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In the problem of horizontal convection a non-uniform buoyancy, $$b_{s}(x,y)$$ , is imposed on the top surface of a container and all other surfaces are insulating. Horizontal convection produces a net horizontal flux of buoyancy, $$\boldsymbol{J}$$ , defined by vertically and temporally averaging the interior horizontal flux of buoyancy. We show that $$\overline{\boldsymbol{J}\boldsymbol{\cdot }\unicode[STIX]{x1D735}b_{s}}=-\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$$ ; the overbar denotes a space–time average over the top surface, angle brackets denote a volume–time average and $$\unicode[STIX]{x1D705}$$ is the molecular diffusivity of buoyancy $$b$$ . This connection between $$\boldsymbol{J}$$ and $$\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$$ justifies the definition of the horizontal-convective Nusselt number, $Nu$ , as the ratio of $$\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$$ to the corresponding quantity produced by molecular diffusion alone. We discuss the advantages of this definition of $Nu$ over other definitions of horizontal-convective Nusselt number. We investigate transient effects and show that $$\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$$ equilibrates more rapidly than other global averages, such as the averaged kinetic energy and bottom buoyancy. We show that $$\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$$ is the volume-averaged rate of Boussinesq entropy production within the enclosure. In statistical steady state, the interior entropy production is balanced by a flux through the top surface. This leads to an equivalent ‘surface Nusselt number’, defined as the surface average of vertical buoyancy flux through the top surface times the imposed surface buoyancy $$b_{s}(x,y)$$ . In experimental situations it is easier to evaluate the surface entropy flux, rather than the volume integral of $$|\unicode[STIX]{x1D735}b|^{2}$$ demanded by $$\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$$ .
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Three-body Faddeev calculations for ΛΛα and ΩΩα hypernuclei
We study the ground-state properties of $$\prescript{6}{YY}{\text{He}}$$ double hyperon for $$\lla$$ and $$\ooa$$ nuclei in a three-body model $$(Y+Y+\alpha)$$. We solve two coupled Faddeev equations corresponding to three-body configurations $$(\alpha Y,Y)$$ and $$(YY, \alpha)$$ in configuration space with the hyperspherical harmonics expansion method by employing the most recent hyperon-hyperon interactions obtained from lattice QCD simulations. Our numerical analysis for $$\lla$$, using three $$\Lambda\Lambda$$ lattice interaction models, leads to a ground state binding energy in the domain $(-7.468, -7.804)$ MeV and the separations $$\langle r_{\Lambda-\Lambda} \rangle$$ and $$\langle r_{\alpha-\Lambda} \rangle$$ in the domains $(3.555, 3.629)$ fm and $(2.867 , 2.902 )$ fm, correspondingly. The binding energy of double-$$\Omega$$ hypernucleus $$\ooa$$ leads to $-67.21$ MeV and consequently to smaller separations $$\langle r_{\Omega-\Omega} \rangle = 1.521$$ fm and $$\langle r_{\alpha-\Omega} \rangle = 1.293 $$ fm. Besides the geometrical properties, we study the structure of ground-state wave functions and show that the main contributions are from the $s-$wave channels. Our results are consistent with the existing theoretical and experimental data.
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- Award ID(s):
- 2000029
- PAR ID:
- 10334088
- Date Published:
- Journal Name:
- Chinese Physics C
- ISSN:
- 1674-1137
- 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/10.1088/1674-1137/ac7a22
