Please use this identifier to cite or link to this item: https://ktisis.cut.ac.cy/handle/10488/14232
Title: On the stationarity of linearly forced turbulence in finite domains
Authors: Gravanis, Elias 
Akylas, Evangelos 
Keywords: Turbulence;Reynolds number;Grid turbulence
Category: Civil Engineering
Field: Engineering and Technology
Issue Date: 28-Jul-2011
Source: 7th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2011, Ottawa Convention CentreOttawa, Canada, 28 July 2011 through 31 July 2011
Conference: International Symposium on Turbulence and Shear Flow Phenomena 
Abstract: © 2011 International Symposium on Turbulence and Shear Flow Phenomena, TSFP07. All rights reserved. A simple scheme of forcing turbulence away from decay was introduced by Lundgren some time ago, the 'linear forcing', which amounts to a force term linear in the velocity field with a constant coefficient. The evolution of linearly forced turbulence towards a stationary final state, as indicated by direct numerical simulations (DNS), is examined from a theoretical point of view based on symmetry arguments. In order to follow closely the DNS the flow is assumed to live in a cubic domain with periodic boundary conditions. The simplicity of the linear forcing scheme allows one to re-write the problem as one of decaying turbulence with a decreasing viscosity. Scaling symmetry considerations suggest that the system evolves to a stationary state, evolution that may be understood as the gradual breaking of a larger approximate symmetry to a smaller exact symmetry. The same arguments show that the finiteness of the domain is intimately related to the evolution of the system to a stationary state at late times, as well as the consistency of this state with a high degree of isotropy imposed by the symmetries of the domain itself. The fluctuations observed in the DNS for all quantities in the stationary state can be associated with deviations from isotropy. Indeed, self-preserving isotropic turbulence models are used to study evolution from a direct dynamical point of view, emphasizing the naturalness of the Taylor microscale as a self-similarity scale in this system. In this context the stationary state emerges as a stable fixed point. Self-preservation seems to be the reason behind a noted similarity of the third order structure function between the linearly forced and freely decaying turbulence, where again the finiteness of the domain plays an significant role.
Description: 7th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2011, Volume 2011-July, 2011
URI: https://ktisis.cut.ac.cy/handle/10488/14232
ISSN: 2-s2.0-85048554109
https://api.elsevier.com/content/abstract/scopus_id/85048554109
Type: Conference Papers
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