03cm−c1.5,μ0+μ2ρsd2=0.02cm−c1.75, where d – grain diameter of the seabed soil. The value φ in (11) and (12) is the quasi-static angle of internal friction, while the angle ψ between the major principal stress and the horizontal axis (for simple shear flow) is equal to equation(14) ψ=π4−φ2. see more In the calculations the following values are assumed:

equation(15) α0ρsgd=1,cm=0.53,c0=0.32,φ=24.4°. All of the parameters and constants used in the bedload model have remained unchanged since the model was tested by Kaczmarek & Ostrowski (2002). In the contact load layer, following Deigaard (1993), the sediment velocity and concentration are modelled using the equations below (with the vertical axis z directed upwards from the theoretical bed level): equation(16) 32αdwsdudz23s+cMcD+β2d2c2s+cM+l2dudz2=uf′2, equation(17) 3αdwsdudz23s+cMcD+β2d2dudzc+l2dudzdcdz=−wsc. The term uf′2(ωt)

is related to the ‘skin friction’, calculated by Fredsøe’s (1984) model for the ‘skin’ roughness k′e = 2.5d. In   equations(16) and (17)ws denotes the settling velocity of grains, s stands for the relative soil density (ρs/ρ), cM and cD are the added mass and drag coefficients, respectively, α and β are the coefficients introduced by Deigaard (1993), and l is the mixing length defined as l = κz (where κ is the von Karman constant). Assuming that the sediment velocity distribution in the contact load layer is logarithmic at a certain distance from the bed and that the roughness related Selleck SCH772984 to this profile depends on the coefficient α, an iterative procedure was proposed by Kaczmarek & Ostrowski (1998) to find this PRKACG coefficient. It is further assumed that the coefficients α and β in the contact load model are equal. Parameters cD and cM were selected during the testing of the model; they have remained unchanged since the publication of Kaczmarek & Ostrowski (2002). Their values,

together with some other important constants, are given in Table 1. The instantaneous sediment transport rates are computed from distributions of velocity and concentration in the bedload layer and in the contact load layer: equation(18) qb+c(t)=∫0δbu(z′,t)c(z′,t)dz′+∫ke′/30δcu(z,t)c(z,t)dz, where δb(ωt) is the bedload layer thickness and δc denotes the upper limit of the nearbed suspension (contact load layer thickness). The quantity δb results from the solution of (11) and (12), while the value of δc is the characteristic boundary layer thickness calculated on the basis of Fredsøe’s (1984) approach (see Kaczmarek & Ostrowski 2002). The net transport rate in the bedload and contact load layers is calculated as follows: equation(19) qb+qc=1T∫0Tqb+ctdt.