Experimental study of the density influence on the incipient motion and erosion modes of muds in unidirectional flows: the case of Huangmaohai Estuary

Abstract

The incipient motion and erosion behavior of bottom muds in coastal areas have wide applications in coastal engineering, water environment management, and also the protection of marine benthic communities. Due to the strong inter-particle cohesion of fine sediments and the diversity in its physical properties, the mechanism of the coastal mud erosion is not well understood and the determination of the threshold for the incipient motion remains a challenge. In order to investigate the influence of the mud density on the incipient motion of fully disturbed coastal mud, experiments were carried out using a 22-m-long laboratory flume and mud samples from Huangmaohai Estuary, South China Sea. Muds with densities ranging from 1100 to 1550 kg/m³ were tested under unidirectional open channel flows, which yielded threshold velocities ranging from 0.11 to 1.67 m/s, corresponding to bed shear stresses ranging from 0.029 to 4.191 N/m². Based on the experimental results, an empirical formula for the threshold velocity at the incipient motion of coastal muds with different densities is presented. The computed results together with the proposed formula were also compared with other theories. Besides, four different erosion patterns of coastal muds at incipient motion were identified according to experimental observations, namely erosion in the pattern of fluid muds, strips, pieces, and blocks. The physical mechanisms for different erosion patterns were also analyzed and interpreted. The presented experimental achievements well enrich our knowledge of coastal mud behavior and lead to a deeper understanding of the mechanisms of the incipient motion of bottom muds.

Appendix

The methodology used to derive the bed shear stress and the mean flow velocity is shown here. For fully developed turbulent open channel flows, the velocity profile over water depth is assumed following a Prandtl–von Karman log profile:

$$ U(z)=\frac{U_{*}}{\kappa } \ln \left(\frac{z}{z_0}\right) $$

(5)

where κ is the von Karman constant, usually κ = 0.4; z is the water depth; z ₀ is a coefficient depending on wall roughness, which takes z ₀ = ν/(9U _*) for a hydraulically smooth bed; and ν is the kinematic viscosity of water. The velocity distribution is converted to the mean flow velocity by integration over the depth, namely:

$$ \overline{U}=\frac{1}{h}{\displaystyle {\int}_{z_0}^hU(z)dz} $$

(6)

By substituting Eq. (5) into Eq. (6), we get:

$$ \overline{U}=\frac{u_{*}}{\kappa}\left[ \ln \left(\frac{h}{z_0}\right)-1\right] $$

(7)

where z ₀ is small relative to h.

To convert the bed shear stress at incipient motion to the expression in the mean flow velocity, the threshold velocity V _c can be expressed in

$$ {V}_c=f\left({\rho}_{\mathrm{m}},h\right) $$

(8)

where ρ _m and h is the mud density and water depth, respectively. For the practical conditions in coastal engineering, where flow velocity is usually low, we assume that the flow is within the range of hydraulically smooth turbulence. Therefore, we get

$$ {z}_0=\nu /\left(9{u}_{*}\right)=\nu /\left(9\sqrt{\frac{\tau_b}{\rho }}\right) $$

(9)

By substituting Eq. (4) into Eq. (9), we get

$$ {z}_0=\nu /\left(9\sqrt{\frac{C_1{\left({\rho}_{\mathrm{m}}-\rho \right)}^{C_2}}{\rho }}\right) $$

(10)

By substituting Eq. (10) into Eq. (7), the following equation is obtained:

$$ {V}_c=\sqrt{\frac{C_1{\left({\rho}_{\mathrm{m}}-\rho \right)}^{C_2}}{\kappa^2\rho }}\left[ \ln \left(\frac{9h}{\nu}\sqrt{\frac{C_1{\left({\rho}_{\mathrm{m}}-\rho \right)}^{C_2}}{\rho }}\right)- \ln (h)-1\right] $$

(11)

where κ is the Karman constant approximated at 0.4.