It is generally believed that low Mach number, i.e., low-velocity, flow may be assumed to be incompressible flow. Under steady-state conditions, an exact equation of continuity may then be used to show that such flow is non-divergent. However, a rigorous, compressible fluid-dynamical derivation proves that the acceleration of fluid in radial laminar motion between parallel disks is proportional to the divergence of the velocity, and, to the contrary, velocity would be constant in non-divergent flow. Briefly, for an ideal gas in steady-state, laminar, and frictionless flow, four equations may be derived to solve the system exactly for the four unknowns -- density, pressure, temperature, and velocity -- without assuming incompressibility or non-divergence. This work shows that this finding is true for water as well. It also exploits the new theory to show that turbulent boundary layers, including jets and plumes, must consist of low-density fluid that expresses some of the corresponding low pressure through the equation of state. In the final analysis, the divergence of the fluid is established to be one of the basic mechanisms that causes turbulent flows to mix with the ambient fluid. The relationship between acceleration and divergence helps explain the role of jets in mixing. Similarly, it helps to explain jet and plume entrainment, including the entrainment of ambient fluid into oceanic megaplumes of volcanic origin.
Produce a computer model utilizing water transport estimates or real-time current-meter data to track the motion of contaminants from point and other sources, and to predict the concentration of pathogens or other pollutants at beach and other sensitive sites.