a1 Department of Aeronautics, Imperial College London, Prince Consort Road, London SW7 2AZ, UK
The amplification of enstrophy is explored using cinematographic stereoscopic particle image velocimetry data. The enstrophy production rate is investigated by observation of the statistical tendency of the vorticity vector (ω) to align with the eigenvectors of the rate of strain tensor (ei). Previous studies have shown that ω preferentially aligns with the intermediate strain-rate eigenvector (e2) and is arbitrarily aligned with the extensive strain-rate eigenvector (e1). This study shows, however, that the nature of enstrophy amplification, whether it is positive (enstrophy production) or negative (enstrophy destruction), is dictated by the alignment between ω and e1. Parallel alignment leads to enstrophy production (ωiSijωj>0), whereas perpendicular alignment leads to enstrophy destruction (ωiSijωj<0). In this way, the arbitrary alignment between ω and e1 is the summation of the effects of enstrophy producing and enstrophy destroying regions. The structure of enstrophy production is also examined with regards to the intermediate strain-rate eigenvalue, s2. Enstrophy producing regions are found to be topologically ‘sheet-forming’, due to an extensive (positive) value of s2 in these regions, whereas enstrophy destroying regions are found to be ‘spotty’. Strong enstrophy producing regions are observed to occur in areas of strong local swirling as well as in highly dissipative regions. Instantaneous visualizations, produced from the volume of data created by Taylor's hypothesis, reveal that these ‘sheet-like’ strong enstrophy producing regions encompass the high enstrophy, strongly swirling ‘worms’. These ‘worms’ induce high local strain fields leading to the formation of dissipation ‘sheets’, thereby revealing enstrophy production to be a complex interaction between rotation and strain – the skew-symmetric and symmetric components of the velocity gradient tensor, respectively.
(Received July 10 2009)
(Revised December 07 2009)
(Accepted December 07 2009)
(Online publication March 19 2010)