Fracture and Singularities of the Mass-Density Gradient Field

2018 ◽  
Vol 132 (2) ◽  
pp. 243-260 ◽  
Author(s):  
Amit Acharya
2015 ◽  
Vol 775 ◽  
pp. 149-177 ◽  
Author(s):  
X. Xiang ◽  
T. J. Madison ◽  
P. Sellappan ◽  
G. R. Spedding

In a stable background density gradient, initially turbulent flows eventually evolve into a state dominated by low-Froude-number dynamics and frequently also contain persistent pattern information. Much empirical evidence has been gathered on these latter stages, but less on how they first got that way, and how information on the turbulence generator may potentially be encoded into the flow in a robust and long-lasting fashion. Here an experiment is described that examines the initial stages of evolution in the vertical plane of a turbulent grid-generated wake in a stratified ambient. Refractive-index-matched fluids allow optically based measurement of early ($Nt<2$) stages of the flow, even when there are strong variations in the local density gradient field. Suitably averaged flow measures show the interplay between internal wave motions and Kelvin–Helmholtz-generated vortical modes. The vertical shear is dominant at the wake edge, and the decay of horizontal vorticity is observed to be independent of $\mathit{Fr}$. Stratified turbulence, originating from Kelvin–Helmholtz instabilities, develops up to non-dimensional time $Nt\approx 10$, and the scale separation between Ozmidov and Kolmogorov scales is independent of $\mathit{Fr}$ at higher $Nt$. The detailed measurements in the near wake, with independent variation of both Reynolds and Froude numbers, while limited to one particular case, are sufficient to show that the initial turbulence in a stratified fluid is neither three-dimensional nor universal. The search for appropriately generalizable initial conditions may be more involved than hoped for.


2014 ◽  
Vol 796 (2) ◽  
pp. 137 ◽  
Author(s):  
Xiao-Dong Li ◽  
Changbom Park ◽  
J. E. Forero-Romero ◽  
Juhan Kim

1999 ◽  
Vol 390 ◽  
pp. 93-126 ◽  
Author(s):  
BRUCE R. SUTHERLAND ◽  
STUART B. DALZIEL ◽  
GRAHAM O. HUGHES ◽  
P. F. LINDEN

We present measurements of the density and velocity fields produced when an oscillating circular cylinder excites internal gravity waves in a stratified fluid. These measurements are obtained using a novel, non-intrusive optical technique suitable for determining the density fluctuation field in temporally evolving flows which are nominally two-dimensional. Although using the same basic principles as conventional methods, the technique uses digital image processing in lieu of large and expensive parabolic mirrors, thus allowing more flexibility and providing high sensitivity: perturbations of the order of 1% of the ambient density gradient may be detected. From the density gradient field and its time derivative it is possible to construct the perturbation fields of density and horizontal and vertical velocity. Thus, in principle, momentum and energy fluxes can be determined.In this paper we examine the structure and amplitude of internal gravity waves generated by a cylinder oscillating vertically at different frequencies and amplitudes, paying particular attention to the role of viscosity in determining the evolution of the waves. In qualitative agreement with theory, it is found that wave motions characterized by a bimodal displacement distribution close to the source are attenuated by viscosity and eventually undergo a transition to a unimodal displacement distribution further from the source. Close quantitative agreement is found when comparing our results with the theoretical ones of Hurley & Keady (1997). This demonstrates that the new experimental technique is capable of making accurate measurements and also lends support to analytic theories. However, theory predicts that the wave beams are narrower than observed, and the amplitude is significantly under-predicted for low-frequency waves. The discrepancy occurs in part because the theory neglects the presence of the viscous boundary layers surrounding the cylinder, and because it does not take into account the effects of wave attenuation resulting from nonlinear wave–wave interactions between the upward and downward propagating waves near the source.


Author(s):  
Henri Gouin ◽  
Pierre Seppecher

Thanks to an expansion with respect to densities of energy, mass and entropy, we discuss the concept of thermocapillary fluid for inhomogeneous fluids. The non-convex state law valid for homogeneous fluids is modified by adding terms taking account of the gradients of these densities. This seems more realistic than Cahn and Hilliard’s model which uses a density expansion in mass-density gradient only. Indeed, through liquid–vapour interfaces, realistic potentials in molecular theories show that entropy density and temperature do not vary with the mass density as it would do in bulk phases. In this paper, we prove using a rescaling process near the critical point, that liquid–vapour interfaces behave essentially in the same way as in Cahn and Hilliard’s model.


2016 ◽  
Author(s):  
H. P. Lehmann ◽  
X. Fuentes-Arderiu ◽  
L. F. Bertello

2019 ◽  
Vol 24 (2) ◽  
pp. 51
Author(s):  
Johan Llamoza ◽  
Desiderio A. Vasquez

Density gradients across reaction fronts propagating vertically can lead to Rayleigh–Taylor instabilities. Reaction fronts can also become unstable due to diffusive instabilities, regardless the presence of a mass density gradient. In this paper, we study the interaction between density driven convection and fronts with diffusive instabilities. We focus in fluids confined in Hele–Shaw cells or porous media, with the hydrodynamics modeled by Brinkman’s equation. The time evolution of the front is described with a Kuramoto–Sivashinsky (KS) equation coupled to the fluid velocity. A linear stability analysis shows a transition to convection that depends on the density differences between reacted and unreacted fluids. A stabilizing density gradient can surpress the effects of diffusive instabilities. The two-dimensional numerical solutions of the nonlinear equations show an increase of speed due to convection. Brinkman’s equation lead to the same results as Darcy’s laws for narrow gap Hele–Shaw cells. For large gaps, modeling the hydrodynamics using Stokes’ flow lead to the same results.


Author(s):  
А.А. Скворцов ◽  
Д.Е. Пшонкин ◽  
М.В. Корячко ◽  
М.Р. Рыбакова

AbstractThe effect of constant magnetic fields on the formation and dynamics of molten Al–Si inclusions in silicon in the field of structural inhomogeneity of a crystal (the dislocation density-gradient field) is considered. The migration rates of liquid inclusions in crystals have been found experimentally under conditions of prevailing melting–crystallization mechanisms at the phase interfaces between the melt and matrix before and after magnetic exposure. It has been found that a preliminarily exposure of dislocation silicon samples in a constant magnetic field leads to an increase in the displacement speed of molten zones in the density-gradient field.


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