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Viscous flow of fluid film on outer surface of a sloped rotating cylinder in gravitational field is studied. Thickness of the fluid layer is assumed to be small compared to the cylinder radius, which allows asymptotic analysis. Go...
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Viscous flow of fluid film on outer surface of a sloped rotating cylinder in gravitational field is studied. Thickness of the fluid layer is assumed to be small compared to the cylinder radius, which allows asymptotic analysis. Governing equation for the thickness dynamics is derived. The equation accounts for viscous effects, gravity, centrifugal and capillary forces. A criterion for existence of steady flow on the sloped cylinder is obtained. Linear stability of stationary solution for the vertical cylinder is given. Film thickness response to oscillations of the cylinder axis around vertical line is studied. Numerical model is implemented for the case of arbitrary slope angle.
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The aim of this work is to show, through analyzing some incorrect results in the literature, (i) the internal layer structure is not so predictable for the linear parabolic differential equations with constant coefficients; and (i...
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The aim of this work is to show, through analyzing some incorrect results in the literature, (i) the internal layer structure is not so predictable for the linear parabolic differential equations with constant coefficients; and (ii) the location of the viscous shock of Burgers' equation in the quarter plane depends on the viscosity, but not in the half plane. Our methods are based on asymptotics of integrals together with special functions to unveil these distinguished features. Contrary to the exponential function as the sole building block of boundary layer functions for differential equations and partial differential equations near the outflow boundary, the class of the complementary error function and its iterated integrals becomes fundamental in this investigation.
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The viscous semigeostrophic solutions obtained for the baroclinic Eady wave fronts are analyzed for the generation of the cross-frontal temperature gradient in the boundary layer. In the case of free-slip boundaries, the cross-fro...
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The viscous semigeostrophic solutions obtained for the baroclinic Eady wave fronts are analyzed for the generation of the cross-frontal temperature gradient in the boundary layer. In the case of free-slip boundaries, the cross-frontal gradient is maximally generated at the surface by meridional temperature advection. In the case of no-slip boundaries, surface friction reduces the meridional temperature advection in the boundary layer: The maximum generation occurs above the surface layer and the temperature gradient at the surface is maintained by vertical diffusion. The no-slip solution is compared with the Ekman-layer model solution. Errors are quantified for the use of the Ekman-layer model in the mature state of frontogenesis.
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摘要 :
The viscous semigeostrophic solutions obtained for the baroclinic Eady wave fronts are analyzed for the generation of the cross-frontal temperature gradient in the boundary layer. In the case of free-slip boundaries, the cross-fro...
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The viscous semigeostrophic solutions obtained for the baroclinic Eady wave fronts are analyzed for the generation of the cross-frontal temperature gradient in the boundary layer. In the case of free-slip boundaries, the cross-frontal gradient is maximally generated at the surface by meridional temperature advection. In the case of no-slip boundaries, surface friction reduces the meridional temperature advection in the boundary layer: The maximum generation occurs above the surface layer and the temperature gradient at the surface is maintained by vertical diffusion. The no-slip solution is compared with the Ekman-layer model solution. Errors are quantified for the use of the Ekman-layer model in the mature state of frontogenesis. The surface frontogenesis is found to be affected by diffusivity both directly and indirectly. The direct effect of diffusivity is represented explicitly by the diffusion term in the potential temperature equation. The indirect effect of diffusivity is related implicitly to the temperature advection caused by the viscous part of the ageostrophic motion whose horizontal velocity component is defined by the frictional wind deflection (away from the geostrophy). The direct effect of diffusivity is frontolytical, whilst the indirect effect of diffusivity is frontogenetic in the mesoscale vicinity of the front. The indirect effect of diffusivity contributes dominantly to the mesoscale surface frontogenesis for the free-slip case, but it is offset by the divergence of the dynamic part of the ageostrophic motion at the surface level for the non-slip case.
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In this paper, we consider a one-dimensional half-space problem for a system of viscous conservation laws which is deduced to a symmetric hyperbolic-parabolic system under assuming that the system has a strictly convex entropy fun...
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In this paper, we consider a one-dimensional half-space problem for a system of viscous conservation laws which is deduced to a symmetric hyperbolic-parabolic system under assuming that the system has a strictly convex entropy function. We firstly prove existence of a stationary solution by assuming that a boundary strength is sufficiently small. The existence of the stationary solution is characterized by the number of negative characteristics. In the case where one characteristic speed is zero at spatial asymptotic state x -> infinity, we assume that the characteristic field corresponding to the characteristic speed 0 is genuinely nonlinear in order to show existence of a degenerate stationary solution with the aid of a center manifold theory. We next prove that the stationary solution is time asymptotically stable under a smallness assumption on an initial perturbation in the Sobolev space. The key to proof is to derive the uniform a priori estimates by using the energy method, where the stability condition of Shizuta-Kawashima type plays an essential role.
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In the present paper, we study a system of viscous conservation laws, which is rewritten to a symmetric hyperbolic-parabolic system, in one-dimensional half space. For this system, we derive a convergence rate of the solutions tow...
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In the present paper, we study a system of viscous conservation laws, which is rewritten to a symmetric hyperbolic-parabolic system, in one-dimensional half space. For this system, we derive a convergence rate of the solutions towards the corresponding stationary solution with/without the stability condition. The essential ingredient in the proof is to obtain the a priori estimate in the weighted Sobolev space. In the case that all characteristic speeds are negative, we show the solution converges to the stationary solution exponentially if an initial perturbation belongs to the exponential weighted Sobolev space. The algebraic convergence is also obtained in the similar way. In the case that one characteristic speed is zero and the other characteristic speeds are negative, we show the algebraic convergence of solution provided that the initial perturbation belongs to the algebraic weighted Sobolev space. The Hardy type inequality with the best possible constant plays an essential role in deriving the optimal upper bound of the convergence rate. Since these results hold without the stability condition, they immediately mean the asymptotic stability of the stationary solution even though the stability condition does not hold.
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Application of damping coatings on metal sheets is a commonly used method to suppress the undesirable vibration and noise levels in various industries. As numerical simulations have a vital role while designing a high-quality prod...
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Application of damping coatings on metal sheets is a commonly used method to suppress the undesirable vibration and noise levels in various industries. As numerical simulations have a vital role while designing a high-quality product with fewer costs, an accurate and practical way of modelling such type of structures is necessary. It was aimed to develop a methodology that helps to define damping parameters of such viscoelastic coating layers through Rayleigh damping coefficients. Machine learning tools were considered to find a prediction formula which yields Rayleigh coefficients based on thicknesses. For this purpose, several tests were conducted with different coating thicknesses on steel plates. In parallel, a great number of simulations were performed not only to make comparisons with the reference values from tests but also to feed the learning algorithms with the data sets. The results were compared including the ones from the Oberst equation. The results from the machine learning showed significantly better matching performance with the tests, as there seems to be a limitation problem for Oberst accuracy.
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The dispersion curves are constructed and propagation of quasi-Lamb waves are studied for wide range of frequencies based on the Navier-Stokes three-dimensional linearized equations for a viscous liquid and linear equations of the...
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The dispersion curves are constructed and propagation of quasi-Lamb waves are studied for wide range of frequencies based on the Navier-Stokes three-dimensional linearized equations for a viscous liquid and linear equations of the classical theory of elasticity for an elastic layer. For a thick liquid layer, the effect of the viscosity of the liquid and the thickness of elastic and liquid layers on the phase velocities and attenuation coefficients of quasi-Lamb modes is analyzed. It is shown that in the case of a thick liquid layer for all modes, there are elastic layers of certain thickness with minimal effect of liquid viscosity on the phase velocities and attenuation coefficients of modes. It is also discovered that for some modes, there are both certain thicknesses and certain ranges of thickness where the effect of liquid viscosity on the phase velocities and attenuation coefficients of these modes is considerable. We ascertain that liquid viscosity promotes decrease of the penetration depth of the lowest quasi-Lamb mode into the liquid. The developed approach and the obtained results make it possible to ascertain for wave processes the limits of applicability of the model of ideal compressible fluid. Numerical results in the form of graphs are adduced and analyzed.
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The Navier-Stokes three-dimensional linearized equations for a viscous fluid and the linear equations of classical elasticity for an elastic layer are used to plot dispersion curves and to study the propagation of acoustic waves o...
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The Navier-Stokes three-dimensional linearized equations for a viscous fluid and the linear equations of classical elasticity for an elastic layer are used to plot dispersion curves and to study the propagation of acoustic waves over a wide frequency range. The effect of the viscosity of the fluid and the thickness of the elastic and liquid layers on the phase velocities and the damping factors of the modes is analyzed for both thin and thick solid layers. It is shown that for the thick elastic layer, there are certain thicknesses of the liquid layer and certain frequencies at which the effect of the viscosity of the fluid on the phase velocities and damping factors of all the modes is the weakest. It is also revealed that for a number of modes, there are certain frequencies and certain frequency ranges for which the effect of the viscosity of the fluid on the phase velocities and damping factors of the modes is strong. The approach developed and the results obtained allow identifying the limits of applicability of the model of ideal compressible fluid. The numerical results are presented in the form of plots and analyzed.
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Since insight into entropy generation is a key to increasing efficiency and thereby reducing fuel consumption and/or waste and _ for wall-bounded flows _ most entropy is generated in the viscous layer, we examine the transient beh...
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Since insight into entropy generation is a key to increasing efficiency and thereby reducing fuel consumption and/or waste and _ for wall-bounded flows _ most entropy is generated in the viscous layer, we examine the transient behaviour of its dominant contributor there for a non-canonical flow. New measurements in oil flow are presented for the effects of favourable streamwise mean pressure gradients on temporal entropy generation rates and, in the process, on key Reynolds-stress-producing events such as sweep front passage and on the deceleration/outflow phase of the overall bursting process. Two extremes have been considered: (1) a high pressure gradient, nearing laminarization', and (2), for comparison, a low pressure gradient correspond_ing to many earlier experiments. In both cases, the peak temporal entropy generation rate occurs shortly after passage of the ejection/sweep interface. Whether sweep and ejection rates appear to decrease or increase with the pressure gradient depends on the feature examined and the manner of sampling. When compared using wall coordinates for velocities, distances and time, the trends and magnitudes of the transient behaviours are mostly the same. The main effects of the higher pressure gradient are (a) changes in the time lag between detections _ representing modification of the shape of the sweep front and the sweep angle with the wall, (b) modification of the magnitude of an instantaneous Reynolds shear stress with wall distance and (c) enlarging the sweeps and ejections. Results, new for both low and high pressure gradients, are the temporal behaviours of the dominant contribution to entropy generation; it is found to be much more sensitive to distance from the wall than to streamwise pressure gradient.
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