Further classification of the jet can be related to how the nearfield zone develops due to the compressible effects that govern it. When the jet first exists the orifice or nozzle, it will expand very quickly, resulting in an over-expansion of the flow (which will also reduce the temperature and density of the flow as quickly as it depressurized). Gases that have expanded to a pressure lower than the one of the surrounding fluid will be compressed inwards, causing an increase in the pressure of the flow. If this re-compression leads to the fluid having a higher pressure than the surrounding fluid, another expansion will happen. 
This process will repeat until the pressure difference between ambient pressure and jet pressure is null (or close to null). 
Compression and expansion are accomplished through a series of shock waves, formed as a result of Prandlt-Meyer expansion and compression waves.
Development of the aforementioned shock waves will be related to the difference in pressure between the stagnant conditions or downstream conditions and the ambient conditions (η = P/P and η = P/P, respectively), as well as the mach number (Ma = V/V, where V is the velocity of the flow and V is the speed of sound of the medium). With varying pressure ratios, under-expanded jets can be classified as:
*Moderately under-expanded jet: Nearfield with diamond shaped structures (each structure is called a cell).  A Prandlt-Meyer expansion generates oblique expansion waves that expand the fluid downstream from the exit orifice. As these waves attain constant pressure from the surrounding fluid, they are deflected back as compression waves, converging in oblique shock waves (called intercepting shock). When they meet on the axis of the jet, reflected shock waves move outwardly until they attain constant pressure from the surrounding fluid, repeating the process, and in turn, recreating the cell structure (this phenomenon occurs in air at a range of 2 ≤ η ≤ 4 or 1.1 ≤ η ≤ 3).
*Highly under-expanded jet: Nearfield with barrel shaped structures. As the pressure ratio increases, the intercepting shock waves cant meet on the axis of the jet anymore, which forces the generation of a normal shock wave when the intercepting shock waves go beyond a certain critical angle (The normal shock wave is called Mach Disk). From the interception point of the mach disk and the intercepting shock', a residual slipstream will reflect outwardly, until it reaches constant pressure from the surrounding fluid, repeating the process, recreating the barrel shaped cell structure (this phenomenon occurs in air at a range of 5 ≤ η ≤ 7 or 2 ≤ η ≤ 4 ).
*Extremely under-expanded jet: Nearfield with a single cell structure. When the pressure ratio goes beyond a critical value (in air at a range of η ≥ 7 or η ≥ 4 ), cell numbers within the nearfield of the jet decrease, until they all coalesce into a single cell with a single mach disk. Due to the increase in velocity and lower pressure zones around the jet, ambient fluid entrainment will increase.