This technical note reports the expression of selected higher-order moments associated with the Mott-Smith solution of the shock-wave profile. The considered moments are the pressure tensor, the heat-flux vector and tensor, the fourth-order double-tensor, its full contraction, and the fifth-order moment vector. The resulting shock profiles are shown for Mach 2 and Mach 10 conditions.
The equations describing the two-dimensional vortices first described by Chaplygin in 1899 and 1903 are shown to have solutions of higher order that differ from a simple dipole. It is also shown that for these higher-order vortices a very small asymmetry dramatically changes the topology of the stream function. These vortices could be important for understanding the phenomenon of atmospheric blocking.
The velocity-vorticity correlation integral (Chkhetiani invariant) is an invariant of a viscous Karman-Howarth equation. In the tree-dimensional space this invariant can naturally determine a turbulent diffusivity (viscosity). It is shown, using results of direct numerical simulations, that distributed chaos dominated by this integral can provide an adequate description of the turbulent Rayleigh-Bénard convection, stably stratified turbulence and Rayleigh-Taylor mixing at Prandtl number $Pr \sim 1$.
A closure theory is developed for inhomogeneous turbulent flow, which enables a systematic derivation of the turbulence constitutive relations without relying on any empirical parameters. Renormalized-perturbation approximation is performed in the convective coordinate frame based on the mean flow, successfully incorporating the convective integration in generally covariant manner.
Analytical expressions for coordinates of stationary points and conditions for their existence in the ABC flow are received. The type of the stationary points is shown analytically to be saddle-node. Exact expressions for eigenvalues and eigenvectors of the stability matrix are given. Behavior of the stationary points along the bifurcation lines is described.
Luke P. Lee is a Tan Chin Tuan Centennial Professor at the National University of Singapore. In this contribution he describes the power of optofluidics as a research tool and reviews new insights within the areas of single cell analysis, microphysiological analysis, and integrated systems.
We investigate the effect of thermal expansion and gravity on the propagation and stability of flames in inhomogeneous mixtures. We focus on laminar flames in the simple configuration of an infinitely long channel with rigid porous walls in order to understand the effect of inhomogeneities on these fundamental structures.
Interactions of supersonic uniform streams with cylindrical bodies, placed in open channels, are studied. Channels of rotation with the interval of cross-sectional area decreasing are considered. Two-dimensional Euler equations are solved by an implicit third order Runge-Kutta scheme. Self-oscillatory regimes are found in CFD studies at stream Mach numbers of 3 to 4.5.
The swimming of a sphere by means of radial helical surface waves is studied on the basis of the Stokes equations. Explicit expressions are derived for the matrices characterizing the mean translational and rotational swimming velocities and the mean rate of dissipation to second order in the wave amplitude.
This document accompanies fluid dyanmics video entry V83911 for APS DFD 2012 meeting. In this video, we present experiments on how drop oscillations can be "frozen" using hydrophobic powders.
In this paper, we derive consistent shallow water equations for bi-layer flows of Newtonian fluids flowing down a ramp. We carry out a complete spectral analysis of steady flows in the low frequency regime and show the occurence of hydrodynamic instabilities, so called roll-waves, when steady flows are unstable.
The commonly accepted description of transition to turbulence in shear flows requires the presence of an external source of disturbances that get amplified by an essentially linear mechanism up to the point where breakdown to turbulence occurs. Microscopic fluctuations are shown here to provide just the right amount of initial disturbances to match the predictions of linear stability theory.
Rayleigh-Taylor instability in a compressible fluid is reconsidered. The density is allowed to vary with pressure under the barotropy assumption. For the case with equal speeds of sound in the two superposed fluids, in order to give a non-trivial compressibility correction to the Rayleigh-Taylor growth rate, the compressibility correction is calculated to $O(g^2/k^2a^4)$. To this order, compressibility effects are found to reduce the growth rate.
The penny just dropped (duh!). Having mentioned Bill Piel's very cool visualisation of phylogenies on Google Earth what about the other cool use of Google Earth in biology, namely Declan Butler's displays of the march of avian flu? Instead of standard diagrams like this one from the Ruben Donis' paper in <em> Emerging Infections Diseases </em> : why not take phylogenies for avian flu virus and add them to the data Declan is displaying?