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International Journal of Fluid Mechanics Research
ESCI SJR: 0.22 SNIP: 0.446 CiteScore™: 0.5

ISSN Print: 1064-2277
ISSN Online: 2152-5110

International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v40.i2.50
pages 148-158

Inviscid Flow Arrangements in Fluid Dynamics

Allan Runstedtler
Natural Resources Canada


It is common knowledge that, as the Reynolds number increases, flows lose their ability to damp out disturbances and they are increasingly composed of swirling eddies or vortices. This work proposes that the formation of inviscid flow arrangements is the mechanism that is responsible for these observations. Inviscid flow arrangements are flows of viscous fluids in which viscous forces vanish, not to be confused with inviscid fluids which have zero viscosity. The presentation begins with analysis of the viscous terms in the Navier−Stokes equation, showing that it is possible to arrange the flow of a viscous fluid so that viscous forces vanish, that these arrangements are vortex-like, and that inviscid arrangements are most likely to form in flow conditions corresponding to high Reynolds number. The author proposes that hurricanes, tornadoes, sink drain vortices, and turbulence are among the possible consequences. To the author's knowledge, this concept has not been presented in the scientific literature. A numerical study is then presented of laminar pipe flow subjected to a disturbance to determine if inviscid flow arrangements form and to study their behavior. An important emphasis is the inclusion of the disturbance in the Reynolds number. Using a novel method to visualize the deviation from laminar flow, inviscid flow arrangements are found to increasingly form as the Reynolds number increases. If it is true that inviscid flow arrangements play a key role in turbulence, then it is ironic that the phenomenon which increases the effective viscosity of a flow is actually a result of the tendency to eliminate the viscous force.


  1. Potter, M. C. and Wiggert, D. C. , Mechanics of Fluids.

  2. Melander, M. V. and Hussain, F. , Core Dynamics on a Vortex Column.

  3. Markoff, J. , Nature Gave Him a Blueprint, but Not Overnight Success.

  4. , Personal communication with ANSYS® technical support.

  5. Willis, A. P., Peixinho, J., Kerswell, R. R., and Mullin. T. , Experimental And Theoretical Progress in Pipe Flow Transition.

  6. Duguet, Y., Willis, A. P., and Kerswell, R. R. , Transition in Pipe Flow: the Saddle Structure on the Boundary of Turbulence.

  7. Wu, X. and Moin, P. , A Direct Numerical Simulation Study on the Mean Velocity Characteristics In Turbulent Pipe Flow.