Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 13 (2020), 97–99 Research Article ISSN: 2008-1898 Journal Homepage: www.isr-publications.com/jnsa Modeling turbulence with the Navier-Stokes equations Bertrand Wong Department of Science and Technology, Eurotech, Singapore Branch. Abstract The Navier-Stokes differential equations describe the motion of fluids which are incompressible. The three-dimensional Navier-Stokes equations misbehave very badly although they are relatively simple-looking. The solutions could wind up be- ing extremely unstable even with nice, smooth, reasonably harmless initial conditions. A mathematical understanding of the outrageous behaviour of these equations would dramatically alter the field of fluid mechanics. This paper describes why the three-dimensional Navier-Stokes equations are not solvable, i.e., the equations cannot be used to model turbulence, which is a three-dimensional phenomenon. Keywords: Navier-Stokes equations, turbulence, forecast, geometries, solutions, experimentalist. 2010 MSC: 76F02, 76F55. c 2020 All rights reserved. 1. The Navier-Stokes equations The general equations of motion for a viscous fluid were obtained by Sir George Stokes in 1845. The following is the fundamental equation (in vectorial form) governing the flow of a viscous fluid: ∂v ∂t +(v.▽)v =- 1 ∂p ▽Pe - ▽φ + ∂η ∂p ▽2v, where v is the velocity of the fluid (as a function of position), Pe is the pressure, φ the gravitational potential, p the density, and η the viscosity. A fluid in motion could be characterized by its velocity field (velocity as a function of position). How- ever, because of the complex nature of the forces affecting fluids (in general, forces of both compression and viscosity) the result of applying basic principles such as Newton’s second law is a set of nonlinear equations. Computational methods therefore play a large part in fluid dynamics. Newton’s second law states that the rate of change of momentum p of a body equals the total force F acting upon it, as is described by the following equation: F = ∂p/∂t. Email address: bwong8@singnet.com.sg (Bertrand Wong) doi: 10.22436/jnsa.013.02.03 Received: 2019-06-26 Revised: 2019-08-06 Accepted: 2019-08-31