On steady compressible flows with compact vorticity; the compressible Stuart vortex

Numerical and analytical solutions to the steady compressible Euler equations corresponding to a compressible analogue of the linear Stuart vortex array are presented. These correspond to a homentropic continuation, to finite Mach number, of the Stuart solution describing a linear vortex array in an incompressible fluid. The appropriate partial differential equations describing the flow correspond to the compressible homentropic Euler equations in two dimensions, with a prescribed vorticity–density–streamfunction relationship. In order to construct a well-posed problem for this continuation, it was found, unexpectedly, to be necessary to introduce an eigenvalue into the vorticity–density–streamfunction equation. In the Rayleigh–Janzen expansion of solutions in even powers of the free-stream Mach number M[infty infinity], this eigenvalue is determined by a solvability condition. Accurate numerical solution by both finite-difference and spectral methods are presented for the compressible Stuart vortex, over a range of M[infty infinity], and of a parameter corresponding to a confined mass-flow rate. These also confirm the nonlinear eigenvalue character of the governing equations. All solution branches followed numerically were found to terminate when the maximum local Mach number just exceeded unity. For one such branch we present evidence for the existence of a very small range of M[infty infinity] over which smooth transonic shock-free flow can occur

Remark on a result of D. Dritschel

A hypothesis put forward by D. Dritschel [J. Fluid Mech. 94, 511 (1988)], namely that an isolated symmetrical disturbance on a uniform vortex patch will filament in time proportional to the inverse square of the disturbance amplitude, is subject to independent testing using a nonintrusive numerical method. The hypothesis that the trend is maintained to substantially smaller amplitudes than were originally considered by Dritschel is both supported and verified. The results may be interpreted as providing limited evidence that contour smoothness is maintained in filamentation and that corner formation does not occur up to the time of wave overturning

Inventory of wetland habitat using remote sensing for the proposed Oahe irrigation unit in eastern South Dakota

An inventory of wetlands for the area included in the proposed Oahe irrigation project was conducted to provide supplemental data for the wildlife mitigation plan. Interpretation techniques for inventoring small wetlands in the low relief terrain of the Lake Dakota Plain were documented and data summaries included. The data were stored and tabulated in a computerized spatial data analysis system

Facing up to the challenge of behavioural observation in infant hearing assessment

The ability to assess detection and discrimination of speech by infants has proved elusive. Dr Iain Jackson and colleagues discuss how new technologies and fresh approaches might offer valuable insight into young infants’ behavioural responses to sound

Boundary-detection algorithm for locating edges in digital imagery

The author has identified the following significant results. Initial development of a computer program which implements a boundary detection algorithm to detect edges in digital images is described. An evaluation of the boundary detection algorithm was conducted to locate boundaries of lakes from LANDSAT-1 imagery. The accuracy of the boundary detection algorithm was determined by comparing the area within boundaries of lakes located using digitized LANDSAT imagery with the area of the same lakes planimetered from imagery collected from an aircraft platform

On steady compressible flows with compact vorticity; the compressible Hill's spherical vortex

We consider steady compressible Euler flow corresponding to the compressible analogue of the well-known incompressible Hill's spherical vortex (HSV). We first derive appropriate compressible Euler equations for steady homentropic flow and show how these may be used to define a continuation of the HSV to finite Mach number M_∞ =U_∞/C_∞, where U_∞, C_∞ are the fluid velocity and speed of sound at infinity respectively. This is referred to as the compressible Hill's spherical vortex (CHSV). It corresponds to axisymmetric compressible Euler flow in which, within a vortical bubble, the azimuthal vorticity divided by the product of the density and the distance to the axis remains constant along streamlines, with irrotational flow outside the bubble. The equations are first solved numerically using a fourth-order finite-difference method, and then using a Rayleigh–Janzen expansion in powers of M^2_∞ to order M^4_∞. When M_∞ > 0, the vortical bubble is no longer spherical and its detailed shape must be determined by matching conditions consisting of continuity of the fluid velocity at the bubble boundary. For subsonic compressible flow the bubble boundary takes an approximately prolate spheroidal shape with major axis aligned along the flow direction. There is good agreement between the perturbation solution and Richardson extrapolation of the finite difference solutions for the bubble boundary shape up to M_∞ equal to 0.5. The numerical solutions indicate that the flow first becomes locally sonic near or at the bubble centre when M_∞ ≈ 0.598 and a singularity appears to form at the sonic point. We were unable to find shock-free steady CHSVs containing regions of locally supersonic flow and their existence for the present continuation of the HSV remains an open question

From an axiological standpoint

I maintain that intrinsic value is the fundamental concept of axiology. Many contemporary philosophers disagree; they say the proper object of value theory is final value. I examine three accounts of the nature of final value: the first claims that final value is non‐instrumental value; the second claims that final value is the value a thing has as an end; the third claims that final value is ultimate or non‐derivative value. In each case, I argue that the concept of final value described is either identical with the classical notion of intrinsic value or is not a plausible candidate for the primary concept of axiology

Classical Scattering in 1+11+1 Dimensional String Theory

We find the general solution to Polchinski's classical scattering equations for $1+1$ dimensional string theory. This allows efficient computation of scattering amplitudes in the standard Liouville $\times$ $c=1$ background. Moreover, the solution leads to a mapping from a large class of time-dependent collective field theory backgrounds to corresponding nonlinear sigma models. Finally, we derive recursion relations between tachyon amplitudes. These may be summarized by an infinite set of nonlinear PDE's for the partition function in an arbitrary time-dependent background.Comment: 15 p