Hydrodynamics of two-dimensional compressible fluid with broken parity : variational principle and free surface dynamics in the absence of dissipation

Autor: Monteiro, Gustavo Machado
Přispěvatelé: UNIVERSIDADE ESTADUAL DE CAMPINAS
Rok vydání: 2020
Předmět:
Zdroj: Repositório da Produção Científica e Intelectual da Unicamp
Universidade Estadual de Campinas (UNICAMP)
instacron:UNICAMP
Repositório Institucional da Unicamp
Popis: Agradecimentos: We are grateful to Paul Wiegmann for many discussions and for careful reading and commenting on an earlier draft of this work. A.G.A.'s research was supported by NSF Grant No. DMR-1606591 and U.S. DOE Grant No. DESC-0017662. A.G.A. and G.M.M. are grateful to the International Institute of Physics, Natal, Brazil, for hospitality. G.M.M. thanks Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) for financial support under Grant No. 2016/13517-0. S.G. acknowledges support from a PSC-CUNY Award. S.G. acknowledges the Aspen Center for Physics where part of this work was carried out, which is supported by National Science Foundation Grant No. PHY-1607611 Abstract: We consider an isotropic compressible nondissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid and the free surface boundary conditions depend explicitly on the parity-breaking nondissipative odd viscosity term. We construct an effective action which gives both bulk hydrodynamic equations and free surface boundary conditions. The free surface boundary conditions require an additional boundary term in the action which resembles a 1 + 1D chiral boson field coupled to the background geometry. We solve the linearized hydrodynamic equations for the deep water case and derive the dispersion of chiral surface waves. We show that in the long-wavelength limit the flow profile exhibits an oscillating vortical boundary layer near the free surface. The layer thickness is controlled by the ratio between the odd viscosity (nu(o)) and the sound velocity (c(s)), delta similar to nu(o)/c(s). In the incompressible limit, c(s) -gt; infinity, the vortical boundary layer becomes singular with the vorticity within the layer diverging as omega similar to c(s). The boundary layer is formed by odd viscosity coupling the divergence of velocity del center dot nu to vorticity del x nu. It results in nontrivial chiral free surface dynamics even in the absence of external forces. The structure of the odd-viscosity-induced boundary layer is very different from the conventional free surface boundary layer associated with dissipative shear viscosity FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP Fechado
Databáze: OpenAIRE
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