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/

Global: Zendy Plus annual

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

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We impose a linearized Eulerian perturbation on a steady, shallow, radialoutflow of a liquid (water), whose local pressure function includes both thehydrostatic and the Laplace pressure terms. The resulting wave equation bearsthe form of a hydrodynamic metric. A dispersion relation, extracted from thewave equation, gives an instability due to surface tension and the cylindricalflow symmetry. Using the dispersion relation, we also derive three knownrelations that scale the radius of the circular hydraulic jump in the outflow.The first two relations are scaled by viscosity and gravity, with acapillarity-dependent crossover to the third relation, which is scaled byviscosity and surface tension. The perturbation as a high-frequency travellingwave, propagating radially inward against the bulk outflow, is blocked justoutside the circular hydraulic jump. The amplitude of the wave also divergeshere because of a singularity. The blocking is associated with surface tension,which renders the circular hydraulic jump a hydrodynamic white hole.

Surface tension and instability in the hydrodynamic white hole of a circular hydraulic jump