3,022 research outputs found
Clebsch Potentials in the Variational Principle for a Perfect Fluid
Equations for a perfect fluid can be obtained by means of the variational
principle both in the Lagrangian description and in the Eulerian one. It is
known that we need additional fields somehow to describe a rotational
isentropic flow in the latter description. We give a simple explanation for
these fields; they are introduced to fix both ends of a pathline in the
variational calculus. This restriction is imposed in the former description,
and should be imposed in the latter description. It is also shown that we can
derive a canonical Hamiltonian formulation for a perfect fluid by regarding the
velocity field as the input in the framework of control theory.Comment: 15 page
A Variational Principle for Dissipative Fluid Dynamics
In the variational principle leading to the Euler equation for a perfect
fluid, we can use the method of undetermined multiplier for holonomic
constraints representing mass conservation and adiabatic condition. For a
dissipative fluid, the latter condition is replaced by the constraint
specifying how to dissipate. Noting that this constraint is nonholonomic, we
can derive the balance equation of momentum for viscous and viscoelastic fluids
by using a single variational principle. We can also derive the associated
Hamiltonian formulation by regarding the velocity field as the input in the
framework of control theory.Comment: 15 page
Clebsch Potentials in the Variational Principle for a Perfect Fluid
Equations for a perfect fluid can be obtained by means of the variational
principle both in the Lagrangian description and in the Eulerian one. It is
known that we need additional fields somehow to describe a rotational
isentropic flow in the latter description. We give a simple explanation for
these fields; they are introduced to fix both ends of a pathline in the
variational calculus. This restriction is imposed in the former description,
and should be imposed in the latter description. It is also shown that we can
derive a canonical Hamiltonian formulation for a perfect fluid by regarding the
velocity field as the input in the framework of control theory.Comment: 15 page
Failure Mechanism of True 2D Granular Flows
Most previous experimental investigations of two-dimensional (2D) granular
column collapses have been conducted using three-dimensional (3D) granular
materials in narrow horizontal channels (i.e., quasi-2D condition). Our recent
research on 2D granular column collapses by using 2D granular materials (i.e.,
aluminum rods) has revealed results that differ markedly from those reported in
the literature. We assume a 2D column with an initial height of h0 and initial
width of d0, a defined as their ratio (a =h0/d0), a final height of h , and
maximum run-out distance of d . The experimental data suggest that for the low
a regime (a <0.65) the ratio of the final height to initial height is 1.
However, for the high a regime (a >0.65), the ratio of a to (d-d0)/d0, h0/h ,
or d/d0 is expressed by power-law relations. In particular, the following
power-function ratios (h0/h=1.42a^2/3 and d/d0=4.30a^0.72) are proposed for
every a >0.65. In contrast, the ratio (d-d0)/d0=3.25a^0.96 only holds for 0.65<
a1.5. In addition,
the influence of ground contact surfaces (hard or soft beds) on the final
run-out distance and destruction zone of the granular column under true 2D
conditions is investigated.Comment: 8 page
- …