The Continuity Equation and Divergence - Department of Earth 地球的连续性方程与发散-.docVIP

The Continuity Equation and Divergence 1. General The Continuity Equation is a restatement of the principle of Conservation of Mass applied to the atmosphere. The principle simply states that matter can neither be created or destroyed and implies for the atmosphere that its mass may be redistributed but can never be disappeared. The Equation of Continuity restates this by telling us that there are TWO basic ways to change the amount of air (density ) within fixed volume of air (an air column, for the sake of this discussion, fixed with respect to the earth and extending from the ground to the top of the atmosphere): (i) if air is flowing laterally through the air column, have the upstream air more (less) dense than the downstream air, hence, air of different density replaces the air in the air column (density advection) (Fig.1); and (ii) even if density is everywhere constant, remove air from the air column (called three dimensional divergence) (Fig. 2). Changes in Density Within An Air are Density Velocity Column Fixed due and/or With Respect to to Advection Divergence the Earth QUALITATIVE EQUATION OF CONTINUITY The Equation of Continuity therefore is: (1) where DIV3d is the three dimensional divergence, which in rectangular coordinates is (2) Example 1. and if positive, contributes to density rises, and states that the advection is the negative of the product of the wind speed and the (change in density in a unit amount of distance). Actually, the concept of advection is very important in many areas of synoptic analysis. Advection is always found by finding the product of the wind speed and the gradient of a quantity (say, temperature). Figure 1: Schematic chart illustrating density advection (wind speed constant) locally increasing the density (mass) in a fixed air column. Example 2: Figure 2: Schematic chart illustrating wind divergence (density constant) locally decreasing density (mass)