English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Spiral structure is one of the most common structures in the nature flows. Ageneral steady spiral solution of incompressible inviscid axisymmetric flow wasobtained analytically by applying separation of variables to the 3D Eulerequations. The solution, depending on 3 parameters, describes the spiral pathof the fluid material element on the Bernoulli surface, whereas some new exactsolutions were obtained to be bounded within the whole region. The first one isa continued typhoon-like vortex solution, where there are two intrinsic lengthscales. One is the radius of maximum circular velocity $r_m$, the other is theradius of the vortex kernel $r_k=\sqrt{2}r_m$. The second one is a multi-planarsolution, periodically in $z$-coordinate. Within each layer, the solution is aumbrella vortex similar to the first one. The third one is also a multi-planarsolution in $z$-coordinate. In each layer, it is a combination of twoindependent solutions like the Rankine vortex, which is also finite butdiscontinued for either vertical or horizontal velocity. The fourth one is amulti-paraboloid vortex solution finite for $z$-coordinate but infinite for$r$-coordinate. Besides, some classical simple solutions (Rankine vortex,Batchelor vortex, Hill spherical vortex, etc.) were also obtained. The aboveexplicit solutions can be applied to study the radial structure of the typhoon,tornados and mesoscale eddies. Both the solutions and approaches used herecould also be applied to other complex flows by the Navier-Stokes equations.

An exact axisymmetric spiral solution of incompressible 3D Euler equations