Green-Ampt approximations

The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W-1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W-1 function and vice versa. An infinite family of asymptotic expansions to W-1 is presented. Although these expansions do not converge near the branch point of the W function (corresponds to Green-Ampt infiltration with immediate ponding), a method is presented for approximating W-1 that is exact at the branch point and asymptotically, with interpolation between these limits. Some existing and several new simple and compact yet robust approximations applicable to Green-Ampt infiltration and flux are presented, the most accurate of which has a maximum relative error of 5 x 10(-5)%. This error is orders of magnitude lower than any existing analytical approximations. (c) 2005 Elsevier Ltd. All rights reserved.

Three horizontal muscle squint surgery for large angle infantile esotropia

Background: To report the long-term outcome of a series of 49 patients who underwent three horizontal muscle squint surgery for large angle infantile esotropia. Methods: The patient records were retrospectively reviewed of 49 (24 girls [49%], 25 boys) consecutive patients with infantile esotropia of angle greater than or equal to60 Delta, who had undergone three horizontal muscle surgery performed by one surgeon (author GG). Surgery consisted of bilateral medial rectus recession combined with graded unilateral lateral rectus resection. Surgeries were carried out over a 6-year period with a mean follow-up period of 32.9 months (3.7-71.8 months). Results: Using Kaplan-Meier life-table analysis, cumulative surgical success (orthotropia +/-10 Delta) was 93.9% at 1 week, 91.8% at 2 and 6 months, 87.7% at 12 and 18 months, 79.9% at 2 years, 77.1% at 3, 4 and 5 years, and 70.6% at 6 years. The mean preoperative deviation was 68.7 Delta. The mean age at surgery was 12.9 months. The failure rate was independent of preoperative deviation. Prevalence of residual esotropia (>10 Delta) varied from 2.0% at 1 week to 17.0% at 6 years. Similarly the prevalence of consecutive exotropia (>10 Delta) varied from 4.0% at 1 week to 12.4% at 6 years. Conclusion: Operating in a graded fashion on three horizontal muscles in children with large angle infantile esotropia has a high success rate, even over long-term follow up. Based on the study's results, amounts of surgery for a given angle of strabismus are proposed.

On the role of magnesium and nitrogen in the infiltration of aluminium by aluminium for rapid prototyping applications

Selective laser sintering has been used to fabricate an aluminium alloy powder preform which is subsequently debound and infiltrated with a second aluminium alloy. This represents a new rapid manufacturing system for aluminium that can be used to fabricate large, intricate parts. The base powder is an alloy such as AA6061. The infiltrant is a binary or higher-order eutectic based on either Al-Cu or At-Si. To ensure that infiltration occurs without loss of dimensional precision, it is important that a rigid skeleton forms prior to infiltration. This can be achieved by the partial transformation of the aluminium to aluminium nitride. In order for this to occur throughout the component, magnesium powder must be added to the alumina support powder which surrounds the part in the furnace. The magnesium scavenges the oxygen and thereby creates a microclimate in which aluminium nitride can form. The replacement of the ionocovalent Al2O3 with the covalent AlN on the surface of the aluminium powders also facilitates wetting and thus spontaneous and complete infiltration. (C) 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

On the role of tin in the infiltration of aluminium by aluminium for rapid prototyping applications

The use of tin as an alloying element in the production of freeformed infiltrated aluminium components is explored. Tin slows the growth of the aluminium nitride skeleton which provides dimensional stability, as well as increasing the rate of infiltration of the aluminium liquid into the aluminium nitride skeleton. (C) 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Wave-generated flow on coral reefs - an analysis for two-dimensional horizontal reef-tops with steep faces

Waves breaking on the seaward rim of a coral reef generate a flow of water from the exposed side of the reef to the sheltered side and/or to either channels through the reef-rim or lower sections of the latter. This wave-generated flow is driven by the water surface gradient resulting from the wave set-up created by the breaking waves. This paper reviews previous approaches to modelling wave-generated flows across coral reefs and discusses the influence of reef morphology and roughness upon these flows. Laboratory measurements upon a two-dimensional horizontal reef platform with a steep reef face provide the basis for extending a previous theoretical analysis for wave set-up on a reef in the absence of a flow [Gourlay, M.R., 1996b. Wave set-up on coral reefs. 2. Set-up on reefs with various profiles. Coastal Engineering 28, 1755] to include the interaction between a unidirectional flow and the wave set-up. The laboratory model results are then used to demonstrate that there are two basic reef-top flow regimes-reef-top control and reef-rim control. Using open channel flow theory, analytical relationships are derived for the reef-top current velocity in terms of the offreef wave conditions, the reef-top water depth and the physical characteristics of the reef-top topography. The wave set-up and wave-generated flow relationships are found to predict experimental values with reasonable accuracy in most cases. The analytical relationships are used to investigate wave-generated flows into a boat harbour channel on Heron Reef in the southern Great Barrier Reef. (c) 2005 Elsevier B.V. All rights reserved.

Field observations of instantaneous water slopes and horizontal pressure gradients in the swash-zone

Field observations of instantaneous water surface slopes in the swash zone are presented. For free-surface flows with a hydrostatic pressure distribution the surface slope is equivalent to the horizontal pressure gradient. Observations were made using a novel technique which in its simplest form consists of a horizontal stringline extending seaward from the beach face. Visual observation, still photography or video photography is then sufficient to determine the surface slope where the free-surface cuts the line or between reference points in the image. The method resolves the mean surface gradient over a cross-shore distance of 5 m or more to within +/- 0.001, or 1/20th -1/100th of typical beach gradients. In addition, at selected points and at any instant in time during the swash cycle, the water surface slope can be determined exactly to be dipping either seaward or landward. Close to the location of bore collapse landward dipping water surface slopes of order 0.05-0.1 occur over a very small region (order 0.5 m) at the blunt or convex leading edge of the swash. In the middle and upper swash the water surface slope at this leading edge is usually very close to horizontal or slightly seaward. Behind the leading edge, the water surface slope was observed to be very close to horizontal or dipping seaward at all times throughout the swash uprush. During the backwash the water surface slope was observed to be always dipping seaward, approaching the beach slope, and remained seaward until a new uprush edge or incident bore passed any particular cross-shore location of interest. The observations strongly Suggest that the swash boundary layer is subject to an adverse pressure gradient during uprush and a favourable pressure gradient during the backwash. Furthermore, assuming Euler's equations are a good approximation in the swash, the observations also show that the total fluid acceleration is negative (offshore) for almost the whole of the uprush and for the entire backwash. The observations are contrary to recent work suggesting significant shoreward directed accelerations and pressure gradients occur in the swash (i.e., delta u/delta t > 0 similar to delta p/delta x < 0), but consistent with analytical and numerical solutions for swash uprush and backwash. The results have important implications for sediment transport modelling in the swash zone.