A two-dimensional (2D), solenoidal vector field  may be described by a scalar stream function , via , where  is the right-handed unit vector perpendicular to the 2D plane. By definition, the stream function is related to the vorticity  via a Poisson equation:  . The Lamb–Chaplygin model follows from demanding the following characteristics: 
* The dipole has a circular atmosphere/separatrix with radius : .
* The dipole propages through an otherwise irrorational fluid ( at translation velocity .    
* The flow is steady in the co-moving frame of reference: .
* Inside the atmosphere, there is a linear relation between the vorticity and the stream function 
The solution  in cylindrical coordinates (), in the co-moving frame of reference reads:
where  are the zeroth and first Bessel functions of the first kind, respectively. Further, the value of  is such that , the first non-trivial zero of the first Bessel function of the first kind.