Revert CATKE mixing length to calibrated default

[simone-silvestri]

Summary

• Remove the ad-hoc override CATKEMixingLength(Cᵇ=0.01) in default_ocean_closure() and use the published calibrated default (Cᵇ=0.28, Wagner et al. 2025).

Motivation

The parameter Cᵇ controls the bottom-distance constraint on the CATKE stable mixing length:

ℓ = min(Cˢ × d_surface, Cᵇ × d_bottom, w★/√N²)

With Cᵇ = 0.01 (28× smaller than the calibrated value of 0.28), the bottom term becomes the tightest constraint for nearly all depths below ~50 m, regardless of ocean depth. In a 5 km deep ocean:

Depth	Cˢ × d_up	Cᵇ × d_down (0.01)	Cᵇ × d_down (0.28)
50 m	56 m	49 m	1386 m
100 m	113 m	49 m	1372 m
500 m	565 m	45 m	1260 m

This artificially caps the mixing length at ~50 m everywhere, directly suppressing the vertical diffusivity κ = ℓ × √e and producing unrealistically shallow mixed layer depths globally.

Below are the MLD diagnostics from an 8-year OMIP run on the ss/omip-prototype branch (two configurations: half-degree TripolarGrid and ORCA-NCAR). Both cases show winter MLD barely reaching 50–100 m, far shallower than observed values (500–2000 m in the Labrador Sea, 200–500 m in the Southern Ocean):

Note: the figure above corresponds to runs performed from the ss/omip-prototype branch using CATKEMixingLength(Cᵇ=0.01).

Test plan

• CI passes (the change is a parameter default, no API change)
• Re-run OMIP simulation and verify deeper MLD in key convection regions

🤖 Generated with Claude Code

[simone-silvestri]

BTW I am not sure this is a fix because the deep mixed layers are produced by convection while this parameter only touches the shear mixing length in stable conditions. However, I will test it out and report back

[codecov]

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