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VELOCITY DERIVATIVES IN TURBULENT FLOW FROM 3D-PTV MEASUREMENTS

Beat Luthi
Institute of Environmental Engineering, ETH Zurich, CH-8093 Zurich, Switzerland

Ulrich Burr
Institut für Hydromechanik und Wasserwirtschaft, ETH-Hönggerberg CH-8093, Zürich, Switzerland

Albert Gyr
Institut für Hydromechanik und Wasserwirtschaft, ETH-Hönggerberg CH-8093, Zürich, Switzerland

Wolfgang Kinzelbach
Institute of Hydromechanics and Water Resources Management, Swiss Federal Institute of Technology, ETH Honggerberg, CH 8093 Zurich, Switzerland

Arkady Tsinober
Department of Fluid Mechanics and Heat Transfer, School of Mechanical Engineering, Tel-Aviv University, Tel-Aviv, Israel; and Institute for Mathematical Sciences and Department of Aeronautics, Imperial College, London, United Kingdom

Abstrakt

Velocity derivatives play an outstanding role in the dynamics of turbulence for a number of reasons. Their importance became especially clear since the papers by Taylor (1938) and Kolmogorov (1941). Taylor emphasized the role of vorticity, whereas Kolmogorov stressed the importance of dissipation, and thereby of strain.
The field of velocity derivatives is very sensitive to the non-Gaussian nature of turbulence or more generally to its structure, and hence reflects a lot of its physics. From the momentum equation it follows that the whole flow field is entirely determined by the field of vorticity, or by that of strain. Therefore, in Lagrangian description, in a frame following a fluid particle, everything happening in its proximity is characterized by the velocity gradient tensor Aij = dui / dxj (Tsinober, 2001).
We report the first attempts to use the particle tracking technique for studying the field of velocity derivatives and material elements. The nonintrusive nature of this method makes it especially suitable for this purpose.