Effect of complex hydraulic variables and physicochemical factors on freshwater mussel density in the largest floodplain lake, China

Ecological Processes

Table 3 Calculation of complex hydraulic variables for four habitats in Poyang Lake

Complex hydraulic variables	Formula	Description
Substrate variables
D (mm)	Laser diffraction particle size analyzer	Mean particle size
Sorting index (S_o, unitless)	\(\frac{\varphi 84-\varphi 16}{2}\)	Substrate heterogeneity
Bed roughness (k_s, mm)	2 \(\times D50\)	Topographical variation of river bed
Hydraulic variables
Froude number (Fr, unitless)	\(\sqrt{\frac{{U}^{2}}{gd}}\)	Ratio of inertial to gravitational forces
Reynolds number (Re, unitless)	\(\frac{ud}{v}\)	Turbulence of free flow
Boundary Reynolds number (Re_*, unitless)	\(\frac{U{k}_{\mathrm{s}}}{v}\)	Near-bed turbulence
Shear velocity (V, m/s)	\(\sqrt{\frac{\tau }{\rho }}\)	Friction velocity
Shear stress (τ, N/m²)	ρ (u_*²)	Force of friction on substrate
Critical shear stress (τ_c, N/m²)	θ_cgD₅₀ (ρ_s–ρ)	Shear stress required to initiate substrate motion

D = the substrate size in the sample (mm), d = water depth (m), ϕ = phi unit size of the substrate size (ϕ = − log₂D [mm]); ϕx = percentage of substrate with particle size x in the sample, U = average velocity (m/s), g = acceleration of gravity (9.8 m/s), v = dynamic viscosity of water (0.0000176 m/s), ρ = density of water (996 kg/m³, average temperature 28 ℃), ρs = density of substrate (2730 kg/s), θc = masking parameter (0.035) (Gordon et al. 2004)