ABSTRACT

The concepts and numerical methods from fluid dynamics and continuum mechanics are powerful tools for solving problems in root physiology. The methods of “kinematics,” i.e., the study of motion or shape change in fluids and continuua, are particularly relevant. (A distinction is made between kinematics and “dynamics,” the study of the forces and energies that produce the observed motions and shape changes.) Applications of kinematic analyses include consideration of the “material” aspects of root development to elucidate spatial-temporal relationships in growing tissue. Growth itself can be characterized in terms of relative elemental rates, analogous to strain rates used in continuum mechanics. In structural studies, kinematic expressions can be used to find basic physical relationships among growth rates, cell division rates, anatomy, and

morphology. In studies of mineral nutrition, kinematic expressions allow us to find local nutrient deposition rates in expanding tissue from spatial concentration patterns. In ecological studies, the growth strain rate field provides a quantitative characterization of effects of environmental variation on growth. And some basic ideas from growth kinematics, including the use of a moving reference frame attached to the growing root tip, allow us to understand the relationship between the growth zone and its rhizosphere.