Table 6 Diffusion coefficients (D_L, D_y) using Empirical equations for free flow

Elder [32]

\(D_{{_{L} }} = 5.93hu_{ * }\)

341.00

Fisher [33]

\(D_{L} = 0.11\left( {\frac{{w^{2} }}{h}} \right)\left( {\frac{{u^{2} }}{{u_{ * } }}} \right)\)

1.72–6.89

Liu [34]

\(D_{L} = \beta \frac{{w^{2} u^{2} }}{{hu_{ * } }}\beta = 0.18\left( {\frac{{u_{ * } }}{u}} \right)^{1.5}\)

21.25–29.91

Seo and Cheng [35]

\(D_{L} = 5.915hu_{ * } \left( {\frac{w}{h}} \right)^{0.62} \left( {\frac{u}{{u_{ * } }}} \right)^{1.428}\)

76.71–206.42

Kashefipour and Falconer [36]

\(D_{L} = 10.612hu\frac{u}{{u_{ * } }}\)

41.52–166.07

\(D_{L} = \left[ {7.428 + 1.775\left( {\frac{w}{h}} \right)^{0.62} \left( {\frac{{u_{ * } }}{u}} \right)^{0.572} } \right]hu\frac{u}{{u_{{_{*} }} }}\)

52.08–178.19

GA model [37]

\(D_{L} = 2\left( {\frac{w}{h}} \right)^{0.96} \left( {\frac{u}{{u_{ * } }}} \right)^{1.25}\)

41.71–99.19

Li et al. [38]

\(D_{y} = 0.062\left( {\frac{w}{h}} \right)^{0.277} hu_{ * }\)

4.32

Deng et al. [39]

\(D_{y} = 0.16hu_{ * }\)

9.12