Abstract. A theory of dipole flow is developed to model flow induced by a vertical circulation well consisting of injection and extraction chambers in a single borehole. Included in the theory are an analytical description of the kinematic flow structure around a vertical circulation well and the drawdown in the well chambers. Using Stokes' stream function, simple criteria are derived to determine the region of intensive recirculation. This region extends (from the dipole center) approximately five distances between chamber centers in the radial direction and two distances between chamber centers in both vertical directions. The vertical scale does not depend on anisotropy of hydraulic conductivity, and the radial scale is corrected for anisotropic aquifers. Based on these estimates, criteria are given for the selection of the appropriate aquifer model to employ in five settings, including infinite, semi-infinite confined, semi-infinite unconfined, finite confined, and finite unconfined aquifers. Applications of dipole flow theory are given for analytical estimation of the capture zone for recirculation wells and for simultaneous measurement of horizontal and vertical hydraulic conductivity in uniform anisotropic aquifers using steady state measurements of drawdown in the well chambers.

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Trees grow by vertically extending their stems, so accurate stem hydraulic models are fundamental to understanding the hydraulic challenges faced by tall trees. Using a literature survey, we showed that many tree species exhibit continuous vertical variation in hydraulic traits. To examine the effects of this variation on hydraulic function, we developed a spatially explicit, analytical water transport model for stems. Our model allows Huber ratio, stem-saturated conductivity, pressure at 50% loss of conductivity, leaf area, and transpiration rate to vary continuously along the hydraulic path. Predictions from our model differ from a matric flux potential model parameterized with uniform traits. Analyses show that cavitation is a whole-stem emergent property resulting from non-linear pressure-conductivity feedbacks that, with gravity, cause impaired water transport to accumulate along the path. Because of the compounding effects of vertical trait variation on hydraulic function, growing proportionally more sapwood and building tapered xylem with height, as well as reducing xylem vulnerability only at branch tips while maintaining transport capacity at the stem base, can compensate for these effects. We therefore conclude that the adaptive significance of vertical variation in stem hydraulic traits is to allow trees to grow tall and tolerate operating near their hydraulic limits.

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Syntrophic systems are common in nature and include forms of obligate mutualisms in which each participating organism or component of an organism obtains from the other an essential nutrient or metabolic product that it cannot provide for itself. Models of how these complementary resources are allocated between partners often assume optimal behavior, but whether mechanisms enabling global control exist in syntrophic systems, and what form they might take, is unknown. Recognizing that growth of plant organs that supply complementary resources, like roots and shoots, can occur autonomously, we present a theory of plant growth in which rootshoot allocation is determined by purely local rules. Each organ uses as much as it can of its locally produced or acquired resource (inorganic nitrogen or photosynthate) and shares only the surplus. Subject to stoichiometric conditions that likely hold for most plants, purely local rules produce the same optimal allocation as would global