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This article analyses the assumptions regarding the influence of pressure forces during the calculation of the motion of a Newtonian fluid. The purpose of the analysis is to determine the reasonableness of the assumptions and their impact on the results of the analytical calculation. The connections between equations, causes of discrepancies in exact solutions of the Navier-Stokes equations at low Reynolds numbers and the emergence of unstable solutions using computer programs are also addressed. The necessity to complement the well-known equations of motion in mechanical stress requires other equations are substantive. It is shown that there are three methods of solving such a problem and the requirements for the unknown equations are described. Keywords: Navier-Stokes, approximate equation, closing equations, holonomic system.
We determine how the differences in the treatment of the subfilter-scale physics affect the properties of the flow for three closely related regularizations of Navier-Stokes. The consequences on the applicability of the regularizations as SGS models
Whether the 3D incompressible Navier-Stokes equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this paper, we present some new numerical evidence that the 3D incompre
We accomplish two major tasks. First, we show that the turbulent motion at large scales obeys Gaussian statistics in the interval 0 < Rlambda < 8.8, where Rlambda is the microscale Reynolds number, and that the Gaussian flow breaks down to yield plac
We present a comprehensive study of the statistical features of a three-dimensional time-reversible Navier-Stokes (RNS) system, wherein the standard viscosity $ u$ is replaced by a fluctuating thermostat that dynamically compensates for fluctuations
We study a correspondence between the multifractal model of turbulence and the Navier-Stokes equations in $d$ spatial dimensions by comparing their respective dissipation length scales. In Kolmogorovs 1941 theory the key parameter $h$, which is an ex