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A classical problem in free-surface hydrodynamics concerns flow in a channel, when an obstacle is placed on the bottom. Steady-state flows exist and may adopt one of three possible configurations, depending on the fluid speed and the obstacle height; perhaps the best known has an apparently uniform flow upstream of the obstacle, followed by a semiinfinite train of downstream gravity waves. When time-dependent behaviour is taken into account, it is found that conditions upstream of the obstacle are more complicated, however, and can include a train of upstream-advancing solitons. This paper gives a critical overview of these concepts, and also presents a new semianalytical spectral method for the numerical description of unsteady behaviour.
The mental health outcomes of military personnel deployed on peacekeeping
missions have been relatively neglected in the military mental health
To assess the mental health impacts of peacekeeping deployments.
In total, 1025 Australian peacekeepers were assessed for current and
lifetime psychiatric diagnoses, service history and exposure to
potentially traumatic events (PTEs). A matched Australian community
sample was used as a comparator. Univariate and regression analyses were
conducted to explore predictors of psychiatric diagnosis.
Peacekeepers had significantly higher 12-month prevalence of
post-traumatic stress disorder (16.8%), major depressive episode (7%),
generalised anxiety disorder (4.7%), alcohol misuse (12%), alcohol
dependence (11.3%) and suicidal ideation (10.7%) when compared with the
civilian comparator. The presence of these psychiatric disorders was most
strongly and consistently associated with exposure to PTEs.
Veteran peacekeepers had significant levels of psychiatric morbidity.
Their needs, alongside those of combat veterans, should be recognised
within military mental health initiatives.
The vertical rise of a round plume of light fluid through a surrounding heavier fluid is considered. An inviscid model is analysed in which the boundary of the plume is taken to be a sharp interface. An efficient spectral method is used to solve this nonlinear free-boundary problem, and shows that the plume narrows as it rises. A generalized condition is also introduced at the boundary, and allows the ambient fluid to be entrained into the rising plume. In this case, the fluid plume first narrows then widens as it rises. These features are confirmed by an asymptotic analysis. A viscous model of the same situation is also proposed, based on a Boussinesq approximation. It qualitatively confirms the widening of the plume due to entrainment of the ambient fluid, but also shows the presence of vortex rings around the interface of the rising plume.
The propagation of a solitary wave in a horizontal fluid layer is studied. There is an interfacial free surface above and below this intrusion layer, which is moving at constant speed through a stationary density-stratified fluid system. A weakly nonlinear asymptotic theory is presented, leading to a Korteweg–de Vries equation in which the two fluid interfaces move oppositely. The intrusion layer solitary wave system thus forms a widening bulge that propagates without change of form. These results are confirmed and extended by a fully nonlinear solution, in which a boundary-integral formulation is used to solve the problem numerically. Limiting profiles are approached, for which a corner forms at the crest of the solitary wave, on one or both of the interfaces.
Waves on a neutrally buoyant intrusion layer moving into otherwise stationary fluid are studied. There are two interfacial free surfaces, above and below the moving layer, and a train of waves is present. A small amplitude linearized theory shows that there are two different flow types, in which the two interfaces are either in phase or else move oppositely. The former flow type occurs at high phase speed and the latter is a low-speed solution. Nonlinear solutions are computed for large amplitude waves, using a spectral type numerical method. They extend the results of the linearized analysis, and reveal the presence of limiting flow types in some circumstances.
Steady flow with constant circulation into a vertical drain is considered. The precise details of the outflow are simplified by assuming that the drain is equivalent to a distributed volume sink, into which the fluid flows with uniform downward speed. It is shown that a maximum outflow rate exists, corresponding to no fluid circulation and vertical entry into the drain hole. Numerical solutions to the full nonlinear problem are computed, using the method of fundamental solutions. An approximate analysis, based on the use of the shallow-water equations, is presented for flows in which the free surface enters the drain. There is, in addition, a second type of solution, having a stagnation point at the free surface and no fluid circulation. These flows are also computed numerically, and results are presented.
This paper is about the ‘skeptical paradox’ which Saul Kripke extracts from the one hundred or so sections of Wittgenstein's Philosophical Investigations preceding §243, and focuses on the dispositionalist response to the skeptic, which seems to me to be a better response than Kripke is willing to allow.
The paradox is: ‘… no course of action could be determined by a rule, because every course of action can be made to accord with the rule’ (Investigations §210). When someone masters a concept, we think of him as grasping a content or meaning which will guide his future applications of the concept and against which those applications will be assessed as correct or incorrect. The challenge the skeptic poses is that of specifying a fact about the subject in virtue of which his later applications are correct, or incorrect. Perhaps, for example, the subject's understanding has degenerated over time, so that the applications he now makes he would once have rejected. The problem is not an epistemological one: the point is not that the subject cannot be sure that his understanding of the concept has not changed, but rather that there may be no such distinction as the purported one between a situation in which his understanding stays the same and one in which it changes. Thus, the skeptic's questions are not about how the subject knows that his understanding is the same as it was previously, for he holds that there is nothing to know here; instead, they are about what makes it the case that it is the same as it was.
The steady simultaneous withdrawal of two inviscid fluids of different
a duct of finite height is considered. The flow is two-dimensional, and
are removed by means of a line sink at some arbitrary position within the
It is assumed that the interface between the two fluids is drawn into the
that the flow is uniform far upstream. A numerical method based on an integral
equation formulation yields accurate solutions to the problem, and it is
under normal operating conditions, there is a solution for each value of
interface height. Numerical solutions suggest that limiting configurations
which the interface is drawn vertically into the sink. The appropriate
Froude number is derived for this situation, and it is shown that a continuum
solutions exists that are supercritical with respect to this Froude number.
branch of subcritical solutions is also presented.
Withdrawal flow through a point sink on the bottom of a fluid of finite depth is considered. The fluid is at rest at infinity, and a stagnation point is present at the free surface, directly above the point sink. Numerical solutions are computed by means of the method of fundamental solutions, and it is observed that flows of this type are apparently possible for Froude number less than about 1.5. Relationships to previous work are discussed.
A simple model for underground mineral leaching is considered, in which liquor is injected into the rock at one point and retrieved from the rock by being pumped out at another point. In its passage through the rock, the liquor dissolves some of the ore of interest, and this is therefore recovered in solution. When the injection and recovery points lie on a vertical line, the region of wetted rock forms an axi-symmetric plume, the surface of which is a free boundary. We present an accurate numerical method for the solution of the problem, and obtain estimates for the maximum possible recovery rate of the liquor, as a fraction of the injected flow rate. Limiting cases are discussed, and other geometries for fluid recovery are considered.
When a line sink is placed beneath the free surface of an otherwise quiescent fluid of infinite depth, two different flow types are now known to be possible. One type of flow involves the fluid being drawn down toward the sink, and in the other type, a stagnation point forms at the surface immediately above the position of the sink.
This paper investigates the second of these two flow types, which involves a free-surface stagnation point. The effects of surface tension are included, and even when small, these are shown to have a very significant effect on the overall solution behaviour. We demonstrate by direct numerical calculation that there are regions of genuine non-uniqueness in the nonlinear solution, when the surface-tension parameter does not vanish. In addition, an asymptotic solution valid for small Froude number is derived.
The flow caused by a point sink immersed in an otherwise stationary fluid is investigated. Low Froude number solutions are sought, in which the flow is radially symmetric and possesses a stagnation point at the surface, directly above the sink. A small-Froude-number expansion is derived and compared with the results of a numerical solution to the fully nonlinear problem. It is found that solutions of this type exist for all Froude numbers less than some maximum value, at which a secondary circular stagnation line is formed at the surface. The nonlinear solutions are reasonably well predicted by the small-Froude-number expansion, except for Froude numbers close to this maximum.
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