Bifurcation phenomena in steady flows of a viscous fluid II. Experiments
T. Benjamin. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 359 (1696):
27--43(January 1978)
DOI: 10.1098/rspa.1978.0030
Abstract
The experimental work is concerned with several phenomena studied theoretically in part I (Benjamin 1977). Observations on Taylor-vortex flows between cylinders of comparatively small but variable length are reported, revealing properties unexplained by older theories. The observed flows are classified as follows: (i) the primary mode which is uniquely possible at small values of the Reynolds number R, and which usually develops smoothly with increasing R; (ii) secondary modes which are possible only above a respective critical value of R, and which are shown to manifest predicted behaviour as this value is approached from above (§4). Two novel and surprising examples of (ii) are reported. A predicted hysteresis phenomenon is confirmed, relating to morphogenesis of the primary mode between two-cell and four-cell forms as the length of the annulus is varied (§5). The experimental results are discussed from a theoretical standpoint in §6.
%0 Journal Article
%1 1978
%A Benjamin, Thomas Brooke
%D 1978
%I The Royal Society
%J Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
%K 76-05-fluid-mechanics-experimental-work 76d05-incompressible-navier-stokes-equations 76e07-hydrodynamic-stability-rotation 76e30-hydrodynamic-stability-nonlinear-effects
%N 1696
%P 27--43
%R 10.1098/rspa.1978.0030
%T Bifurcation phenomena in steady flows of a viscous fluid II. Experiments
%U https://royalsocietypublishing.org/doi/10.1098/rspa.1978.0030
%V 359
%X The experimental work is concerned with several phenomena studied theoretically in part I (Benjamin 1977). Observations on Taylor-vortex flows between cylinders of comparatively small but variable length are reported, revealing properties unexplained by older theories. The observed flows are classified as follows: (i) the primary mode which is uniquely possible at small values of the Reynolds number R, and which usually develops smoothly with increasing R; (ii) secondary modes which are possible only above a respective critical value of R, and which are shown to manifest predicted behaviour as this value is approached from above (§4). Two novel and surprising examples of (ii) are reported. A predicted hysteresis phenomenon is confirmed, relating to morphogenesis of the primary mode between two-cell and four-cell forms as the length of the annulus is varied (§5). The experimental results are discussed from a theoretical standpoint in §6.
@article{1978,
abstract = {The experimental work is concerned with several phenomena studied theoretically in part I (Benjamin 1977). Observations on Taylor-vortex flows between cylinders of comparatively small but variable length are reported, revealing properties unexplained by older theories. The observed flows are classified as follows: (i) the primary mode which is uniquely possible at small values of the Reynolds number R, and which usually develops smoothly with increasing R; (ii) secondary modes which are possible only above a respective critical value of R, and which are shown to manifest predicted behaviour as this value is approached from above (§4). Two novel and surprising examples of (ii) are reported. A predicted hysteresis phenomenon is confirmed, relating to morphogenesis of the primary mode between two-cell and four-cell forms as the length of the annulus is varied (§5). The experimental results are discussed from a theoretical standpoint in §6.},
added-at = {2021-05-14T01:17:13.000+0200},
author = {Benjamin, Thomas Brooke},
biburl = {https://www.bibsonomy.org/bibtex/2efc74aaf13761ec30a0caac6d6de4606/gdmcbain},
doi = {10.1098/rspa.1978.0030},
interhash = {585ddbc9581bd9eba3df8d9bf5cefe8a},
intrahash = {efc74aaf13761ec30a0caac6d6de4606},
journal = {Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences},
keywords = {76-05-fluid-mechanics-experimental-work 76d05-incompressible-navier-stokes-equations 76e07-hydrodynamic-stability-rotation 76e30-hydrodynamic-stability-nonlinear-effects},
month = jan,
number = 1696,
pages = {27--43},
publisher = {The Royal Society},
timestamp = {2021-05-14T01:17:45.000+0200},
title = {Bifurcation phenomena in steady flows of a viscous fluid {II}. Experiments},
url = {https://royalsocietypublishing.org/doi/10.1098/rspa.1978.0030},
volume = 359,
year = 1978
}