Free-Surface Flows over an Obstacle: Problem Revisited

Hydraulic falls under a floating ice plate due to submerged obstructions

“…A similar phenomenon was observed for weak gravity-capillary hydraulic falls (i.e. with τ < 1 3 , where τ is the Bond number defined by τ = σ /(ρgH 2 ) with σ being the surface tension coefficient) found in the neighbourhood of the minimum of the upstream gravity-capillary linear dispersion relation (see Guayjarernpanishk & Asavanant 2012;Page et al 2014).…”

“…We therefore look for flows where the depth of the fluid under the ice plate is different upstream and downstream of the obstacle (see, for example, Dias & Vanden-Broeck 2002). In the absence of an ice plate, when the forces of both gravity and surface tension are considered, gravity-capillary hydraulic falls have been obtained (Guayjarernpanishk & Asavanant 2012;Page, Grandison & Pȃrȃu 2014). The flexural-gravity problem has similarities to the gravity-capillary problem, but has additional complexity in the dynamic boundary condition.…”

The influence of surface tension upon trapped waves and hydraulic falls

“…The two integral equations (18) and (19), together with the dynamic condition (16) and the parametric equation (15), complete the reformulation of the problem, and provide the system of integro-differential equations, to be solved via Newton's method.…”

“…The relationship between F and A 2 can be seen in Figure 2 for τ = 0.2 and τ = 0.5. Guayjarernpanishk and Asavanant [16] found that critical flow solutions do not exist when surface tension is present, for obstacles below some critical height. Further, they found that as the height of the obstacle decreases towards the critical height, with τ up fixed, the free-surface immediately before the hydraulic fall develops a slight elevation.…”

“…However, they restricted their study to the first type of basic solution, in the presence of a single disturbance. Page, Pȃrȃu and Grandison [15] then studied gravitycapillary forced solitary waves generated by two localised pressure distributions, and Guayjarernpanishk and Asavanant [16] included the effects of surface tension in their study, and found basic flows of types one, two and three. In this paper, we include the effects of surface tension, and consider types three and four of the basic solutions; hydraulic falls and generalised hydraulic falls, as well as the effect of a second disturbance in the channel.…”