Abstract. In this study, a dimensionally consistent governing equation of
transient unconfined groundwater flow in fractional time and
multi-fractional space is developed. First, a fractional continuity equation
for transient unconfined groundwater flow is developed in fractional time
and space. For the equation of groundwater motion within a multi-fractional
multidimensional unconfined aquifer, a previously developed dimensionally
consistent equation for water flux in unsaturated/saturated porous media is
combined with the Dupuit approximation to obtain an equation for groundwater
motion in multi-fractional space in unconfined aquifers. Combining the
fractional continuity and groundwater motion equations, the fractional
governing equation of transient unconfined aquifer flow is then obtained.
Finally, two numerical applications to unconfined aquifer groundwater flow
are presented to show the skills of the proposed fractional governing
equation. As shown in one of the numerical applications, the newly developed
governing equation can produce heavy-tailed recession behavior in unconfined
aquifer discharges.
Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time
