Generator

Stable in every mode, and 100 times larger first

Stable in every mode, and 100 times larger first
Stable in every mode, and 100 times larger firstThe energy of the worst-case disturbance against time, on a logarithmic scale, at four Reynolds numbers and at the one the slider selects. Time is in units of Re, which is what makes the four curves the same shape; what changes with Reynolds number is the height, and it changes as the square. Every eigenvalue of this operator is negative throughout, so nothing that grows here is an instability in the sense a stability analysis reports.01234501234time, in units of Relog₁₀ of the energy gaint = Re ln 2no growth at allRe = 10: peak 7×Re = 40: peak 100×Re = 160: peak 1600×Re = 640: peak 25600×Re = 325: peak 6602×eigenvalues, all Re:−1/Re and −2/Reboth negative, alwaysso nothing here isan instability‖exp(At)‖² by singular-value decomposition at each timea model system, not a flow — no fluid property appears anywhere in it

The energy of the worst-case disturbance against time, on a logarithmic scale, at four Reynolds numbers and at the one the slider selects. Time is in units of Re, which is what makes the four curves the same shape; what changes with Reynolds number is the height, and it changes as the square. Every eigenvalue of this operator is negative throughout, so nothing that grows here is an instability in the sense a stability analysis reports.

1 essay calls transient-growth. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

It is also the blast radius. Changing transient-growth changes every figure listed here at once, and on this site it may change what they assert as well as what they show — which is what has to be rebuilt and looked at before the change is believed.

Where it is called

What each of these essays asks for instead of the defaults is on the regime index, which reads the parameters back out of the finished figures rather than out of the placements.

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