1. Ben Green Group meeting, 9/13/2013
Tropical Cyclones and Large Eddy Simulations: From Idealized to Real-Data Cases
Ben Green
Group meeting, 9/13/2013

2. Background More computing power = higher resolution NWP
Current mesoscale NWP has Δx ~O(1 km)
Caution! Going to higher resolution is not as simple as changing a number in a namelist file
Δx > 1 km: all turbulence is fully parameterized
Δx < 100 m: largest turbulent eddies are explicitly resolved
100 m < Δx < 1 km: “no man’s land” for turbulent eddies
Bottom line: Large Eddy Simulation (LES) is the next step in real-time mesoscale NWP

3. What is LES? Largest eddies contain/produce the most energy
Smallest eddies dissipate nearly all of the energy
Energy is transferred from largest eddies to smallest eddies (inertial subrange)
LES decomposes equations into 2 parts:
Resolved scales (large eddies): use Navier-Stokes equations
Subgrid (unresolved) scales (smallest eddies): use closure model
Caution! LES grid spacing (filter width) needs to be in inertial subrange!

4. What is LES? kcutoff = π/Δ log(E) Inertial subrange Dissipation range
Large eddies (energy- containing)
kcutoff = π/Δ
log(E)
Inertial subrange
Dissipation range
Energy cascade
log(k=2π/x)
kcutoff
Explicitly resolved turbulence on LES grid
Closure model (subgrid scale)

5. Tropical Cyclones (TCs) and LES
Planetary boundary layer (PBL) is a crucial but unknown part of TCs – active area of research
Limited observations: dangerous!
Not many simulations: high wind speed = high computational cost
Two ways to use LES in TC research
Idealized studies: How does turbulence behave at very high winds?
Real data cases: Can LES improve TC intensity forecasts?
Each way has advantages + disadvantages

6. Real-data TC LES
Cray is willing to give free computing to Fuqing to simulate Katrina (or other infamous TC) at LES-scale
Amazing opportunity (especially if intensity forecasts improve)
Very risky endeavor…
Why is real-data TC LES so risky?
High computational cost: increased by a factor of ~2000 compared to current real-time forecasts
Turn off PBL scheme: necessary, but will forecast improve?
Is Δx really in the inertial subrange? Probably not (for Δx = 333 m), so not all energy-containing eddies will be resolved (see Bryan and Rotunno 2009, BAMS)
A 3-hour test for Katrina was run – output seems realistic. Stay tuned…

7. Idealized TC LES Continuation of my work at NCAR this summer
Old approach (Eulerian): Simulate passage of quasi-idealized TC over a fixed location in physical space
New approach (Lagrangian): Simulate PBL of idealized slow-moving TC at a fixed location relative to TC center

8. Idealized TC LES: Experimental setup
Unchanged between experiments (all used NCAR LES):
Δx = Δy = Δz = 40m; time step = 0.1 seconds
500x500x100 grid (20km x 20km x 4km)
Initial θ profile: θsurface = 300 K; θ increases 4 K every 1 km up
No surface heat flux (as in Nakanishi and Niino 2012, JAS)
Initial gradient wind: Ugradient = 35 m s-1; Vgradient = 0 m s-1 everywhere
Periodic lateral boundary conditions
Changes between experiments:
LAND_GEO:
z0 = 0.1 m (roughness over land)
No centrifugal force
DONELAN_GEO:
z0 follows Donelan curve (sea)
LAND_CURVED:
z0 = 0.1 m (roughness over land)
Centrifugal force (see NN2012)
DONELAN_CURVED:
z0 follows Donelan curve (sea)

9. Results (time series)
Solid = land; Dashed = Donelan (sea)
Thick = curvature; Thin = no curvature
Time (hours)
Time (hours)
Land: higher PBL top (zi) and thus higher surface temperature
Curvature: faster spinup of turbulence, lower equilibrium zi(?)

10. Results (time series) Land: higher u* and much higher TKE
Solid = land; Dashed = Donelan (sea)
Thick = curvature; Thin = no curvature
Time (hours)
Time (hours)
Land: higher u* and much higher TKE
Curvature: higher u*, faster spinup, comparable TKE by 5.5 hours

11. Results (profiles at ~5.5 hours)
Solid = land; Dashed = Donelan (sea)
Thick = curvature; Thin = no curvature
Curvature: supergradient jet, faster surface wind (especially azimuthal), faster spinup of turbulence, shallower inflow layer, strongest inflow closer to ground
Land: Warmer/deeper thermodynamic PBL, weaker surface winds, stronger/deeper inflow layer

12. Summary of results
Time to spin-up turbulence changes between all experiments
More curvature = faster spinup (consistent w/ Nakanishi & Niino 2012)
More friction = faster spinup
What is the significance of this? (I don’t know)
Curvature allows supergradient jet to develop at PBL top
But, more curvature = weaker jet (Kepert 2001; NN2012)
Question: what would happen for little curvature (say, R = 1000 km)?
Side note: Magnitude of supergradient jet is still much less than “geostrophic” value corresponding to same PGF and Coriolis values
More friction = stronger vertical fluxes (duh) and higher PBL top
Characteristics of inflow layer sensitive to both drag and curvature

13. Future work Run additional tests More analysis
Increase Ug and/or decrease radius
Possibly add Charnock-based Cd for faster Ug experiments
More analysis
TKE budgets
Structural analysis of rolls (power spectra)
Compare with mesoscale model output