Symbolic analysis of reduced forms of the Navier-Stokes equations

AbstractA unified development of symbolic analysis is presented. Symbolic analysis is used to identify reduced forms of the linearized steady Navier-Stokes equations which permit computational solutions to be obtained in a single spatial march in the dominant flow direction. In particular it is demonstrated that the “parabolized” form of the Navier-Stokes equations, although not parabolic, is well-posed as an initial-value problem in space, provided the solution is restricted to functions with compact support. The effectiveness of symbolic analysis for determining the well-posedness of complex systems of equations, such as the Navier-Stokes equations, is clearly demonstrated

Large negative velocity gradients in Burgers turbulence

We consider 1D Burgers equation driven by large-scale white-in-time random force. The tails of the velocity gradients probability distribution function (PDF) are analyzed by saddle-point approximation in the path integral describing the velocity statistics. The structure of the saddle-point (instanton), that is velocity field configuration realizing the maximum of probability, is studied numerically in details. The numerical results allow us to find analytical solution for the long-time part of the instanton. Its careful analysis confirms the result of [Phys. Rev. Lett. 78 (8) 1452 (1997) [chao-dyn/9609005]] based on short-time estimations that the left tail of PDF has the form ln P(u_x) \propto -|u_x|^(3/2).Comment: 10 pages, RevTeX, 10 figure

A retrospective evaluation of the impact of a dedicated obstetric and neonatal transport service on transport times within an urban setting

OBJECTIVE:To determine whether the establishment of a dedicated obstetric and neonatal flying squad resulted in improved performance within the setting of a major metropolitan area.DESIGN AND SETTING:The Cape Town metropolitan service of the Emergency Medical Services was selected for a retrospective review of the transit times for the newly implemented Flying Squad programme. Data were imported from the Computer Aided Dispatch programme. Dispatch, Response, Mean Transit and Total Pre-hospital times relating to the obstetric and neonatal incidents was analysed for 2005 and 2008. RESULTS: There was a significant improvement between 2005 and 2008 in all incidents evaluated. Flying Squad dispatch performance improved from 11.7% to 46.6% of all incidents dispatched within 4 min (p < 0.0001). Response time performance at the 15-min threshold did not demonstrate a statistically significant improvement (p = 0.4), although the improvement in the 30-min performance category was statistically significant in both maternity and neonatal incidents. Maternity incidents displayed the greatest improvement with the 30-min performance increasing from 30.3% to 72.9%. The analysis of the mean transit times demonstrated that neonatal transfers displayed the longest status time in all but one of the categories. Even so, the introduction of the Flying Squad programme resulted in a reduction in a total pre-hospital time from 177 to 128 min. CONCLUSION: The introduction of the Flying Squad programme has resulted in significant improvement in the transit times of both neonatal and obstetric patients. In spite of the severe resource constraints facing developing nations, the model employed offers significant gains