The Effects of Stratification on Flow Separation

Separation of stratified flow over a two-dimensional hill is inhibited or facilitated by acceleration or deceleration of the flow just outside the attached boundary layer. In this note, an expression is derived for this acceleration or deceleration in terms of streamline curvature and stratification. The expression is valid for linear as well as nonlinear deformation of the flow. For hills of vanishing aspect ratio a linear theory can be derived and a full regime diagram for separation can be constructed. For hills of finite aspect ratio scaling relationships can be derived that indicate the presence of a critical aspect ratio, proportional to the stratification, above which separation will occur as well as a second critical aspect ratio above which separation will always occur irrespective of stratification.

Quantifying particle size and turbulent scale dependence of dust uplift in the Sahara using aircraft measurements

The first size-resolved airborne measurements of dust fluxes and the first dust flux measurements from the central Sahara are presented and compared with a parameterization by Kok (2011a). High-frequency measurements of dust size distribution were obtained from 0.16 to 300 µm diameter, and eddy covariance fluxes were derived. This is more than an order of magnitude larger size range than previous flux estimates. Links to surface emission are provided by analysis of particle drift velocities. Number flux is described by a −2 power law between 1 and 144 µm diameter, significantly larger than the 12 µm upper limit suggested by Kok (2011a). For small particles, the deviation from a power law varies with terrain type and the large size cutoff is correlated with atmospheric vertical turbulent kinetic energy, suggesting control by vertical transport rather than emission processes. The measured mass flux mode is in the range 30–100 µm. The turbulent scales important for dust flux are from 0.1 km to 1–10 km. The upper scale increases during the morning as boundary layer depth and eddy size increase. All locations where large dust fluxes were measured had large topographical variations. These features are often linked with highly erodible surface features, such as wadis or dunes. We also hypothesize that upslope flow and flow separation over such features enhance the dust flux by transporting large particles out of the saltation layer. The tendency to locate surface flux measurements in open, flat terrain means these favored dust sources have been neglected in previous studies.

Wormlike micelle formation and flow alignment of a pluronic block copolymer in aqueous solution

The self-assembly into wormlike micelles of a poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) triblock copolymer Pluronic P84 in aqueous salt solution (2 M NaCl) has been studied by rheology, small-angle X-ray and neutron scattering (SAXS/SANS), and light scattering. Measurements of the flow curves by controlled stress rheometry indicated phase separation under flow. SAXS on solutions subjected to capillary flow showed alignment of micelles at intermediate shear rates, although loss of alignment was observed for high shear rates. For dilute solutions, SAXS and static light scattering data on unaligned samples could be superposed over three decades in scattering vector, providing unique information on the wormlike micelle structure over several length scales. SANS data provided information on even shorter length scales, in particular, concerning "blob" scattering from the micelle corona. The data could be modeled based on a system of semiflexible self-avoiding cylinders with a circular cross-section, as described by the wormlike chain model with excluded volume interactions. The micelle structure was compared at two temperatures close to the cloud point (47 degrees C). The micellar radius was found not to vary with temperature in this region, although the contour length increased with increasing temperature, whereas the Kuhn length decreased. These variations result in an increase of the low-concentration radius of gyration with increasing temperature. This was consistent with dynamic light scattering results, and, applying theoretical results from the literature, this is in agreement with an increase in endcap energy due to changes in hydration of the poly(ethylene oxide) blocks as the temperature is increased.

First-dimension separation with the MicroRotoforTM cell prior to SDS-PAGE and LC-MS/MS analysis

Free-flow isoelectric focusing (IEF) is a gel-free method for separating proteins based on their isoelectric point (pl) in a liquid environment and in the presence of carrier ampholytes. this method has been used with the RotoforTM cell at the preparative scale to fractionate proteins from samples containing several hundred milligrams of protein; see the refeences listed in Bio-Rad bulletin 3152. the MicroRotofor cell applies the same method to much sl=maller protein samples without dilution, separating and recoverng milligram quantities of protein in a total volume of about 2 ml.

Separation of astaxanthin from cells of Phaffia rhodozyma using colloidal gas aphrons (CGA) in a flotation column

The aim of this study is to investigate the separation of astaxanthin from the cells of Phaffia rhodozyma using colloidal gas aphrons (CGA), which are surfactant stabilized microbubbles, in a flotation column. It was reported in previous studies that optimum recoveries are achieved at conditions that favor electrostatic interactions. Therefore, in this study, CGA generated from the cationic surfactant hexadecyl trimethyl ammonium bromide (CTAB) were applied to suspensions of cells pretreated with NaOH. The different operation modes (batch or continuous) and the effect of volumetric ratio of CGA to feed, initial concentration of feed, operating height, and flow rate of CGA on the separation of astaxanthin were investigated. The volumetric ratio was found to have a significant effect on the separation of astaxanthin for both batch and continuous experiments. Additionally, the effect of homogenization of the cells on the purity of the recovered fractions was investigated, showing that the homogenization resulted in increased purity. Moreover, different concentrations of surfactant were used for the generation of CGA for the recovery of astaxanthin on batch mode; it was found that recoveries up to 98% could be achieved using CGA generated from a CTAB solution 0.8 mM, which is below the CTAB critical micellar concentration (CMC). These results offer important information for the scale-up of the separation of astaxanthin from the cells of P. rhodozyma using CGA.

Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship A E =cA P between pseudoenergy A E and pseudomomentum A P, where c is the horizontal phase speed in the direction of symmetry associated with A P, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.

A Hamiltonian weak-wave model for shallow-water flow

A reduced dynamical model is derived which describes the interaction of weak inertia–gravity waves with nonlinear vortical motion in the context of rotating shallow–water flow. The formal scaling assumptions are (i) that there is a separation in timescales between the vortical motion and the inertia–gravity waves, and (ii) that the divergence is weak compared to the vorticity. The model is Hamiltonian, and possesses conservation laws analogous to those in the shallow–water equations. Unlike the shallow–water equations, the energy invariant is quadratic. Nonlinear stability theorems are derived for this system, and its linear eigenvalue properties are investigated in the context of some simple basic flows.