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Cato edited Payam & DNA.tex
almost 11 years ago
Commit id: 940fd1c3911237394b3dedf5b6c48eb6fede05cb
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I want to think about {\it which time scale is more appropriate in this context and why?}
\item So, {\it what should the time-scale be from }physical {\it reasoning: what is the physics behind establishing the flow profile $\vec{v}(\vec{x})$ in the fluid around the DNA/jet?}\\
\citet{1959flme.book.....L} argue $\vec{v}(\vec{x})$ purely from momentum conservation / Gauss' Law, and
symmetries in the
form of momentum flux tensor. Time doesn't enter into the
stress tensor: no time component. analysis; nor does Navier-Stokes.
\item {\it Does Payam assume incompressible
flow?} fluid?} Yes -- he follows \citet{1959flme.book.....L} pp. 86-88 in setting up the submerged jet; they assume zero divergence in the velocity field \& use stress tensor for incompressible flow. (The derivation in \citet{Broman_Rudenko_2010} also assumes incompressibility.) This means that the sound speed in his model will be infinite, and sonic information transfer will be irrelevant.
\item {\it Should I re-visit the derivation with sound included?}
Method 1: I would have to derive the formulae for the submerged jet in a compressible fluid, and perhaps solve the time-dependent Navier-Stokes equation.\\