Developed liquid film passing a trailing edge under the action of gravity and capillarity

We consider the asymptotic structure of a steady developed viscous thin film passing the sharp trailing edge of a horizontally aligned flat plate under the weak action of gravity acting vertically and surface tension. The surprisingly rich details of the flow in the immediate vicinity of the trailing edge are elucidated both analytically and numerically. As a central innovation, we demonstrate how streamline curvature serves to regularise the edge singularity apparent on larger scales via generic viscous–inviscid interaction. This is shown to be provoked by weak disturbances of accordingly strong exponential downstream growth, which we trace from the virtual origin of the flow towards the trailing edge. They represent a prototype of the precursor to free interaction in the most general sense, which, interestingly, has not attracted due attention previously. Moreover, we delineate how an increased effect of gravity involves marginally choked flow at the edge.

Propagation of weak disturbances in warm water with air bubbles

The features of reflection and refraction of harmonic waves at the interface between a ”pure“ liquid and a liquid with bubbles with a vapor-gas mixture under direct and oblique incidence are studied. A numerical analysis is made of the effect of the initial volumetric gas content αg0 for two initial bubble sizes a0=10–6 m and 10–3 m. The influence of the disturbance frequencies on the reflection and refraction coefficients of sound in direct incidence and on the dependence of the angle of refraction on the angle of incidence is studied.

The ITCZ in the Central and Eastern Pacific on Synoptic Time Scales

The ITCZ in the central and eastern Pacific on synoptic time scales is highly dynamic. The active season extends roughly from May through October. During the active season, the ITCZ continuously breaks down and re-forms, and produces a series of tropical disturbances. The life span of the ITCZ varies from several days to 3 weeks. Sixty-five cases of ITCZ breakdown have been visually identified over five active seasons (1999–2003) in three independent datasets. ITCZ breakdown can be triggered by two mechanisms: 1) interaction with westward-propagating disturbances (WPDs) and 2) the vortex rollup (VR) mechanism. Results show that the frequency of occurrence of ITCZ breakdown from these two mechanisms is the same. The VR mechanism may have been neglected because the produced disturbances are rather weak and they may dissipate quickly. The ITCZ shows a strong tendency to re-form within 1–2 days in the same location. The ITCZ may break down via the VR mechanism without any other support, and thus it may continuously generate numerous tropical disturbances throughout the season. There are two main differences between the two mechanisms: 1) The WPDs-induced ITCZ breakdown tends to create one or two vortices that may be of tropical depression strength. The VR-induced ITCZ breakdown generates several nearly equal-sized weak disturbances. 2) The WPDs tend to disturb the ITCZ in the eastern Pacific only. Disturbances generally move along the Mexican coast after shedding off from the ITCZ and do not further disturb the ITCZ in the central Pacific. Therefore, the VR mechanism is observed more clearly and is the dominating mechanism for ITCZ breakdown in the central Pacific.

Behaviour of a sonic wave in dissociating gases

The present communication is devoted to the study of weak solutions of the system of hyperbolic partial differential equations in dissociating gas flows. As an application of the singular surface theory, the law of propagation and the growth equation of a sonic wave are obtained, and the breakdown of a sonic wave is also discussed. It is found that weak disturbances in dissociating gases propagate with the effective velocity of sound relative to the gas flow. The effects of dissociation and the wave geometry on the global behaviour of the wave amplitude are discussed. It is concluded that dissociation has a stabilizing effect on the sonic wave in the sense that either it disallows or delays shock formation. The two cases of diverging and converging waves are discussed separately.