Govindarajan, Rama and L’vov, Victor S and Procaccia, Itamar and Sameen, A (2003) Stabilization of hydrodynamic flows by small viscosity variations. In: Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 67 (2). 26310-1-11.
Motivated by the large effect of turbulent drag reduction by minute concentrations of polymers, we study the effects of a weakly space-dependent viscosity on the stability of hydrodynamic flows. In a recent paper [Phys. Rev. Lett. 87, 174501, (2001)], we exposed the crucial role played by a localized region where the energy of fluctuations is produced by interactions with the mean flow (the ‘‘critical layer’’). We showed that a layer of a weakly space-dependent viscosity placed near the critical layer can have a very large stabilizing effect on hydrodynamic fluctuations, retarding significantly the onset of turbulence. In this paper we extend these observations in two directions: first we show that the strong stabilization of the primary instability is also obtained when the viscosity profile is realistic (inferred from simulations of turbulent flows with a small concentration of polymers). Second, we analyze the secondary instability (around the time-dependent primary instability) and find similar strong stabilization. Since the secondary instability develops around a time-dependent solution and is three dimensional, this brings us closer to the turbulent case. We reiterate that the large effect is not due to a modified dissipation (as is assumed in some theories of drag reduction), but due to reduced energy intake from the mean flow to the fluctuations. We propose that similar physics act in turbulent drag reduction.
|Item Type:||Journal Article|
|Additional Information:||The DOI is currently only displayed. Copyright for this article belongs to American Physical Society (APS)|
|Department/Centre:||Division of Mechanical Sciences > Aerospace Engineering (Formerly, Aeronautical Engineering)|
|Date Deposited:||28 May 2004|
|Last Modified:||19 Sep 2010 04:12|
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