2. The blown‐up of fluid and two‐phaseness of currents and waves

In this paper, mathematical properties of nonlinearity of the equations in Navier‐Stokes model of currents are studied based on the reasoning logic of systems evolutions, combined with methods of analysis and synthesis. It is discovered that the derivative terms are the same as the nonlinear forcing term, in that they all evolve with time and contain discontinuous reversing changes. Consequently, a theoretical and application system is proposed. The concept of blown‐ups constitutes a key step toward the understanding of whole evolution of non‐linear models. The range of applications of this concept is not only limited to research of almost 240‐years‐old mystery of the nonlinearity of currents, but also encompasses the reconsideration of many important principled issues in various theoretical disciplines and related applications.