The Structured Wall-Turbulence, a Galilean Relativistic Phenomenon

Abstract

The relationship between heavenly bodies and earthly behavior along with its importance took many centuries before the rigor scientific understanding enabled the true influences on Earth, such as its complicated motion and perceived other regularities in the behavior of earthly objects. One of these was the tendency for all things in one vicinity to move in the same downward direction according to the influence that is known as gravity property. Moreover, matter was observed to transform, sometimes, from one form into another, such as with melting of ice or vaporizing/cavitation of water, but the total quantity of that matter never seemed to change, which reflects the law at which we now refer to as the conservation/ integrity of mass, including its latent energy. Much latter it is noticed that planet Earth forms a self-regulating complex system, i.e. the Earth’s surface is alive, that is known as the Gaia hypothesis, reflected in the Newton-Galilei dynamics through the law of equal action and reaction for stress vector and tensor, respectively. In addition, at was noticed that there are many material bodies with the important property that they retain their shapes, excepting the flowing fluids, whence the idea of rigid spatial motion arose, and it becomes possible to understood spatial relationships in terms a precise, well-defined geometry, the Euclidian three-dimensional geometry. Though the heavenly bodies are permanently moving in a self-built on universe like a timeless perpetuum mobile, the time remains an important property for the behaviors/motions of an Earth-bound object due to their relativity as against the diurnal rotation depending on the velocities of the impacted object. In contrast to the constant inertia condition where for small starting velocities and accelerations the Newton’s determinist principle is applied, the onset of a motion of the Earth-bound material bodies, at higher velocities and accelerations (O(g)), involves changes of moving matter/inertia under influence of gravitational field via some intrinsic latent motions/processes. They achieve the kinetic-gravitational mutual energy transfer obeying the Galilei’s law of inertia for self-equilibrating impact forces. The intrinsic motions, at the cellular scale (10-6 m), are responsible for the kinetic trinity of the momentum, kinetic energy and power, and they represent what it is called structured turbulence, i.e. a Galilean space-time structure according to the mathematical idea of a bundle (or fibre bundle) and its gauge connection. The bundle and gauge connection are a kind of Galilean transformation to a system moving with constant velocity carrying its relativistic non-inertial fraction as a blend of structure less turbulence and non-rigorously defined intermittency of a non-inertial motion.