Application of the wavelet transform in the laminar turbulent transition for a flow in a mixed convection phenomenon
Institut Universitaire des Systèmes Thermiques Industriels (UMR CNRS 6995) ,
Université d'Aix-Marseille 13453, Marseille Cedex 13, France
Revised: 28 April 1999
Published online: 15 February 2000
The aim of this paper is to show the effect of secondary flows caused by natural convection on the laminar-turbulent hydrodynamic transition. It is not a question of measuring a critical threshold value of Reynolds number of transition but only to estimate the degree of turbulence in the transition regime, i.e. weak turbulence in the case of superposition (mixed convection) or not (forced convection) of secondary flows on the forced flow. This is possible thanks to the application of the wavelet transform. The calculation of the Hölder exponent, associated with the maximum value of the singularity spectrum for two configurations, vertical (forced convection) and horizontal (mixed convection) allows the degree of turbulence to be measured in both cases. The variation of the Hölder exponent versus the Reynolds number has enabled it to be shown that the secondary flows stabilise the main flow and stifle the beginnings of the turbulence during the regime of transition to turbulence; these kinds of results have also been shown in literature. Generally, large-sized secondary flows (for example Dean's flows) stabilise the turbulence. Our work confirms this, through an experiment carried out in identical conditions for mixed convection (horizontal flow) and forced convection (vertical flow).
PACS: 47.27.Cn – Transition to turbulence / 02.50.-r – Probability theory, stochastic processes, and statistics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000