Symbolic computation of turbulence and energy dissipation in the Taylor vortex model

Using a classic example proposed by G I Taylor we reconsider through the use of computer algebra the mathematical analysis of a fundamental pro cess in turbulent ow namely How do large scale eddies evolve into smaller scale ones to the point where they are e ectively absorbed by viscosity The explicit symbolic series solution of this problem even for cleverly chosen spe cial cases requires daunting algebra and so numerical methods have become quite popular Yet an algebraic approach can provide substantial insight especially if it can be pursued with modest human e ort The speci c example we use dates to when Taylor and Green rst published a method for explicitly computing successive approximations to formulas describing the dimensional evolution over time of what is now called a Taylor Green vortex With the aid of a computer algebra system we have duplicated Taylor and Green s e orts and obtained more detailed time series results We have extended their approximation of the energy dissipation from order in time to order including the variation with viscosity Rather than attempting additional interpretation of results for uid ow for which see papers by Brachet et al we examine the promise of computer algebra in pursuing such problems in uid mechanics