3,073 research outputs found

### Thermosolutal and binary fluid convection as a 2 x 2 matrix problem

We describe an interpretation of convection in binary fluid mixtures as a
superposition of thermal and solutal problems, with coupling due to advection
and proportional to the separation parameter S. Many properties of binary fluid
convection are then consequences of generic properties of 2 x 2 matrices. The
eigenvalues of 2 x 2 matrices varying continuously with a parameter r undergo
either avoided crossing or complex coalescence, depending on the sign of the
coupling (product of off-diagonal terms). We first consider the matrix
governing the stability of the conductive state. When the thermal and solutal
gradients act in concert (S>0, avoided crossing), the growth rates of
perturbations remain real and of either thermal or solutal type. In contrast,
when the thermal and solutal gradients are of opposite signs (S<0, complex
coalescence), the growth rates become complex and are of mixed type.
Surprisingly, the kinetic energy of nonlinear steady states is governed by an
eigenvalue problem very similar to that governing the growth rates. There is a
quantitative analogy between the growth rates of the linear stability problem
for infinite Prandtl number and the amplitudes of steady states of the minimal
five-variable Veronis model for arbitrary Prandtl number. For positive S,
avoided crossing leads to a distinction between low-amplitude solutal and
high-amplitude thermal regimes. For negative S, the transition between real and
complex eigenvalues leads to the creation of branches of finite amplitude, i.e.
to saddle-node bifurcations. The codimension-two point at which the saddle-node
bifurcations disappear, separating subcritical from supercritical pitchfork
bifurcations, is exactly analogous to the Bogdanov codimension-two point at
which the Hopf bifurcations disappear in the linear problem

### Notes on aerodynamic forces on airship hulls

For a first approximation the air flow around the airship hull is assumed to obey the laws of perfect (i.e. free from viscosity) incompressible fluid. The flow is further assumed to be free from vortices (or rotational motion of the fluid). These assumptions lead to very great simplifications of the formulae used but necessarily imply an imperfect picture of the actual conditions. The value of the results depends therefore upon the magnitude of the forces produced by the disturbances in the flow caused by viscosity with the consequent production of vortices in the fluid. If these are small in comparison with the forces due to the assumed irrotational perfect fluid flow the results will give a good picture of the actual conditions of an airship in flight

### Standing and travelling waves in cylindrical Rayleigh-Benard convection

The Boussinesq equations for Rayleigh-Benard convection are simulated for a
cylindrical container with an aspect ratio near 1.5. The transition from an
axisymmetric stationary flow to time-dependent flows is studied using nonlinear
simulations, linear stability analysis and bifurcation theory. At a Rayleigh
number near 25,000, the axisymmetric flow becomes unstable to standing or
travelling azimuthal waves. The standing waves are slightly unstable to
travelling waves. This scenario is identified as a Hopf bifurcation in a system
with O(2) symmetry

### Symmetry breaking and turbulence in perturbed plane Couette flow

Perturbed plane Couette flow containing a thin spanwise-oriented ribbon
undergoes a subcritical bifurcation at Re = 230 to a steady 3D state containing
streamwise vortices. This bifurcation is followed by several others giving rise
to a fascinating series of stable and unstable steady states of different
symmetries and wavelengths. First, the backwards-bifurcating branch reverses
direction and becomes stable near Re = 200. Then, the spanwise reflection
symmetry is broken, leading to two asymmetric branches which are themselves
destabilized at Re = 420. Above this Reynolds number, time evolution leads
first to a metastable state whose spanwise wavelength is halved and then to
complicated time-dependent behavior. These features are in agreement with
experiments

### Stabilization of Ab Initio Molecular Dynamics Simulations at Large Time Steps

The Verlet method is still widely used to integrate the equations of motion
in ab initio molecular dynamics simulations. We show that the stability limit
of the Verlet method may be significantly increased by setting an upper limit
on the kinetic energy of each atom with only a small loss in accuracy. The
validity of this approach is demonstrated for molten lithium fluoride.Comment: 9 pages, 3 figure

### Mean flow of turbulent–laminar patterns in plane Couette flow

A turbulent–laminar banded pattern in plane Couette flow is studied numerically. This pattern is statistically steady, is oriented obliquely to the streamwise direction, and has a very large wavelength relative to the gap. The mean flow, averaged in time and in the homogeneous direction, is analysed. The flow in the quasi-laminar region is not the linear Couette profile, but results from a non-trivial balance between advection and diffusion. This force balance yields a first approximation to the relationship between the Reynolds number, angle, and wavelength of the pattern. Remarkably, the variation of the mean flow along the pattern wavevector is found to be almost exactly harmonic: the flow can be represented via only three cross-channel profiles as U(x, y, z) ≈ U0(y) + Uc(y) cos(kz) + Us(y) sin(kz). A model is formulated which relates the cross-channel profiles of the mean flow and of the Reynolds stress. Regimes computed for a full range of angle and Reynolds number in a tilted rectangular periodic computational domain are presented. Observations of regular turbulent–laminar patterns in other shear flows – Taylor–Couette, rotor–stator, and plane Poiseuille – are compared

### Spirals and ribbons in counter-rotating Taylor-Couette flow: frequencies from mean flows and heteroclinic orbits

A number of time-periodic flows have been found to have a property called
RZIF: when a linear stability analysis is carried out about the temporal mean
(rather than the usual steady state), an eigenvalue is obtained whose Real part
is Zero and whose Imaginary part is the nonlinear Frequency. For
two-dimensional thermosolutal convection, a Hopf bifurcation leads to traveling
waves which satisfy the RZIF property and standing waves which do not. We have
investigated this property numerically for counter-rotating Couette-Taylor
flow, in which a Hopf bifurcation gives rise to branches of upwards and
downwards traveling spirals and ribbons which are an equal superposition of the
two. In the regime that we have studied, we find that both spirals and ribbons
satisfy the RZIF property. As the outer Reynolds number is increased, the
ribbon branch is succeeded by two types of heteroclinic orbits, both of which
connect saddle states containing two axially stacked pairs of axisymmetric
vortices. One heteroclinic orbit is non-axisymmetric, with excursions that
resemble the ribbons, while the other remains axisymmetric

### A two-dimensional optical Fourier analyzer for image evaluation

Imperial Users onl

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