To identify the relevant parameters of the 3D simulations which trigger the differences with the 2D results, the relative error between the depth-averaged velocity magnitudes ΔV_2D−3D,rel was correlated to depth-averaged turbulence-related quantities from the 3D simulations: the turbulence intensity I = (2/3 k)^1/2/⁠, where k is the turbulent kinetic energy; the eddy viscosity ν_T; the non-dimensional horizontal and vertical vorticity components = (ω_hor h)/V and = (ω_vert h)/V, which are related to the shear layers in the vertical and horizontal planes, respectively, and are evaluated from the depth-averaged vorticity components ω_hor and ω_vert. The relative velocity error was also correlated to the absolute horizontal angle between the velocities at the surface and at the bottom of each stack of cells in the 3D model, |Δdir_s-b| = |dir(v_s)−dir(v_b)|, which is an efficient index of the local three-dimensional character of the flow field. The Pearson correlation coefficients are listed in Table 1 for the four discussed flow cases in the concave elliptical basin: constant W₁₀ = 11 m/s wind, IBL W_10,l = 10 m/s wind, IBL wind with η = +0.7 m, IBL wind with η = −0.7 m.

Table 1

Correlation coefficients between ΔV_2D−3D,rel and the selected variables from the 3D simulations on the test elliptical lake (non-significant values with p > 0.01 are in italics)

τs distribution .	Constant .	IBL .	IBL .	IBL .
η [m] .	0 .	0 .	+ 0.7 .	−0.7 .
I	0.360	0.342	0.368	0.522
νT	0.271	0.261	0.188	0.061
	0.623	0.810	0.960	0.743
	0.321	0.100	0.376	0.163
|Δdirs-b|	0.322	0.373	0.308	0.429

τs distribution .	Constant .	IBL .	IBL .	IBL .
η [m] .	0 .	0 .	+ 0.7 .	−0.7 .
I	0.360	0.342	0.368	0.522
νT	0.271	0.261	0.188	0.061
	0.623	0.810	0.960	0.743
	0.321	0.100	0.376	0.163
|Δdirs-b|	0.322	0.373	0.308	0.429

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