Visualizing the Meanings of Mathematical Expressions Used in Fluid Mechanics, Oceanography, and Ocean Engineering

Abstract

This paper calls attention to a tool and an approach that can facilitate understanding the mathematical expressions commonly used to describe fluid flows. The tool recommended is the ducted rotor current meter. This device can visually represent changes in flow speed through the use of moving parts that can be observed, photographed, or videotaped. Being ducted, this device also facilitates visualizing flows that have been divided into components moving along whatever coordinate axes have been chosen. For visualizing the meanings of the mathematical expressions used in fluid mechanics, oceanography, and ocean engineering, ducted rotors must be used in arrays, most often in pairs or groups of four. The approach recommended is less important for visualizing the meanings of the simplest mathematical expressions such as the partial derivatives that describe gradients of velocity shear. The same approach becomes more important for visualizing the meanings of the more complicated mathematical expressions such as those that describe rotational flow fields or nonlinear accelerations.