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Abstract We considerG, a linear algebraic group defined over$$\Bbbk $$, an algebraically closed field (ACF). By considering$$\Bbbk $$as an embedded residue field of an algebraically closed valued fieldK, we can associate to it a compactG-space$$S^\mu _G(\Bbbk )$$consisting of$$\mu $$-types onG. We show that for each$$p_\mu \in S^\mu _G(\Bbbk )$$,$$\mathrm {Stab}^\mu (p)=\mathrm {Stab}\left (p_\mu \right )$$is a solvable infinite algebraic group when$$p_\mu $$is centered at infinity and residually algebraic. Moreover, we give a description of the dimension of$$\mathrm {Stab}\left (p_\mu \right )$$in terms of the dimension ofp.
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Plunging breakers. Part 2. Droplet generation
An experimental study of the dynamics and droplet production in three mechanically generated plunging breaking waves is presented in this two-part paper. In the present paper (Part 2), in-line cinematic holography is used to measure the positions, diameters ($$d\geq 100\ \mathrm {\mu }{\rm m}$$), times and velocities of droplets generated by the three plunging breaking waves studied in Part 1 (Erininet al.,J. Fluid Mech., vol. 967, 2023, A35) as the droplets move up across a horizontal measurement plane located just above the wave crests. It is found that there are four major mechanisms for droplet production: closure of the indentation between the top surface of the plunging jet and the splash that it creates, the bursting of large bubbles that were entrapped under the plunging jet at impact, splashing and bubble bursting in the turbulent zone on the front face of the wave and the bursting of small bubbles that reach the water surface at the crest of the non-breaking wave following the breaker. The droplet diameter distributions for the entire droplet set for each breaker are fitted with power-law functions in separate small- and large-diameter regions. The droplet diameter where these power-law functions cross increases monotonically from 820 to 1480$$\mathrm {\mu }{\rm m}$$from the weak to the strong breaker, respectively. The droplet diameter and velocity characteristics and the number of the droplets generated by the four mechanisms are found to vary significantly and the processes that create these differences are discussed.
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- PAR ID:
- 10483876
- Publisher / Repository:
- Journal of Fluid Mechanics
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 967
- ISSN:
- 0022-1120
- Page Range / eLocation ID:
- A36
- Subject(s) / Keyword(s):
- Wave breaking, air/sea interactions
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2023.378
