In fully developed three dimensional fluid turbulence the fluctuating energy is supplied at large scales, cascades through intermediate scales, and dissipates at small scales. It is the hallmark of turbulence that for intermediate scales, in the so c
alled inertial range, the average energy flux is constant and independent of viscosity [1-3]. One very important question is how this range is altered, when an additional agent that can also transport energy is added to the fluid. Long-chain polymers dissolved at very small concentrations in the fluid are such an agent [4,5]. Based on prior work by de Gennes and Tabor [6,7] we introduce a theory that balances the energy flux through the turbulent cascade with that of the energy flux into the elastic degrees of freedom of the dilute long-chain polymer solution. We propose a refined elastic length scale, $r_varepsilon$, which describes the effect of polymer elasticity on the turbulence energy cascade. Our experimental results agree excellently with this new energy flux balance theory.
We report an experimental study of the three-dimensional spatial structure of the low frequency temperature oscillations in a cylindrical Rayleigh-B{e}nard convection cell. It is found that thermal plumes are not emitted periodically, but randomly an
d continuously, from the top and bottom plates. We further found that the oscillation of the temperature field does not originate from the boundary layers, but rather is a result of the horizontal motion of the hot ascending and cold descending fluids being modulated by the twisting and sloshing motion of the bulk flow field.
We report an experimental study of the large-scale circulation (LSC) in a turbulent Rayleigh-B{e}nard convection cell with aspect ratio unity. The temperature-extremum-extraction (TEE) method for obtaining the dynamic information of the LSC is presen
ted. With this method, the azimuthal angular positions of the hot ascending and cold descending flows along the sidewall are identified from the measured instantaneous azimuthal temperature profile. The motion of the LSC is then decomposed into two different modes: the azimuthal mode and the translational or off-center mode. Comparing to the previous sinusoidal-fitting (SF) method, it is found that both methods give the same information about the azimuthal motion of the LSC, but the TEE method in addition can provide information about the off-center motion of the LSC, which is found to oscillate time-periodically around the cells central vertical axis with an amplitude being nearly independent of the turbulent intensity. It is further found that the azimuthal angular positions of the hot ascending flow near the bottom plate and the cold descending flow near the top plate oscillate periodically out of phase by $pi$, leading to the torsional mode of the LSC. These oscillations are then propagated vertically along the sidewall by the hot ascending and cold descending fluids. When they reach the mid-height plane, the azimuthal positions of the hottest and coldest fluids again oscillate out of phase by $pi$. It is this out-of-phase horizontal positional oscillation of the hottest and coldest fluids at the same horizontal plane that produces the off-center oscillation of the LSC. A direct velocity measurement further confirms the existence of the bulk off-center mode of the flow field near cell center.
