Energy and enstrophy spectra and fluxes for the inertial-dissipation range of two-dimensional turbulence.

In this paper, using Pao's conjecture [Y.-H. Pao, Phys. Fluids 8, 1063 (1965)10.1063/1.1761356], we derive expressions for the spectra and fluxes of kinetic energy and enstrophy for two-dimensional (2D) forced turbulence that extend beyond the inertial range. In these expressions, the fluxes and the spectra contain additional factors of the exponential form. To validate these model predictions, we perform numerical simulations of 2D turbulence with external force applied at wavenumber band (k_{f},k_{f}+1) in the intermediate range. The numerical results match with the model predictions, except for the energy and enstrophy fluxes for k

Appearance of deterministic mixing behavior from ensembles of fluctuating hydrodynamics simulations of the Richtmyer-Meshkov instability.

We obtain numerical solutions of the two-fluid fluctuating compressible Navier-Stokes (FCNS) equations, which consistently account for thermal fluctuations from meso- to macroscales, in order to study the effect of such fluctuations on the mixing behavior in the Richtmyer-Meshkov instability (RMI). The numerical method used was successfully verified in two stages: for the deterministic fluxes by comparison against air-SF_{6} RMI experiment, and for the stochastic terms by comparison against the direct simulation Monte Carlo results for He-Ar RMI. We present results from fluctuating hydrodynamic RMI simulations for three He-Ar systems having length scales with decreasing order of magnitude that span from macroscopic to mesoscopic, with different levels of thermal fluctuations characterized by a nondimensional Boltzmann number (Bo). For a multidimensional FCNS system on a regular Cartesian grid, when using a discretization of a space-time stochastic flux Z(x,t) of the form Z(x,t)→1/sqrt[h▵t]N(ih,nΔt) for spatial interval h, time interval Δt, h, and Gaussian noise N should be greater than h_{0}, with h_{0} corresponding to a cell volume that contains a sufficient number of molecules of the fluid such that the fluctuations are physically meaningful and produce the right equilibrium spectrum. For the mesoscale RMI systems simulated, it was desirable to use a cell size smaller than this limit in order to resolve the viscous shock. This was achieved by using a modified regularization of the noise term via Z(x,t)→1/sqrt[▵tmax(h^{3},h_{0}^{3})]N(ih,nΔt), with h_{0}=ξh∀h

Dynamics of micro-bubble sonication inside a phantom vessel.

A model for sonicated micro-bubble oscillations inside a phantom vessel is proposed. The model is not a variant of conventional Rayleigh-Plesset equation and is obtained from reduced Navier-Stokes equations. The model relates the micro-bubble oscillation dynamics with geometric and acoustic parameters in a consistent manner. It predicts micro-bubble oscillation dynamics as well as micro-bubble fragmentation when compared to the experimental data. For large micro-bubble radius to vessel diameter ratios, predictions are damped, suggesting breakdown of inherent modeling assumptions for these cases. Micro-bubble response with acoustic parameters is consistent with experiments and provides physical insight to the micro-bubble oscillation dynamics.

Glandular regulation of interstitial diffusion: a model and simulation of a novel physiological mechanism.

In endocrine glands, vigorous and coordinated responses are often elicited by modest changes in the concentration of the agonist molecule. The mammalian parathyroid gland is a representative case. Small (5%) changes in serum calcium result in 10-fold (1,000%) changes in glandular parathyroid hormone (PTH) release. In vitro, single isolated cells are observed to secrete fewer hormones than cells residing within a connected group, suggesting that a network has emergent regulatory properties. In PTH-secreting tumors, however, the ability to respond quickly to changes in calcium is strongly damped. A unifying hypothesis that accounts for these phenomena is realized by extracellular modulation of calcium diffusivity. A theoretical model and computational experiments demonstrate qualitative agreement with published experimental results. Our results suggest that, in addition to the cellular mechanisms, endocrine glandular networks may have regulatory prowess at the level of interstitial transport.