Why are the turbulent temperature and moisture flux scales reduced by the turbulent Prandtl number?

[glwagner]

Why these lines?

ClimaOcean.jl/src/OceanSeaIceModels/CrossRealmFluxes/similarity_theory_turbulent_fluxes.jl

Lines 256 to 257 in 10a3375

	θ★ = θ★ / similarity_theory.turbulent_prandtl_number
	q★ = q★ / similarity_theory.turbulent_prandtl_number

[glwagner]

cc @simone-silvestri

[simone-silvestri]

The turbulent Prandtl number scales the size of the thermal (and scalar) boundary layer with respect to the momentum boundary layer. By default is one though.

[glwagner]

The question is why this gets applied here, after solving for the scales. It this consistent with

ClimaOcean.jl/src/OceanSeaIceModels/CrossRealmFluxes/similarity_theory_turbulent_fluxes.jl

Line 386 in 10a3375

θ★ = χθ * Δθ

For example, when we compute the buoyancy scale:

ClimaOcean.jl/src/OceanSeaIceModels/CrossRealmFluxes/similarity_theory_turbulent_fluxes.jl

Line 364 in 10a3375

b★ = buoyancy_scale(θ★, q★, 𝒬ₒ, ℂ, g)

We assume that θ★ is the scale for the temperature flux. But if the actual temperature flux is θ★ / similarity_theory.turbulent_prandtl_number then this also needs to be incorporated into computing the buoyancy scale.