Hamiltonian formulation of inviscid flows with free boundaries

Journal Article · Sat Oct 01 04:00:00 EDT 1988 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.866987· OSTI ID:6830118

Abarbanel, H D.I.; Brown, R; Yang, Y M

The formulation of the Hamiltonian structures for inviscid fluid flows with material free surfaces is presented in both the Lagrangian specification, where the fundamental Poisson brackets are canonical, and in the Eulerian specification, where the dynamics is given in noncanonical form. The noncanonical Eulerian brackets are derived explicitly from the canonical Lagrangian brackets. The Eulerian brackets are, with the exception of a single term at each material free surface separating flows in different phases, identical to those for isentropic flow of a compressible, inviscid fluid. The dynamics of the free surface is located in the Hamiltonian and in the definition of the Eulerian variables of mass density, rho(x, t), momentum density, M(x,t) (which is rho times the fluid velocity v(x,t)), and the specific entropy, sigma(x,t). The boundary conditions for the Eulerian variables and the evolution equations for the free surfaces come from the Euler equations of the flow. This construction provides a unified treatment of inviscid flows with any number of free surfaces.

• Research Organization: Institute for Nonlinear Science, Department of Physics, and the Marine Physical Laboratory of the Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California 92093
• OSTI ID: 6830118
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 31:10; ISSN PFLDA
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOUNDARY LAYERS
CANONICAL DIMENSION
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID FLOW
HAMILTONIANS
IDEAL FLOW
LAYERS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
POISSON EQUATION
QUANTUM OPERATORS
SCALE DIMENSION