Enhanced drag in pipe turbulent flow by an aqueous electrolyte: an electroviscous effect

Drag enhancement is reported for turbulent pipe flow of aqueous electrolyte solutions. No electroviscous effect was obtained with laminar flow. Nor was any unusual pressure drop observed for laminar or turbulent flow of non-electrolyte aqueous solutions such as sugar. An electroviscous theory was advanced that predicted the drag enhancement for a 1/1 electrolyte solution. The theory depended on consideration of Debye length

Pattern formation without heating in an evaporative convection experiment

We present an evaporation experiment in a single fluid layer. When latent heat associated to the evaporation is large enough, the heat flow through the free surface of the layer generates temperature gradients that can destabilize the conductive motionless state giving rise to convective cellular structures without any external heating. The sequence of convective patterns obtained here without heating, is similar to that obtained in B\'enard-Marangoni convection. This work present the sequence of spatial bifurcations as a function of the layer depth. The transition between square to hexagonal pattern, known from non-evaporative experiments, is obtained here with a similar change in wavelength.Comment: Submitted to Europhysics Letter

Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Benard convection

An alternative computational procedure for numerically solving a class of variational problems arising from rigorous upper-bound analysis of forced-dissipative infinite-dimensional nonlinear dynamical systems, including the Navier-Stokes and Oberbeck-Boussinesq equations, is analyzed and applied to Rayleigh-Benard convection. A proof that the only steady state to which this numerical algorithm can converge is the required global optimal of the relevant variational problem is given for three canonical flow configurations. In contrast with most other numerical schemes for computing the optimal bounds on transported quantities (e.g., heat or momentum) within the "background field" variational framework, which employ variants of Newton's method and hence require very accurate initial iterates, the new computational method is easy to implement and, crucially, does not require numerical continuation. The algorithm is used to determine the optimal background-method bound on the heat transport enhancement factor, i.e., the Nusselt number (Nu), as a function of the Rayleigh number (Ra), Prandtl number (Pr), and domain aspect ratio L in two-dimensional Rayleigh-Benard convection between stress-free isothermal boundaries (Rayleigh's original 1916 model of convection). The result of the computation is significant because analyses, laboratory experiments, and numerical simulations have suggested a range of exponents alpha and beta in the presumed Nu similar to (PrRa beta)-Ra-alpha scaling relation. The computations clearly show that for Ra <= 10(10) at fixed L = 2 root 2, Nu <= 0.106Pr(0)Ra(5/12), which indicates that molecular transport cannot generally be neglected in the "ultimate" high-Ra regime.NSF DMS-0928098 DMS-1515161 DMS-0927587 PHY-1205219Simons FoundationNSFONRInstitute for Computational Engineering and Sciences (ICES

Phase instabilities in hexagonal patterns

The general form of the amplitude equations for a hexagonal pattern including spatial terms is discussed. At the lowest order we obtain the phase equation for such patterns. The general expression of the diffusion coefficients is given and the contributions of the new spatial terms are analysed in this paper. From these coefficients the phase stability regions in a hexagonal pattern are determined. In the case of Benard-Marangoni instability our results agree qualitatively with numerical simulations performed recently.Comment: 6 pages, 6 figures, to appear in Europhys. Let