Abstracts - KTH Mechanics

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118 breakup probability 0.8 0.6 0.4 0.2 0 0 0.02 0.04 (a) 0.06 x (m) 0.8 0.6 0.4 0.2 A c =20 A c =25 A c =30 exp. 0 0 0.02 0.04 (b) 0.06 x (m)
Nonlinear long waves on an interface of steady-state flow of the two-layered viscous liquid in a horizontal channel D. G. Arkhipov ∗ and G. A. Khabakhpashev ∗ Problems for gravity waves on free surfaces of shallow liquid currents with a shear of the longitudinal velocity draw attention of specialists in the area of hydromechanics for a long time. Recently, however, an interest to the similar researches has increased noticeably (see, for example, 1 ). In the paper 2 there was derived the evolution intergro-differential equation for long plane nonlinear interface perturbations which travelling in the direction of the two-layered laminar flow in a channel with the horizontal lid and bottom or opposite it. In this paper it is allowed that the steady-state two-layered current of viscous incompressible liquids may be at an arbitrary angle of the wave propagation direction. There are assumed that liquids with arbitrary ratio of densities are incompressible and immiscible, their flows in a horizontal channel are laminar, amplitudes of perturbations are small but finite, characteristic horizontal lengths of disturbances are larger and thickness of unsteady viscous boundary layers are smaller than the fluid depths, and finally, capillary effects are moderate. Besides the vertical profiles of the normal velocity are accepted be linear. More general evolution equation for the interface disturbances η, which taking into account long-wave contributions of the layers inertias and the surface tension, a weakly non-linearity of perturbations, and nonstationary shear stresses at all boundaries of the system, was obtained. For the case when ∂η/∂y ∼ ε∂η/∂x (ε is a small parameter) it has the following form: ∂2η ∂t2 + u0i (1 + Sf ) ∂2η ∂t∂x + v0i (1 + Sf ) ∂2η ∂t∂y − (c20 − Sf u 2 0i) ∂2η + ∂x2 + 2 u0i v0i Sf ∂2η ∂x∂y − Cd ∂2eta ∂t2 − Cn ∂x2 ∂2η 2 = ∂x2 t 0 ∂ Cb 2η ∂x2 dt ′ √ t − t ′ . Here the coefficients Sf , c 2 0, Cd, Cn, and Cb are depended not only on the geometrical (the layers depths) and the physical (the acceleration of the free fall, densities, viscosities, the surface tension) parameters of the problem, but on the liquids velocities components of the steady-state flow at the interface (u0i and v0i). Allowing for dissipation the transformation of plane solitary waves of a various length were investigated numerically. It is shown the effect of value and direction of an unperturbed flow to amplitudes and profiles of disturbances. If the initial spatial solitary waves were symmetric not only with respect to x but also with respect to y three-dimensional horseshoe-shaped perturbations were found after a time. This work was supported by the Russian Foundation for Basic Research (Grant 04-01-00183) and by the Siberian Branch of the Russian Academy of Sciences (Basic Grant 4.2-04). ∗ Dept of Phys. Hydrodynamics, Institute of Thermophysics SB RAS, 630090 Novosibirsk, Russia. 1 Grimshaw et al., Nonlinear Processes in Geophysics 9, 221 (2002). 2 Arkhipov and Khabakhpashev, Fluid Dynamics 40, 126 (2005). 119
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EFMC6 KTH Electronic version Abstra
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Euromech Fluid Mechanics Lecturer H
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Prediction of wall bounded flows us
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Uncertainty Quantification in Large
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Stratified turbulence G. Brethouwer
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Investigations of turbulence statis
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Coupling weather-scale flow with st
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Flow Separation from a Free Surface
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Phase-Field Simulations of Free Bou
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Evaluation of a universal transitio
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