Why do we need cubic_profile in the forcing functions?

[navidcy]

E.g., here:

OceanScalingTests.jl/src/bathymetry_and_forcings.jl

Lines 61 to 70 in f034fdb

	@inline function wind_stress_coefficients(south_north_limit)
	below_45_coeffs = cubic_profile(-south_north_limit, -45.0, 0.0, 0.2, 0.0, 0.0) ./ 1000
	below_15_coeffs = cubic_profile(-45.0, -15.0, 0.2, -0.1, 0.0, 0.0) ./ 1000
	below_00_coeffs = cubic_profile(-15.0, 0.0, -0.1, -0.02, 0.0, 0.0) ./ 1000
	above_00_coeffs = cubic_profile(0.0, 15.0, -0.02, -0.1, 0.0, 0.0) ./ 1000
	above_15_coeffs = cubic_profile(15.0, 45.0, -0.1, 0.1, 0.0, 0.0) ./ 1000
	above_45_coeffs = cubic_profile(45.0, south_north_limit, 0.1, 0.0, 0.0, 0.0) ./ 1000
	return (below_45_coeffs, below_15_coeffs, below_00_coeffs, above_00_coeffs, above_15_coeffs, above_45_coeffs)
	end

cc @glwagner

[simone-silvestri]

I decided to use a piecewise cubic function for the wind stress (and salinity flux). I guess we could use a parabolic one also

[navidcy]

Is it constant values in between?

[glwagner]

How about

τ₀ * (cos(3π * φ/Δφ) - exp(-φ^2 / 2Δφₑ^2))

?

[navidcy]

I think that should work. Perhaps we should ensure that wind stress goes to zero at the North-South latitudinal boundaries otherwise you get Kelvin waves and circulation at the boundaries.

[glwagner]

Ah nice. Then Δφ is the total latitudinal extent of the domain. Δφₑ is the width of the equatorial bump, typically about 10 degrees latitude. We can also add a parameter to express the relative magnitude of the equatorial bump.