The challenge of fluid flow 1. The diversity of flow phenomena

Abstract

You look up at the sky, and see a lovely cloud; you look down, and may see lovely ripples on a rivulet (or river). On a hot summer afternoon you see dancing dust devils; on a cold winter evening you can see smoke rising lazily from achulah, and hang up there as if it has given up. You peer at a telescope, and see intense supersonic jets, or vast whirling galaxies; you measure in a wind tunnel, and sense powerful tornadoes behind an aircraft wing. The universe is full of fluid that flows in crazy, beautiful or fearsome ways. In our machines and in the lab, as in terrestrial nature, one sees this amazing diversity in the flow of such a simple liquid like water or a simple gas like air. What is it that makes fluid flows so rich, so complex-some times so highly ordered that their patterns can adorn a saree border, sometimes so chaotic as to defy analysis? Do thesame laws governall that extraordinary variety? We begin with a picture gallery of a number of visible or visualized flows, and consider which ones we understand and which ones we do not, which ones we can compute and which ones we cannot; and it will be argued that behind those all-too-common but lovely flows lie deep problems in physics and mathematics that still remain mysteries.