Polymer heat transport enhancement in thermal convection: the case of Rayleigh-Taylor turbulence G. Boffetta $^{1}$, A. Mazzino$^{2}$, S. Musacchio3 and L. Vozella 2 $^{1}$Dipartimento di Fisica Generale and INFN, Universit` a di Torino, via P.Giuria 1, 10125 Torino (Italy) $^{2}$Dipartimento di Fisica, Universit` a di Genova, INFN and CNISM, via Dodecaneso 33, 16146 Genova (Italy) (3) CNRS, Lab. J.A. Dieudonn´e UMR 6621, Parc Valrose, 06108 Nice (France) (Dated: May 22, 2018) We study the effects of polymer additives on turbulence generated by the ubiquitous Rayleigh- Taylor instability. Numerical simulations of complete viscoelastic models provide clear evidence that the heat transport is enhanced up to 50% with respect to the Newtonian case. This phenomenon is accompanied by a speed up of the mixing layer growth. We give a phenomenological interpretation of these results based on small-scale turbulent reduction induced by polymers. PACS numbers: Controlling transport properties in a turbulent flow is an issue of paramount importance in a variety of situa- tions ranging from pure sciences to technological applica- tions [1–3]. After Toms [4], one of the most spectacular way to achieve this goal consists in adding inside the fluid solvent a small amount of long-chain polymers (parts per million by weight). The resulting fluid solution acquires a non-Newtonian character and the most interesting dy- namical effect played by polymers is encoded in the drag coefficient, a dimensionless measure of the power needed to maintain a given throughput in a pipe. With respect the Newtonian case (i.e., in the absence of polymers), it can be reduced up to 80% [5, 6]. In many relevant situations ( e.g. atmospheric convec- tion) the velocity field is two-way coupled to the tem- perature field with the result that, together with mass, also heat is transported by the flow. Because drag re- duction is associated to mass transport enhancement, an intriguing question is on whether this is accompanied by a similar variation in the heat transport. In this Letter we demonstrate the simultaneous occur- rence of mass transport enhancement (drag reduction) and heat transport enhancement induced by polymers in a three-dimensional buoyancy driven turbulent flow originated by the ubiquitous Rayleigh–Taylor (RT) in- stability [7, 8]. This instability arises at the interface between a layer of light fluid and a layer of heavy fluid placed above and develops in a turbulent mixing layer (see Fig. 1) which grows accelerated in time. Heuris- tically, the RT system can be assimilated to a channel inside which vertical motion of thermal plumes is main- tained by the available potential energy. Our idea on the possibility of observing drag reduction in this system is suggested by recent analytical results which show a speed-up of the instability due to polymer additives [9]. Moreover, examples of turbulent drag reduction without boundaries have been recently provided, e.g. , in [10–13] Direct numerical simulations of primitive equations show that thermal plumes are faster in the presence of polymers (see Fig. 1), therefore the mixing layer acceler- We consider the incompressible RT system in the Boussinesq approximation generalized to a viscoelastic ates (up to 30% at final observation time) with respect to the Newtonian case and complete mixing is achieved in a shorter time. A second and more dramatic effect, also clearly detectable in Fig. 1, is that polymers reduce small scale turbulence [10–12]. As a consequence, ther- mal plumes in the viscoelastic case are more coherent and transport heat more efficiently. Quantitatively, the enhancement of the heat transport corresponds to larger values (more than 50% at final observation time) of the Nusselt number with respect the Newtonian case. FIG. 1: Vertical sections of temperature field for Newto- nian (left) and viscoelastic (right) RT simulation at time t = 2 τ starting from the same initial conditions. White (black) regions correspond to hot (cold) fluid. Boussinesq- Oldroyd-B equations (1) are integrated by a standard fully dealiased pseudo-spectral code on uniform grid at resolution 512 × 512 × 1024. Physical parameters are P r = ν/κ = 1, η = 0 . 2 ( η = 0 for Newtonian run), βg = 0 . 5, θ$_{0}$ = 1 ( Ag = 0 . 25). Deborah number De = τ p /τ is De = 0 . 2. The initial perturbation is seeded in both cases by adding a 10% of white noise (same realization for both runs) to the initial temperature profile in a small layer around the middle plane z = 0. arXiv:1001.3314v1 [nlin.CD] 19 Jan 2010