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Recent statistical analyses of field trials and wind tunnel experiments show a new feature of fluctuations of tracer concentration dispersing in turbulent shear flow. For an ensemble of releases, the scatter‐plot of the skewness S versus kurtosis K collapses to a quadratic curve lying above K=S2+1. Several explanations for this collapse have been put forth in the literature, including a model for cloud meander in instantaneous releases that does not treat the effects of turbulence on the internal structure of the cloud. In this paper, a model is proposed for the creation of internal striations within the cloud due to convection by the ABC‐velocity field that is a paradigm for three‐dimensional helical motions. The numerical simulations conducted here show that the collapse of the K‐S scatter plot obtains under this more complicated situation where the smaller than cloud size structure is created by chaotic advection. Further, these simulations complement a recent multiscale analysis for eddy diffusivity o...

The Helmholtz–Smoluchowski (HS) slip velocity boundary condition is often used in computational models of microchannel flows because it allows the motion of the electric double layer (EDL) to be approximated without resolving the charge density profiles close to the walls while dramatically reducing the computational effort required to solve the flow model. The approximation works well for straight channel flows but breaks down in areas of high wall curvature such as sharp corners, where large nonphysical velocities are generated. Many microfluidic applications such as the on-chip focusing and separation of biomolecules rely on the interaction of electroosmosis and electrophoresis in complex channel geometries. In order for these effects to be properly treated using the slip velocity boundary condition, the errors introduced into the solution at corners must be understood. In this article, a complete model for the ion concentrations, electric field, and fluid flow in complex microchannel geometries is presented and is used to compute a pure electroosmotic flow in a two-dimensional microchannel cross slot. The full model solution near the corner at the edge of the EDL is compared to the approximate solution computed by using the HS boundary condition, and it is shown that the accuracy of the approximate solution may be greatly increased by “patching” the full solution as a boundary condition for the approximate solution at the edge of the double layer region. Finally, an empirically derived modified slip velocity boundary condition for electroosmotic flow is proposed. It is shown to improve the accuracy of the flow solution at sharp corners by about 60% when compared to the original boundary condition while also delivering a modest improvement in computational performance because of the elimination of a singularity in the velocity field.

Double diffusion of a viscous fluid is simulated for heat leakage driven by buoyant convection under cryogenic storage conditions in a cylindrical tank with laminar flow. If the tank is stably stratified, there is a potential instability due to the inability of the fluid in the lower layer to release heat to the top vapor space, whereas the upper liquid layer can exchange heat and mass through sensible heat transfer and evaporation with the vapor space. Eventually, the lower layer becomes less dense due to thermal expansion and is no longer constrained in the stratification. The rapid rise and overturning of the fluid is termed rollover, and can be accompanied by a potentially explosive release of vapor. In this paper, hydrodynamics and heat and mass transport are used to study the stability characteristics of rollover. The transient state is used as a base state for a linear stability analysis which shows the transition from a “corner eddy” mode spinning down to spinning up is the driver for the rollover instability. Four different vapor-liquid interfacial boundary conditions are tested, with similar results for the time to rollover. Surprisingly, the long time prerollover state is dominated in the laminar flow regime by heat conduction and diffusion, as the expected double roll structure is suppressed and advection plays a small roll in the majority of the prerollover period. Scalings are suggested for controlling dimensionless groups on this prerollover basis that can be used as a guideline to determine the regime of double diffusion—a single roll or a double roll stratification, as well as the severity of the eventual rollover event. An energy analysis demonstrates the switch from practically advection free to free convection regimes.