth and rough walls. But near-wall boundary condition for transitional/rough walls requires a quadratic drag law formulation based on the roughness, just like RANS. LES in estuary: 2 km by 2 km estuary with depth = 1 mDx=Dy=20 cm, Dz=5 cm 2 billion grid cells “doable” Boundary conditions: No slip Quadratic drag law (u=0)

6. Nonhydrostatic pressure is not important unless • Internal solitary waves (Vitousek and Fringer 2011): (Require ): • Gravity currents/fronts (Require ) Nonhydrostatic Hydrostatic Hydrostatic Nonhydrostatic

7. Primitive equations, Reynolds averaged (LES not possible)

8. Primitive equations are ill-posed Consider the hydrostatic lock exchange problem At the front: w u Hydrostatic Nonhydrostatic

9. Artificial diffusion Due to a lack of physical horizontal turbulent diffusion, these equations are also badly posed because there is no physical mechanism to reduce horizontal variance. All primitive equation models must either employ an advection scheme that is diffusive, or add enough artificial diffusion to prevent grid-scale energy pile-up: Smagorinsky model:

10. Model errors Assume interested in resolving process with velocity scale U and length scale L (x*=x/L, u*=u/U): Higher-order is more accurate than lower-order only when Any near-grid scale variability makes the errors for both methods equivalent.

11. The drag coefficient Depth-averaged equations (K>>nT) Typically,

12. How can we make models better? • Reduce/quantify boundary condition errors: • Employ more grid resolution • Focus on better parameterizations for CD

13. Directionally-dependent bottom drag Depth H = 4 m From Fong et al. JHE 2009 Flood tide Ebb tide Separation during flood tide produces more form drag and higher CD.

14. Wave-current bottom drag • Wave-current bottom stress is given by (e.g. Grant and Madsen 1986): ()Currents: (Hydrodynamics; )Waves: (Wave model; ) • Wave-current interactions (Grant and Madsen 1986) and sediment-induced stratification ignored (Glenn and Grant 1987; Styles and Glenn 2000 ) Currents Waves

15. DNS of wave-current turbulent boundary layers • Parameters representative of a shallow site in San Francisco Bay (e.g. Brand et al. 2010). Fine sediments  smooth wall. • Currents: u = 4, 7, 10 cm/sRe=uH/n=4000,7000,10000 (Turbulent)Ret=u*H/n=200,350,500Viscous sublayer thickness: d=n/u*=0.5, 0.3, 0.2 mm • Waves:Bottom orbital velocity, ub= 10 cm/sWave period T= 3 sRew=ub2/wn=4774 (Laminar)Wave boundary layer thickness D = (n/w)1/2=1 mm • 7 Total cases: 3 Currents (C), 3 Waves+Currents (WC), 1 Wave only (W) waves H=0.1 m Length = 15 H, Width = 3.12 H currents Nelson and Fringer (JGR; submitted) z y x

16. Effects of waves on drag coefficient Governing equation Time- and volume-averaging in the periodic domain implies that Turbulent wave-current models imply waves should increase the drag coefficient, but these results imply the opposite.

17. Conclusions • Parameterizations? • Bottom drag! But before we can do that, we need to reduce/quantify errors due to BC’s and reduce numerical errors. • Possible areas include: • Wave-current drag • Directionally-dependent drag over asymmetric bedforms • Drag over dunes + ripples and better parameterizations for their formation and migration • Vegetation drag • Numerical methods? Improved treatment of the vertical coordinate to reduce spurious numerical mixing. • Remote-sensing?Use remote sensing along with assimilation techniques to reduce errors associated with boundary conditions (e.g. bathymetry/bedforms/sediment properties). • How can coastal modeling better leverage HPC resources?Make it easier to apply for and obtain supercomputing time and support more collaboration with computer scientists/applied mathematicians to help accelerate performance of existing methods. Barnard et al. (2006)

18. RANS & URANS RANS (Steady) URANS (Unsteady; turbulent time scales << mean time scale) RANS/URANS:

19. LES

20. LES vs URANS RANS/URANS: Model all turbulence LES: Model subfilter-scale turbulence

21. DES (Detached-eddy simulation) LES requires at least one grid point in the viscous sublayer (i.e. DNS requires ) DES = RANS + LES Near wall: a=1, Far from wall, a=0, r