TY - JOUR
T1 - Collapse, symmetry breaking, and hysteresis in swirling flows
AU - Shtern, Vladimir
AU - Hussain, Fazle
PY - 1999
Y1 - 1999
N2 - The paper reviews striking features of swirling flows - collapse, swirl generation, vortex breakdown, hysteresis, and axisymmetry breaking - and the mechanisms involved with the help of conical similarity solutions of the Navier-Stokes equations. The strong accumulation of axial and angular momenta, observed in tornadoes and flows over delta wings, corresponds to collapse, i.e. the singularity development in these solutions. Bifurcation of swirl explains the threshold character of swirl development in capillary and electrovortex flows. Analytical solutions for fold catastrophes and hysteresis reveal why there are so few stable states and why the jump transitions between the states occur - features typical of tornadoes, of flows over delta wings, and in vortex devices. Finally, the divergent instability explains such effects as the splitting of a tornado and the development of spiral branches in tree and near-wall swirling flows.
AB - The paper reviews striking features of swirling flows - collapse, swirl generation, vortex breakdown, hysteresis, and axisymmetry breaking - and the mechanisms involved with the help of conical similarity solutions of the Navier-Stokes equations. The strong accumulation of axial and angular momenta, observed in tornadoes and flows over delta wings, corresponds to collapse, i.e. the singularity development in these solutions. Bifurcation of swirl explains the threshold character of swirl development in capillary and electrovortex flows. Analytical solutions for fold catastrophes and hysteresis reveal why there are so few stable states and why the jump transitions between the states occur - features typical of tornadoes, of flows over delta wings, and in vortex devices. Finally, the divergent instability explains such effects as the splitting of a tornado and the development of spiral branches in tree and near-wall swirling flows.
KW - Axisymmetry breaking
KW - Conical similarity solutions
KW - Fold catastrophe
KW - Swirl accumulation
KW - Vortex breakdown
UR - http://www.scopus.com/inward/record.url?scp=0033489576&partnerID=8YFLogxK
U2 - 10.1146/annurev.fluid.31.1.537
DO - 10.1146/annurev.fluid.31.1.537
M3 - Article
AN - SCOPUS:0033489576
SN - 0066-4189
VL - 31
SP - 537
EP - 566
JO - Annual Review of Fluid Mechanics
JF - Annual Review of Fluid Mechanics
ER -