Analysis of turbulent flow patterns of soil water under field conditions using Burgers equation and porous suction-cup samplers

This paper presents results using the Burgers equation in spherical coordinates for the investigation of soil water dynamics around porous cup samplers under field conditions. The analysis reveals that the yield (V) of the porous suction-cup sampler is a power function of inflow duration (T) and source moisture strength (A). It also shows that the shock front velocity and moving boundary of the front are both power functions of A and time. The analysis further demonstrates that the asymptotic shock front velocity derived from a similarity solution is the same for different versions of Burgers equation, indicating the validity of different versions of Burgers equation for the flow patterns. The observation using time domain reflectometry shows that a moisture shock was induced around the sampler following application of a vacuum, which justifies the application of Burgers equation. The values of A were derived using field data to determine the location and the front velocity of the shock.