%0 Journal Article %1 jewell2006instability %A Jewell, Nathaniel %A Denier, James P. %D 2006 %J The Quarterly Journal of Mechanics and Applied Mathematics %K 76e05-parallel-shear-flows 76e99-hydrodynamic-stability-other %N 4 %P 651–673 %R 10.1093/qjmam/hbl021 %T The instability of the flow in a suddenly blocked pipe %U https://academic.oup.com/qjmam/article/59/4/651/1943109 %V 59 %X This paper considers the decay of Poiseuille flow within a suddenly blocked pipe. For small to moderate times the flow is shown to consist of an inviscid core flow coupled with a boundary layer at the pipe wall. A small-time asymptotic solution is developed and it is shown that this solution is valid for times up to the point at which the boundary layer fills the whole pipe. A small-time composite solution is used to initiate a numerical marching procedure which overcomes the small-time singularity that arises in the flow and so allows us to describe the ultimate decay of the flow within a blocked pipe. The stability of this flow is then considered using both a quasi-steady approximation and a transient-growth analysis based upon marching solutions of the linearized Navier–Stokes equations. Our transient stability analysis predicts a critical Reynolds number, for transition to turbulence, in the range 970 < Re < 1370.

@article{jewell2006instability, abstract = { This paper considers the decay of Poiseuille flow within a suddenly blocked pipe. For small to moderate times the flow is shown to consist of an inviscid core flow coupled with a boundary layer at the pipe wall. A small-time asymptotic solution is developed and it is shown that this solution is valid for times up to the point at which the boundary layer fills the whole pipe. A small-time composite solution is used to initiate a numerical marching procedure which overcomes the small-time singularity that arises in the flow and so allows us to describe the ultimate decay of the flow within a blocked pipe. The stability of this flow is then considered using both a quasi-steady approximation and a transient-growth analysis based upon marching solutions of the linearized Navier–Stokes equations. Our transient stability analysis predicts a critical Reynolds number, for transition to turbulence, in the range 970 < Re < 1370.}, added-at = {2019-10-22T00:50:51.000+0200}, author = {Jewell, Nathaniel and Denier, James P.}, biburl = {https://www.bibsonomy.org/bibtex/2df4e3218d6d30ba46fea1eecaca8f3bd/gdmcbain}, doi = {10.1093/qjmam/hbl021}, interhash = {cebda091cacccd8f350b7b409232b34e}, intrahash = {df4e3218d6d30ba46fea1eecaca8f3bd}, journal = {The Quarterly Journal of Mechanics and Applied Mathematics}, keywords = {76e05-parallel-shear-flows 76e99-hydrodynamic-stability-other}, month = nov, number = 4, pages = {651–673}, timestamp = {2019-10-22T00:50:51.000+0200}, title = {The instability of the flow in a suddenly blocked pipe}, url = {https://academic.oup.com/qjmam/article/59/4/651/1943109}, volume = 59, year = 2006 }