Kinematics of plant growth

Abstract

Many of the concepts and equations which have been used in the study of compressible fluids can be applied to problems of plant development. Growth field variables, i.e. functions of position in the plant and of time, can be specified in either Eulerian (spatial) or Lagrangian (material) terms. The two specifications coincide only when the spatial distribution of the variable is steady, and steady patterns are most likely to emerge when an apex is chosen as origin of the co-ordinate system. The growth field itself can be described locally by the magnitude and orientation of the principal axes of the rate of strain tensor and by the vorticity tensor. Material derivatives can be calculated if the temporal and spatial variation in both growth velocity, u (rate of displacement from a material origin), and the variable of interest are known. The equation of continuity shows the importance of including both growth velocity, u, and growth rate, ▽ ·u in estimates of local biosynthesis and transport rates in expanding tissue, although the classical continuity equation must be modified to accommodate the compartmentalized distributions characteristic of plant tissue. Relatively little information on spatial variation in plant organs can be found in the botanical literature, but the current availability of interactive computer graphics equipment suggests that analysis of the spatial distribution of growth rates at least is no longer difficult.