The divergence formula of two-dimensional vector is a mathematical tool to describe the divergence or convergence degree of vector field in a certain region. Common divergence formulas for two-dimensional vectors are as follows:

Divergence formula in 1. Cartesian coordinate system: For a vector field F(x, y)=(P(x, y), Q(x, y)), its divergence S is defined as: S=_P/_x+_Q/_y at point (x, y). This formula represents the sum of the change rate of the component of the vector field in the X axis direction and the component in the Y axis direction.

2. Divergence formula in polar coordinate system: For a vector field F(r, θ)=(P(r, θ), Q(r, θ)), its divergence S is defined as: s = r 2 * (_ p/_ r+_ q/_ θ) at point (r, θ). This formula represents the sum of the rate of change of the radial component and the angular component of the vector field.

3. Divergence formula in cylindrical coordinate system: For a vector field F(r, φ, z)=(P(r, φ, z), Q(r, φ, z), R(r, φ, z)), its divergence S is defined as: s = at point (r, φ, z). This formula represents the sum of the change rates of the components of the vector field in radial direction, angular direction and height direction.

4. Divergence formula in spherical coordinate system: For a vector field F(r, θ, φ)=(P(r, θ, φ), Q(r, θ, φ), R(r, θ, φ)), its divergence S is defined as: s = at point (r, θ, φ). This formula represents the sum of the component change rates of the vector field in radial, angular and azimuth directions.

These divergence formulas have different forms in different coordinate systems, but their essence is to describe the divergence or convergence of vector fields in all directions. By calculating divergence, we can understand the properties of vector fields, such as whether they are active or sink, and their strength and direction.