Small Wave – Vortex Disturbances in Stratified Fluid

AbstractThe theoretical description of small hydrodynamic perturbations caused by mass, force and thermal sources in some models of stratified fluid is given. The focus is on the model of a uniformly stratified heat-conducting viscous fluid. It is shown that the small perturbations can be conveniently described by several scalar quasipotentials. One quasipotential is defined by solution of the inhomogeneous differential equation of diffusion. Other quasipotentials satisfy the same high order differential equations with different right-hand sides. The linear differential operator of these equations plays a key role in the theory of small perturbations and corresponding Green's function. It is established that Green's function of small perturbations in an incompressible stratified heat-conducting viscous fluid vanishes at negative times, i.e. satisfies the causality condition. Analysis of the integral Fourier expansion of Green's function in frequencies and wave numbers is performed. It is shown that small perturbations are divided into the aperiodically damped perturbations with large wave numbers and the damped internal waves with small wave numbers. The simplifications arising in the case of unit Prandtl's number and in the limit of ideal stratified fluid are found

Non-Newtonian thin films with normal stresses: dynamics and spreading

The dynamics of thin films on a horizontal solid substrate is investigated in the case of non-Newtonian fluids exhibiting normal stress differences, the rheology of which is strongly non-linear. Two coupled equations of evolution for the thickness of the film and the shear rate are proposed within the lubrication approximation. This framework is applied to the motion of an advancing contact line. The apparent dynamic contact angle is found to depend logarithmically on a lengthscale determined solely by the rheological properties of the fluid and the velocity of the contact line

Elastic properties of fullerites and diamond-like phases

Diamond‐like structures, that include sp2 and sp3 hybridized carbon atoms, are of considerable interest nowadays. In the present work, various carbon auxetic structures are studied by the combination of molecular dynamics (MD) and analytical approach. Two fullerites based on the fullerene C60 and fullerene‐like molecule C48 are investigated as well as diamond‐like structures based on other fullerene‐like molecules (called fulleranes), carbon nanotubes (called tubulanes) and graphene sheets. MD is used to find the equilibrium states of the structures and calculate compliance and stiffness coefficients for stable configurations. Analytical methods are used to calculate the engineering elastic coefficients (Young's modulus, Poisson's ratio, shear modulus and bulk modulus), and to study their transformation under rotation of the coordinate system. All the considered structures are partial auxetics with the negative value of Poisson's ratio for properly chosen tensile directions. It is shown that some of these structures, in a particular tension direction, have a very high Young's modulus, that is, 1852 GPa for tubulane TA6

Linear Stability Analysis for Plane-Poiseuille Flow of an Elastoviscoplastic fluid with internal microstructure

We study the linear stability of Plane Poiseuille flow of an elastoviscoplastic fluid using a revised version of the model proposed by Putz and Burghelea (Rheol. Acta (2009)48:673-689). The evolution of the microstructure upon a gradual increase of the external forcing is governed by a structural variable (the concentration of solid material elements) which decays smoothly from unity to zero as the stresses are gradually increased beyond the yield point. Stability results are in close conformity with the ones of a pseudo-plastic fluid. Destabilizing effects are related to the presence of an intermediate transition zone where elastic solid elements coexist with fluid elements. This region brings an elastic contribution which does modify the stability of the flow

Similarity solutions for unsteady shear-stress-driven flow of Newtonian and power-law fluids : slender rivulets and dry patches

Unsteady flow of a thin film of a Newtonian fluid or a non-Newtonian power-law fluid with power-law index N driven by a constant shear stress applied at the free surface, on a plane inclined at an angle α to the horizontal, is considered. Unsteady similarity solutions representing flow of slender rivulets and flow around slender dry patches are obtained. Specifically, solutions are obtained for converging sessile rivulets (0 < α < π/2) and converging dry patches in a pendent film (π/2 < α < π), as well as for diverging pendent rivulets and diverging dry patches in a sessile film. These solutions predict that at any time t, the rivulet and dry patch widen or narrow according to |x|3/2, and the film thickens or thins according to |x|, where x denotes distance down the plane, and that at any station x, the rivulet and dry patch widen or narrow like |t|−1, and the film thickens or thins like |t|−1, independent of N

Geometric scaling of elastic instabilities in the Taylor–Couette geometry:A theoretical, experimental and numerical study

We investigate the curvature-dependence of the visco-elastic Taylor-Couette instability. The radius of curvature is changed over almost a decade and the critical Weissenberg numbers of the first linear instability are determined. Experiments are performed with a variety of polymer solutions and the scaling of the critical Weissenberg number with the curvature against the prediction of the Pakdel-McKinley criterion is assessed. We revisit the linear stability analysis based on the Oldroyd-B model and find, surprisingly, that the experimentally observed scaling is not as clearly recovered. We extend the constitutive equation to a two-mode model by incorporating the PTT model into our analysis to reproduce the rheological behaviour of our fluid, but still find no agreement between the linear stability analysis and experiments. We also demonstrate that that conclusion is not altered by the presence of inertia or viscous heating. The Pakdel-McKinley criterion, on the other hand, shows a very good agreement with the data.Comment: 17 pages, 18 figures, submitted to J. Non-Newtonian Fluid Mec

GENERATION AND DYNAMICS OF SMALL DISTURBANCES IN STRATIFIED LIQUIDS

The general theory of radiating the linear internal waves by the moving, oscillating and collapsing sources with application of the mathematical tooling of the Green functions, integral Fouries decompositions, decompositions into the series and evaluations of the integral characteristics has been constructed. The theoretical analysis on the evolution of the localized plane and eddy disturbances and degeneration of the turbulence in the stratified liquids has been developed.Available from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio