Mesoscale Ocean Large Eddy Simulation (MOLES)

Transcription

1 Mesoscale Ocean Large Eddy Simulation (MOLES) Baylor Fox-Kemper (Brown) Scott Bachman (Cambridge) Frank Bryan & David Bailey (NCAR)

2 Viscosity Parameterizations GCMs use horizontal eddy viscosity to account for the diffusion of momentum due to unresolved eddies Usually use a friction term with constant viscosity e.g. Parameterized Viscosity Too large - Double counting - Resolved eddies damped Too small - Energy build up near grid-scale - Spurious diapycnal mixing (Ilicak et al., 2012)

3 Viscosity Parameterizations Constant viscosity implies: ν is independent of scales A change in resolution or scale of eddies (e.g. with latitude) does not affect mixing by sub-grid eddies ν does not depend on local flow But the resolved flow, and therefore, presumably, the sub-grid flow, show spatial variation Neither of these assumptions are true Need a viscosity which is scale- and flow-dependent!

4 Large Eddy Simulation Useful when some, but not all, scales of turbulence are resolved Viscosity is parameterized to be consistent with a theoretical or observed inertial cascade in a given turbulent flow Smagorinsky (3D turbulence) Kolmogorov energy cascade Captures boundary layer turbulence k -5/3 1/Δx The large-scale ocean is not driven by 3D turbulence, ) it is driven by quasi- 2D turbulence! ln(k

5 2D Leith In 2D turbulence there is a downscale enstrophy cascade 2D Leith viscosity is designed to capture the enstrophy cascade Scale Aware Flow Aware QG Leith viscosity proposed by Bachman & Fox-Kemper (in prep.)

6 MITgcm Simulations Idealized frontal spin-down using MITgcm (Bachman & Fox-Kemper, in prep.) All simulations resolve some mesoscale eddies ν * =ĸ=μ (GM scheme) Viscosity matched with diffusivities

7 Energy Spectra Laplacian and Smagorinsky schemes 2D Leith Biharmonic QG Leith

8 Energy Spectra QG Leith naturally maintains energy spectrum over a range of grid scales (< L d ) Biharmonic, 2D Leith QG Leith

9 CESM 2D Leith viscosity 0.1 o CESM hybrid simulation 2D Leith and biharmonic viscosity schemes are compared. 2D Leith viscosity is matched with the isopycnal and buoyancy diffusivities. Viscosity averaged over one day.

10 1000 [m 2 s -1 ] D Leith viscosity

11 Biharmonic (default) τ 4 1 F Hx ν = u = u u τ 2D Leith F Hx 1 ν * = u = ( u) u [s -1 ] (100 years) -1 (1 year) -1 (10 days) -1

12 Biharmonic (default) Magnified by 100 2D Leith [s -1 ] (100 years) -1 (1 year) -1 (10 days) -1

13 Summary Turbulence in the ocean on km scales and larger is almost 2D. 2D/QG Leith provides a flow-dependent and scale-dependent parameterization for the effects of sub-grid eddies In idealized simulations, QG Leith viscosity (without tuning) produces better energy spectra than Laplacian, biharmonic, 2D Leith etc. In High-Res (0.1 o ) POP, the 2D Leith friction is significantly smaller than the biharmonic friction

14 Biharmonic (default) 2D Leith [m s -2 ]

15 Gridscale Reynolds number Small Re * minimizes spurious diapycnal mixing (Ilicak et al., 2012), and indicates whether model is viscous enough Basic QG Leith and QG Leith (large filter)

16 QG Leith When grid-scale is below first baroclinic Rossby deformation radius, L d, some mesoscale eddies are resolved (MOLES) Eddies produce a quasi-geostrophic potential enstrophy cascade QG Leith viscosity proposed by Bachman & Fox-Kemper (in prep.) Transitions to 2D Leith under strong or weak stratification