Analytical solution for the submerged free jet

Avishai Oved, Herman D. Haustein*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Laminar submerged free jet theory still falls short in the near-nozzle region and transition to Schlichting's self-similar jet. The author's recent solution, based on mass conservation, is found lacking beyond the near-nozzle jet-core region. Instead, it is here constrained to conserve momentum, resulting in a locally linearized convection-diffusion equation, valid over jet width and up to self-similarity, when compared to simulations. This new solution leads to profile-specific values of virtual-origin correction to Schlichting's solution. Additionally, extensive jet characteristics are examined: (1) curvature core, (2) radial inflection location, (3) radial velocity, (4) vorticity field, (5) issuing mass, and (6) jet width. All are well predicted, and new insights are gained for a variety of issuing profiles: from uniform, through a non-monotonous profile and up to fully developed. The issuing mass of all non-uniform profiles undergoes an initial contraction proportional to the profile's level of development. Interestingly, the submerged jet contracts identically to the free-surface jet in the very near-nozzle region, before significant influence of their differing boundary conditions. Moreover, unless the issuing profile contains a radial inflection point, the inflection always occurs in the entrained fluid, just beyond the bounds of the issuing mass. It also follows an initial contraction and only later a widening toward the self-similar trend. Despite this contraction, the entrained fluid causes monotonous total jet-widening, at a rate inversely proportional to the level of development. Finally, this new solution correctly captures additional jet features, such as the local radial velocity and decay of the primary vorticity.

Original languageEnglish
Article number033618
JournalPhysics of Fluids
Issue number3
StatePublished - 1 Mar 2024


FundersFunder number
PAZY Foundation22/467


    Dive into the research topics of 'Analytical solution for the submerged free jet'. Together they form a unique fingerprint.

    Cite this