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Full-Text Articles in Physical Sciences and Mathematics
Kinematics Of Fluids, Andrei Ludu
Kinematics Of Fluids, Andrei Ludu
Publications
The goal of this chapter is to discuss the general frame of hydrodynamics, like particle trajectories (path lines), streamlines, streak lines, free surfaces, and fluid surfaces, and to compare their behavior in the Eulerian and Lagrangian frames. The following sections and chapters proceed on the assumption that the fluid is practically continuous and homogeneous in structure. Of course, the concept of continuum is an abstraction that does not take into account the molecular and nuclear structure of matter. In that, we assume that the properties of the fluid do not change if we consider smaller and smaller amounts of matter …
Hydrodynamics, Andrei Ludu
Hydrodynamics, Andrei Ludu
Publications
The mathematical description of the states of a fluid is based on the study of three fields defined on the domain occupied by the fluid: the velocity field V, the density ρ, and the pressure field P. These three “unknowns” are determined by integrating other five scalar equations, namely the mass conservation (continuity equation), the three components of the equation of momentum balance (Euler or Navier–Stokes), and the energy balance. This last equation needs in addition information about the thermodynamics of the fluid, so it may need to be supplied with some equation of state. In addition to these five …
The Replacement Rule For Nonlinear Shallow Water Waves, A. Ludu, Z. Zong
The Replacement Rule For Nonlinear Shallow Water Waves, A. Ludu, Z. Zong
Publications
When a (1 + 1)-dimensional nonlinear PDE in real function η(x, t) admits localized traveling solutions we can consider L to be the average width of the envelope, A the average value of the amplitude of the envelope, and V the group velocity of such a solution. The replacement rule (RR or nonlinear dispersion relation) procedure is able to provide a simple qualitative relation between these three parameters, without actually solve the equation. Examples are provided from KdV, C-H and BBM equations, but the procedure appears to be almost universally valid for such (1 + 1)-dimensional nonlinear PDE and their …