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Cato edited Payam.tex
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\item Dimensional analysis argument not fully understood: I think $t_{\rm h}\sim \ell/c_{\rm s}$ on physical grounds, but Payam says $t_{\rm h}\sim \ell^2\rho/\eta$ from dimensional analysis. What is the interpretation of Payam's $t_{\rm h}$? Are the two compatible?
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\begin{itemize}
\item The two $t_{\rm h}$s are measuring different things. Payam's $t_{\rm h}$ is considering the {\it diffusion }of a particle's momentum: the characteristic time in the velocity autocorrelation. My $t_{\rm h}$ is about information flow via sonic waves: this is much smaller than the vorticity
time-scale. time-scale.\\
I want to think about {\it which time scale is more appropriate in this context and why?}
\item
So, {\it
What what should the time-scale be from physical reasoning: what is the physics behind establishing the flow profile $\vec{v}(\vec{x})$ in the fluid around the DNA/jet? (Read \citet{Broman_Rudenko_2010}, \citet{1959flme.book.....L} pp. 86-88).}
\item {\it
Which process (sound or vorticity) carries Does Payam assume incompressible flow?} 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?}\\
I would have to re-derive the formulae for the submerged jet, and perhaps solve the time-dependent Navier-Stokes equation.\\
However, it would (arguably) be a better model (see references below), and may be more
momentum?} Read \citet{1959flme.book.....L}, chapter 8, on sound. illuminating as to how the velocity profile is set up, and the nature of interactions between neighbouring DNA molecules.
\item {\it
Does Payam assume incompressible flow?} Yes -- he follows \citet{1959flme.book.....L} pp. 86-88 in setting up the submerged jet; and 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!\\
{\it Would there be any point in re-visiting the derivation with incompressibility assumption dropped?} Which process (sound or vorticity) carries more momentum?} Read \citet{1959flme.book.....L}, chapter 8, on sound.
\item Another thing to consider: {\it does it even matter?} The time-scale they use
in the paper is
much larger than the sound-time, and places a more stringent test on the steady-state assumption. So my objection would only strengthen the
conclusion. The conclusion.\\The vorticity moves slowest, and the fluid velocity profile might only assume the anticipated form once this final contribution has had time to influence the entire profile.
\item Could the problems in Payam's other paper conceivably be explained by this phenomenon?