Orr-Sommerfeld

Description: Orr-Sommerfeld Operator for Couette Flow

This benchmark models Orr-Sommerfeld Operator for a Couette flow. More details can be found in and , .

Origin

This benchmark is part of the SLICOT Benchmark Examples for Model Reduction.

Data

The system matrix \(A\) is available from the SLICOT benchmarks page: Orr-Som.zip and is stored as MATLAB .mat file.

Note that the data file only contains an \(A\) matrix! For \(B = C^\intercal \) any normalized vector \(B^\intercal B = 1\), can be chosen.

Dimensions

System structure:

\[ \begin{array}{rcl} \dot{x}(t) &=& Ax(t) + Bu(t) \\ y(t) &=& Cx(t) \end{array} \]

System dimensions\[A \in \mathbb{R}^{100 \times 100}\], \(B \in \mathbb{R}^{100 \times 1}\), \(C \in \mathbb{R}^{1 \times 100}\).

Citation

To cite this benchmark, use the following references:

• For the benchmark itself and its data:

Niconet e.V., SLICOT - Subroutine Library in Systems and Control Theory, http://www.slicot.org

@MANUAL{slicot_orrs,
 title =        {{SLICOT} - Subroutine Library in Systems and Control Theory},
 organization = {Niconet e.V.}
 address =      {\url{http://www.slicot.org}},
 key =          {SLICOT}
}

• For the background on the benchmark:

@ARTICLE{FarI01,
 author =       {B.F. Farrell and P.J. Ioannou},
 title =        {Accurate Low-Dimensional Approximation of the Linear Dynamics of Fluid Flow},
 journal =      {Journal of the Atmospheric Sciences},
 volume =       {58},
 number =       {18},
 pages =        {2771--2789},
 year =         {2001},
 doi =          {10.1175/1520-0469(2001)058<2771:ALDAOT>2.0.CO;2}
}