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Related Concept Videos

Bernoulli's Equation for Flow Normal to a Streamline01:16

Bernoulli's Equation for Flow Normal to a Streamline

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Plane Potential Flows01:23

Plane Potential Flows

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Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure
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Variational framework for flow optimization using seminorm constraints.

D P G Foures1, C P Caulfield, P J Schmid

  • 1DAMTP, University of Cambridge, Centre for Mathematical Sciences, Cambridge, United Kindgom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

We developed a new framework for optimizing and analyzing evolving fluid flows governed by partial differential equations. This method quantizes the impact of different physical mechanisms on flow behavior, revealing new energy production pathways.

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Area of Science:

  • Fluid dynamics
  • Computational mathematics
  • Nonlinear dynamics

Background:

  • Constrained optimization and sensitivity analysis are crucial for understanding complex physical systems governed by partial differential equations (PDEs).
  • Seminorm constraints frequently arise in optimization problems where the objective function involves contributions from multiple physical mechanisms.
  • Existing frameworks may not adequately address the nuanced interplay of complementary seminorm constraints in evolving flows.

Purpose of the Study:

  • To introduce a general variational framework for constrained optimization and sensitivity analysis of flows described by PDEs.
  • To specifically address optimization problems involving seminorm constraints arising from multiple physical mechanisms.
  • To demonstrate the framework's utility in analyzing the stability of evolving flows with dynamic turbulent viscosity.

Main Methods:

  • Development of a general variational framework incorporating constrained optimization and sensitivity analysis for PDE-governed flows.
  • Introduction of new parameters to quantify the relative magnitudes of complementary seminorm perturbations.
  • Application of the framework to the nonmodal stability analysis of a stochastically forced Burgers equation with evolving turbulent viscosity.

Main Results:

  • The framework enables quantitative analysis of the influence of individual seminorm components on the total perturbation norm.
  • Optimization is achieved by prescribing new parameters as initial conditions on admissible perturbations.
  • The study reveals that evolving turbulent viscosity leads to qualitatively different flow dynamics compared to frozen viscosity, including a new perturbation energy production mechanism.

Conclusions:

  • The proposed variational framework provides a robust method for analyzing complex fluid flows with seminorm constraints.
  • The framework's ability to handle evolving parameters like turbulent viscosity is essential for accurate stability analysis.
  • Understanding the interplay between evolving turbulent viscosity and mean flow is critical for predicting flow behavior and identifying novel energy production mechanisms.