Michael Kelly Rivera

Soap film flows: Statistics of two-dimensional turbulence

Soap film flows provide a very convenient laboratory model for studies of two-dimensional (2-D) hydrodynamics including turbulence. For a gravity-driven soap film channel with a grid of equally spaced cylinders inserted in the flow, we have measured the simultaneous velocity and thickness fields in the irregular flow downstream from the cylinders. The velocity field is determined by a modified digital particle image velocimetry method and the thickness from the light scattered by the particles in the film. From these measurements, we compute the decay of mean energy, enstrophy, and thickness fluctuations with downstream distance, and the structure functions of velocity, vorticity, thickness fluctuation, and vorticity flux. From these quantities we determine the microscale Reynolds number of the flow Rλ≈100 and the integral and dissipation scales of 2D turbulence. We also obtain quantitative measures of the degree to which our flow can be considered incompressible and isotropic as a function of downstream ...

Fluid Mixing in Stratified Gravity Currents: The Prandtl Mixing Length

Shear-induced vertical mixing in a stratified flow is a key ingredient of thermohaline circulation. We experimentally determine the vertical flux of momentum and density of a forced gravity current using high-resolution velocity and density measurements. A constant eddy-viscosity model provides a poor description of the physics of mixing, but a Prandtl mixing length model relating momentum and density fluxes to mean velocity and density gradients works well. For the average gradient Richardson number Ri(g) approximately 0.08 and a Taylor Reynolds number Re(lambda) approximately 100, the mixing lengths are fairly constant, about the same magnitude, comparable to the turbulent shear length.

Universal distribution of centers and saddles in two-dimensional turbulence.

The statistical properties of the local topology of two-dimensional turbulence are investigated using an electromagnetically forced soap film. The local topology of the incompressible 2D flow is characterized by the Jacobian determinant Lambda(x,y) = 1 / 4(omega(2)-sigma(2)), where omega(x,y) is the local vorticity and sigma(x,y) is the local strain rate. For turbulent flows driven by different external force configurations, P(Lambda) is found to be a universal function when rescaled using the turbulent intensity. A simple model that agrees with the measured functional form of P(Lambda) is constructed using the assumption that the stream function, psi(x,y), is a Gaussian random field.

An epidemiological model of spatial coupling for trips longer than the infectious period.

One of the standard methods of accounting for inter-population disease spread in equation-based epidemiology models is through a transportation operator. Implicit in the use of the transportation operator, however, is an assumption that daily travel volumes are small compared to overall population sizes, an assumption that can break down for modern rates of international travel or local commuter traffic. Alternative types of coupling have been proposed in the limit that trip durations are much shorter than the infectious period. We present an extension of these phenomenological models that relaxes both assumptions. We show that the approach produces more accurate results when assessing the impact of mitigative actions using modern travel volumes.

Laboratory Measurement of Entrainment and Mixing in Oceanic Overflows

The mixing and entrainment processes existing in oceanic overflows, e.g., Denmark Strait Overflow (DSO), affect the global thermohaline circulation. Owing to limited spatial resolution in global climate prediction simulations, the small-scale dynamics of oceanic mixing must be properly modeled. A series of experiments are performed in an Oceanic Overflow Facility to study the mixing and entrainment of a gravity current along an inclined plate, flowing into a steady ambient medium. At small values of the Richardson number, the shear dominates the stabilizing effect of the stratification and the flow at the interface of the current becomes unstable, resulting in turbulent mixing. In addition, the level of turbulence is enhanced by an active grid device. Using PIV and PLIF to measure, respectively, the velocity and density fields, we characterize the statistical properties of the mixing. We also study the entrainment of the ambient fluid by the flow. An accurate parametrization of the mixing and entrainment can be a valuable input for ocean circulation models.

Regional input–output tables and trade flows: an integrated and interregional non-survey approach

ABSTRACT Regional input–output tables and trade flows: an integrated and interregional non-survey approach. Regional Studies. Regional analyses require detailed and accurate information about dynamics happening within and between regional economies. However, regional input–output tables and trade flows are rarely observed and they must be estimated using up-to-date information. Common estimation approaches vary widely but consider tables and flows independently. By using commonly used economic assumptions and available economic information, this paper presents a method that integrates the estimation of regional input–output tables and trade flows across regions. Examples of the method implementation are presented and compared with other approaches, suggesting that the integrated approach provides advantages in terms of estimation accuracy and analytical capabilities.

Computable general equilibrium model fiscal year 2013 capability development report

This report provides an overview of the development of the NISAC CGE economic modeling capability since 2012. This capability enhances NISACs economic modeling and analysis capabilities to answer a broader set of questions than possible with previous economic analysis capability. In particular, CGE modeling captures how the different sectors of the economy, for example, households, businesses, government, etc., interact to allocate resources in an economy and this approach captures these interactions when it is used to estimate the economic impacts of the kinds of events NISAC often analyzes.

Lagrangian statistics in weakly forced two-dimensional turbulence

Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale ri. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. Lagrangian correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in terms of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of Lagrangian velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary Eulerian velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.

Force fluctuations in granular disks near the jamming threshold

We study experimentally the force fluctuations felt by a probe disk as it is dragged at a nominally constant rate through a two-dimensional bi-disperse system of randomly packed photo-elastic disks. As the packing fraction increases from loose packing to a value where the disks are jammed, lines of connected force - stress chains - develop that couple the entire domain. We consider the transition from an unjammed state with no long range force distribution to a jammed state with stress chains spanning the system size. We characterize this transition using the measured force fluctuations and the determination of stress chains as visualized by the photo-elastic disks. Length and time scales obtained from these measurements are used to describe both the transition to jamming and the nature of the jammed state. The reorganization of disks and the force fluctuations have a stick-slip character in the jammed state.

Measurement of Turbulent Mixing Along Slope in Stratified Flow

The mixing phenomenon of ocean currents, which have different densities as well as velocities, are important to ocean dynamics and global climate modeling. One example is the outflow of the Greenland-Iceland-Norwegian Seas, where dense Arctic water overflows a ridge and spills downslope in a density-driven plume until it reaches the deep abyss of the Atlantic Ocean. On the way down it mixes with ambient water of different temperature and salinity. This process affects the global thermohaline circulation, which is a significant element in changes of the global climate. Laboratory experiments are conducted to investigate this problem. A turbulent jet is introduced into a water tank along an inclined plate. The density difference between the jet and the tank water produces a stably stratified boundary current. Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF) are applied to obtain simultaneous measurement of velocity field and density field along the slope at different downstream locations. On-going efforts are also discussed.Copyright