We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form-valued 2-forms, and their divergence as a covariant exterior derivative. We review the necessary tools of differential geometry and obtain the ...
when multiplied by the square of the free stream velocity, equals the integral of the momentum defect. Alternatively, the total loss of momentum flux is equivalent to the removal of momentum through a distanceθ. It is a theoretical length scale to quantify the effects of fluid viscosity near ...
flux divergences a wave-induced correction of hydrostatic balance in the vertical momentum equation, which cannot be obtained from Boussinesq or anelastic ... U Achatz,R Klein,F Senf - 《Journal of Fluid Mechanics》 被引量: 48发表: 2010年 The Limits of Hamiltonian Structures in Three-Dimensional...
From the laser illumination distribution, the optical force density distributed within the HR coating is simulated by the finite-difference time-domain (FDTD) method in two dimensions (2D)21. This method solves the electromagnetic-material momentum continuity equation in the experimental configuration of...
作者: G Ruocco 摘要: Transfer of momentum is the second physical mechanism we encounter, through which the mechanics of fluidscan be examined, including their interaction with the solid structures that may contain, and... DOI: 10.1007/978-3-319-66822-2_3 年份: 2018 收藏...
Angular momentum equation • For angular momentum equation, B =H O the angular momentum vector about point O which moments are desired. • Where β is • The Reynolds transport equation can be written as follows: • For one‐dimensional inlets and outlets, the flux terms become: Integra...
In 1845, Stokes extends Navier’s model of a viscous fluid in the bulk and in the boundary layer. He proposes the following constitutive equation for the momentum flux: $$ {\mathbf p}=p{\mathbf I}-2\mu\left({\mathbf d}-\delta{\mathbf I}\right)-3\kappa\delta{\mathbf I}= p{\ma...
internal energy, and pressure are within zones; temporally, variables are usually centered at the integer time step except for velocity which is at the half step.The momentum equation is found to lead to an exactly conserved energy flux between internal energy in the zones and kinetic energy at...
On the left hand side of Equation (5), the first term reflects the change rate of the slide’s momentum in the control volume, and the second term represents the momentum flux across the left boundary of the control volume. The right-hand sides of Equations (5)–(8) reveal that two ...
The components of a conserved vector are the density and flux terms of a conservation law. The Lie point symmetry associated with a conserved vector is easier to calculate than the Lie point symmetry of the corresponding partial differential equation because the order of the derivative in the ...