%0 Journal Article %1 tatsumi1958stability %A Tatsumi, T. %A Kakutani, T. %B Journal of Fluid Mechanics %D 1958 %I Cambridge University Press %K 76d25-wakes-and-jets 76e05-parallel-shear-flows %N 3 %P 261-275-- %R 10.1017/S0022112058000422 %T The stability of a two-dimensional laminar jet %U https://www.cambridge.org/core/article/stability-of-a-twodimensional-laminar-jet/218ABEB7FC508DF8B04CF77FA600118C %V 4 %X This paper deals with the stability of a two-dimensional laminar jet against the infinitesimal antisymmetric disturbance. The curve of the neutral stability in the (α, R)-plane (α, the wave-number; R, Reynolds number) is calculated using two different methods for the different parts of the curve; the solution is developed in powers of (αR)−1 for obtaining the upper branch of the curve and in powers of αR for the lower branch.The asymptotic behaviour of these branches is that for branch I,$2, \;\; c 23$ for $R ınfty$; and for branch II, $R 1\cdot12\alpha^-1|2,\; c 120 \alpha^2$ for α → 0. Some discussion is given on the validity of the basic assumption of the stability theory in relation to the numerical result obtained here.

@article{tatsumi1958stability, abstract = {This paper deals with the stability of a two-dimensional laminar jet against the infinitesimal antisymmetric disturbance. The curve of the neutral stability in the (α, R)-plane (α, the wave-number; R, Reynolds number) is calculated using two different methods for the different parts of the curve; the solution is developed in powers of (αR)−1 for obtaining the upper branch of the curve and in powers of αR for the lower branch.The asymptotic behaviour of these branches is that for branch I,$\alpha \rightarrow 2, \;\; c \rightarrow \frac{2}{3}$ for $R \rightarrow \infty$; and for branch II, $R \sim 1\cdot12\alpha^{-1|2},\; c \sim 1\cdot 20 \alpha^2$ for α → 0. Some discussion is given on the validity of the basic assumption of the stability theory in relation to the numerical result obtained here.}, added-at = {2020-06-30T02:43:14.000+0200}, author = {Tatsumi, T. and Kakutani, T.}, biburl = {https://www.bibsonomy.org/bibtex/238e80fb25a78a333579279c58da04ec8/gdmcbain}, booktitle = {Journal of Fluid Mechanics}, doi = {10.1017/S0022112058000422}, interhash = {e3ca3b616cdc5e88aa391b6b715141f0}, intrahash = {38e80fb25a78a333579279c58da04ec8}, issn = {00221120}, keywords = {76d25-wakes-and-jets 76e05-parallel-shear-flows}, number = 3, pages = {261-275--}, publisher = {Cambridge University Press}, timestamp = {2020-06-30T02:43:14.000+0200}, title = {The stability of a two-dimensional laminar jet}, url = {https://www.cambridge.org/core/article/stability-of-a-twodimensional-laminar-jet/218ABEB7FC508DF8B04CF77FA600118C}, volume = 4, year = 1958 }