BREE 533 Lecture Notes - Lecture 7: Recreation Area, Advection, Reynolds Number
23 Jan 2018
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Diffusion and dispersion: diffusion is the random advection of tracer molecules on scales smaller than some defined length scale. Turbulent and laminar flow: re(cid:455)(cid:374)old"s (cid:374)u(cid:373)(cid:271)e(cid:396, tu(cid:396)(cid:271)ule(cid:374)t diffusio(cid:374): (cid:272)aused (cid:271)(cid:455) tu(cid:396)(cid:271)ule(cid:374)(cid:272)e. Fick"s law (cid:894)microscopic(cid:895: dispe(cid:396)si(cid:448)e (cid:373)ass flu(cid:454) is p(cid:396)opo(cid:396)tio(cid:374)al to (cid:272)o(cid:374)(cid:272)e(cid:374)t(cid:396)atio(cid:374) g(cid:396)adie(cid:374)t (cid:894)(cid:396)e(cid:272)all da(cid:396)(cid:272)(cid:455)"s la(cid:449)(cid:895) (cid:2186)= ((cid:2185)/) (cid:2186) is dispersive mass flux (m/(l2t)) D is the dispersion coefficient tensor (l2/t) c is the concentration of the solute/contaminant (m/l3). Advective flow (macroscopic, larger scale: flu(cid:454) asso(cid:272)iated (cid:449)ith the la(cid:396)ge(cid:396)-scale (advective) fluid motions: Vi is the large scale fluid velocity (l/t) c is the concentration of the solute/contaminant (m/l3). Advection-dispersion equation: t(cid:396)a(cid:272)e(cid:396)s a(cid:396)e t(cid:396)a(cid:374)spo(cid:396)ted si(cid:373)ulta(cid:374)eousl(cid:455) (cid:271)(cid:455) (cid:271)oth ad(cid:448)e(cid:272)tio(cid:374) & dispe(cid:396)sio(cid:374), the total flu(cid:454) of a tracer (qi)is given by, ad(cid:448)e(cid:272)tio(cid:374)-dispe(cid:396)sio(cid:374) e(cid:395)uatio(cid:374) (cid:894)fi(cid:272)k"s la(cid:449) + (cid:373)ass (cid:272)o(cid:374)se(cid:396)(cid:448)atio(cid:374) la(cid:449)-tracer mass neither created nor distroyed): If a tracer of mass m is introduced instantaneously at x=0 at time t=0, and the tracer concentrations are always=0 at x= infinite.
