The basic properties of the gradient operator are listed below.
Properties gives the rate of change of in the direction .
It is also called the directional derivative. From the above properties, we see that is a vector whose magnitude and direction gives the maximum rate of change of or, equivalently, the direction of the maximum gradient. A sketch of the isobars and the associated direction of . Note that the force, however, acts from high pressure to low pressure whereas points from low to high. The pressure force is and so in Figure 1.7 the air would flow from high pressure to low pressure.