Substituting ϕ, M, B ( eq. (5)) in equations (2), (3), (6), and using some algebraic manipulation, one obtains the system of (7), (8), (9), (10) and (11a,b). The abbreviated symbols u and Δρ are used instead of u(s) and Δρ(s) for the sake of simplicity: equation(7) duds=2gλ2Δρρm0usinθ−2αub, equation(8) dbds=2α−gλ2Δρbρm0u2sinθ, equation(9) dθds=2gλ2Δρρm0u2cosθ, Buparlisib equation(10) dΔρds=(1+λ2)λ2dρmdzsinθ−2αΔρb, equation(11a,b) dxds=cosθ,dzds=sinθ.

The dilution S is defined according to Fan et al. (1966): equation(12) S(s)=4λ2ub2(1+λ2)u0d2. Integration of (7), (8), (9), (10) and (11a,b) begins where the Gaussian profiles (eq. (4)) are fully developed, e.g. at a distance of s  0 = 6.2d   ( Featherstone 1984). The initial velocity u  (s   = s  0 = 6.2d  ) is equal to the mean

exit velocity at the diffuser nozzle 4ϕ0  /(πd  2), whereas the initial plume radius is obtained from the conservation of momentum b0=d/2. The initial deflection of the nozzle axis from the Trichostatin A research buy horizontal plane θ0 retains the same value up to the distance s0 or θ(s = s0 = 6.2d) = θ0 The value θ0 = 00 is used for the numerical simulations, representing a horizontal nozzle set-up. The initial density difference at s0 is assumed with the equality Δρ(s = s0 = 6.2d) = Δρ0 = [(ρ0m – ρ0)(1 + λ2)/(2λ2)], the initial coordinates of the central plume trajectory with x(s = s0 = 6.2d) = x0 = s0 cos θ0 or z(s = s0 = 6.2d) = z0 = s0 sin θ0 and the initial dilution with S(s = s0 = 6.2d) = S0 = 2λ2/(1 + λ2). To solve the system of equations and in order to minimize local errors in the near-field model, the fourth-order Runge-Kutta method with a variable spatial step was used. The model stops the integration when the effluent plume reaches the recipient surface or exceeds the neutral buoyancy level. It should be stressed that some commercially available modelling systems, such as Cormix V6.0

(www.mixzon.com), address the full range of discharge geometries (single or multiport 3D orientation etc.) with different flow configurations (trapped, buoyant or sinking plumes). On the other hand, Cormix requires an analytical scheme of the vertical density distribution. The measured Lepirudin profile should therefore be approximated by one of three proposed stratification profile types. The performance of the near-field model described above (Featherstone 1984) is not restricted in that way, and direct use of the measured density profile is also possible. The dilution at the end of the near field was previously calculated using the Cormix model and Featherstone’s (1984) model for 20 submarine outfalls in the eastern Adriatic (Lončar 2010). In comparison with the Cormix model, the results are on average 5% (10%) greater for dilution during the summer (winter) period than in the model described and used in this study. The greater dilution obtained with the Cormix model is probably the consequence of taking ambient currents into account.