TY - JOUR
T1 - Minimal advective travel time along arbitrary streamlines of porous media flows
T2 - The Fermat-Leibnitz-Bernoulli problem revisited
AU - Kacimov, A. R.
AU - Yakimov, N. D.
PY - 2009/9/15
Y1 - 2009/9/15
N2 - Travel time of marked fluid particles along arbitrary streamlines in arbitrary porous streamtubes is estimated from below based on the Cauchy-Bunyakovskii (Schwartz) and Jensen inequalities. In homogeneous media the estimate is strict and expressed through the length of the streamline, hydraulic conductivity, porosity and the head fall. The minimum is attained at streamlines of unidirectional flow. The bounds for heterogeneous soils, non-Darcian flows and unsaturated media are also written. If such bounds are attained the corresponding trajectories become brachistochrones. For example, in a two-layered aquifer and seepage perpendicular to the layers there is a unique conductivity-porosity ratio which makes a broken streamline brachistocronic. Similarly, if conductivities of two layers are fixed there is a unique incident angle between flow in one medium and the interface which makes a refracted streamline brachistocronic.
AB - Travel time of marked fluid particles along arbitrary streamlines in arbitrary porous streamtubes is estimated from below based on the Cauchy-Bunyakovskii (Schwartz) and Jensen inequalities. In homogeneous media the estimate is strict and expressed through the length of the streamline, hydraulic conductivity, porosity and the head fall. The minimum is attained at streamlines of unidirectional flow. The bounds for heterogeneous soils, non-Darcian flows and unsaturated media are also written. If such bounds are attained the corresponding trajectories become brachistochrones. For example, in a two-layered aquifer and seepage perpendicular to the layers there is a unique conductivity-porosity ratio which makes a broken streamline brachistocronic. Similarly, if conductivities of two layers are fixed there is a unique incident angle between flow in one medium and the interface which makes a refracted streamline brachistocronic.
KW - Darcy's law
KW - Hydraulic conductivity
KW - Integral inequalities
KW - Porosity
KW - Streamline
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U2 - 10.1016/j.jhydrol.2009.06.031
DO - 10.1016/j.jhydrol.2009.06.031
M3 - Article
AN - SCOPUS:69549119084
SN - 0022-1694
VL - 375
SP - 356
EP - 362
JO - Journal of Hydrology
JF - Journal of Hydrology
IS - 3-4
ER -