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In this paper direct numerical simulations of exchange flows of large density ratios are presented and are compared with experiments by Gröbelbauer et al. [J. Fluid Mech. 250, 669 (1993)]. These simulations, which make use of a dynamic mesh adaptation technique, cover the whole density ratio range of the experiments and very good agreement with the experimental front velocities and the Froude number variations is obtained. Moreover, in order to establish more definitely the Froude number dependency on density ratio, the simulations were carried up to ratios of 100 compared with 21.6 accessible in experiments. An empirical law for the dense front Froude number as a function of the density parameter is proposed. The mathematical difficulty of the problem is discussed. This difficulty arises because, when the density ratio is large, the existence of a solution is dependent on a compatibility condition between the diffusion and viscous terms model. Moreover, a specific numerical technique is required to treat the finite, nonuniform divergence of the mass-averaged velocity field described by the continuity equation. [ABSTRACT FROM AUTHOR]

The Reynolds number similarity hypothesis of Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, UK, 1976)] states that the turbulence beyond a few roughness heights from the wall is independent of the surface condition. The underlying assumption is that the boundary layer thickness δ is large compared to the roughness height k. This hypothesis was tested experimentally on two types of three-dimensional rough surfaces. Boundary layer measurements were made on flat plates covered with sand grain and woven mesh roughness in a closed return water tunnel at a momentum thickness Reynolds number Reθ of ∼14 000. The boundary layers on the rough walls were in the fully rough flow regime (ks+>=100) with the ratio of the boundary layer thickness to the equivalent sand roughness height δ/ks greater than 40. The results show that the mean velocity profiles for rough and smooth walls collapse well in velocity defect form in the overlap and outer regions of the boundary layer. The Reynolds stresses for the two rough surfaces agree well throughout most of the boundary layer and collapse with smooth wall results outside of 3ks. Higher moment turbulence statistics and quadrant analysis also indicate the differences in the rough wall boundary layers are confined to y<5ks. The present results provide support for Townsend’s Reynolds number similarity hypothesis for uniform three-dimensional roughness in flows where δ/ks>=40. [ABSTRACT FROM AUTHOR]

Kinetic equations modeling the behavior of the velocity probability density function (PDF) in homogeneous anisotropic decaying turbulence are hypothesized and their implications for return-to-isotropy are investigated. Anisotropic turbulent decay is a parametrically simple but theoretically complex turbulent flow that is dominated by nonlinear interactions. The physical implications of the Bhatnagar–Gross–Krook model, a relaxation model, and the Fokker–Planck model for the “collision” term in the PDF evolution equation are analyzed in detail. Using fairly general assumptions about the physics, three different parameter-free return-to-isotropy models are proposed. These models are compared with experimental data, classical models, and analytical limits. The final model expression is particularly interesting, and can easily be implemented in classic Reynolds stress transport models. [ABSTRACT FROM AUTHOR]

Free surface flows of thixotropic fluids such as paints, self-compacting concrete, or natural mudflows are of noticeable practical interest. Here we study the basic characteristics of the uniform flow of a layer of thixotropic fluid under gravity. A theoretical approach relying on a simple thixotropy constitutive equation shows that after some time at rest over a small slope angle the fluid layer should start to flow rather abruptly beyond a new, larger, critical slope angle. The theory also predicts that the critical time at which the layer velocity should significantly increase is proportional to the duration of the preliminary rest and tends to infinity when the new slope approaches the critical slope. Experiments carried out with different suspensions show that the qualitative trends of the flows are in very good agreement with the theoretical predictions, except that the critical time for flow start appears to be proportional to a power 0.6 of the time of rest whereas the theory predicts a linear dependence. We show that this indicates a restructuration process at rest differing from the restructuration process under flow. [ABSTRACT FROM AUTHOR]

We consider the effect of a shock passing through an arbitrarily shaped interface y(x,0) between two fluids. The evolution of the interface into a new shape, written formally as y(x,t)=y(x,0)+tF(x), is found by applying the linear, classical Richtmyer–Meshkov instability result to each mode in the Fourier expansion of the original interface. We provide several examples where the new shape F(x) can be found analytically. For any interface y(x,0) we define an associated dual interface ydual(x,0) and show that F(x)=dydual(x,0)/dx. Representing a shock by a new mathematical operator we find how y(x,0), ydual(x,0), and F(x) transform under the effect of a shock. Kink-singularities are found in F(x) when and where y(x,0) has a discontinuous change in its first derivative. These are the locations where jetting occurs. We briefly discuss the effects of nonlinearity, compressibility, viscosity, etc., all of which suppress kink-singularities, and present hydrocode simulations of shock tube and high-explosive-driven experiments to highlight the influence of compressibility, nonlinearity, and material strength. [ABSTRACT FROM AUTHOR]

Experimental studies are made on the collapse of macroscopic cavity regions placed in an otherwise homogeneous granular material due to viscous flow. First, an initially circular two-dimensional hole is exposed to a uniform flow at infinity and the process of boundary shape deformation due to locally enhanced stress components is clarified. Above a certain critical velocity, particles on the upstream-side boundary lose contact with neighboring ones, and are carried to the other side of the boundary. At the same time the fluidized region develops towards upstream direction in the granular material. A simple scaling law on the reduction of the void area is obtained. Second, attention is paid to the interaction of two circular cavities of equal radii, whose center-to-center distance and angle of attack are varied. In some configuration of cavities, lowering of the critical velocity of collapse is recognized. Successive processes on the collapse of upstream-side and downstream-side cavities are classified depending on the magnitude of velocity and the configuration of cavities. A possible scenario on the growth of global scale patterns in granular material such as water vein formation and landslides is suggested. [ABSTRACT FROM AUTHOR]