128 research outputs found
Nonlinear theory of a hot-wire anemometer
A theoretical analysis is presented for the hot-wire anemometer to determine the differences in resistance characteristics as given by King's equation for an infinite wire length and those given by the additional considerations of (a) a finite length of wire with heat loss through its ends and (b) heat loss due to a nonlinear function of the temperature difference between the wire and the air
Large-wavelength instabilities in free-surface Hartmann flow at low magnetic Prandtl numbers
We study the linear stability of the flow of a viscous electrically
conducting capillary fluid on a planar fixed plate in the presence of gravity
and a uniform magnetic field. We first confirm that the Squire transformation
for MHD is compatible with the stress and insulating boundary conditions at the
free surface, but argue that unless the flow is driven at fixed Galilei and
capillary numbers, the critical mode is not necessarily two-dimensional. We
then investigate numerically how a flow-normal magnetic field, and the
associated Hartmann steady state, affect the soft and hard instability modes of
free surface flow, working in the low magnetic Prandtl number regime of
laboratory fluids. Because it is a critical layer instability, the hard mode is
found to exhibit similar behaviour to the even unstable mode in channel
Hartmann flow, in terms of both the weak influence of Pm on its neutral
stability curve, and the dependence of its critical Reynolds number Re_c on the
Hartmann number Ha. In contrast, the structure of the soft mode's growth rate
contours in the (Re, alpha) plane, where alpha is the wavenumber, differs
markedly between problems with small, but nonzero, Pm, and their counterparts
in the inductionless limit. As derived from large wavelength approximations,
and confirmed numerically, the soft mode's critical Reynolds number grows
exponentially with Ha in inductionless problems. However, when Pm is nonzero
the Lorentz force originating from the steady state current leads to a
modification of Re_c(Ha) to either a sublinearly increasing, or decreasing
function of Ha, respectively for problems with insulating and conducting walls.
In the former, we also observe pairs of Alfven waves, the upstream propagating
wave undergoing an instability at large Alfven numbers.Comment: 58 pages, 16 figure
Linear waves in sheared flows. Lower bound of the vorticity growth and propagation discontinuities in the parameters space
This study provides sufficient conditions for the temporal monotonic decay of
enstrophy for two-dimensional perturbations traveling in the incompressible,
viscous, plane Poiseuille and Couette flows. Extension of J. L. Synge's
procedure (1938) to the initial-value problem allowed us to find the region of
the wavenumber-Reynolds number map where the enstrophy of any initial
disturbance cannot grow. This region is wider than the kinetic energy's one. We
also show that the parameters space is split in two regions with clearly
distinct propagation and dispersion properties
Wavelet phase analysis of two velocity components to infer the structure of interscale transfers in a turbulent boundary-layer
Scale-dependent phase analysis of velocity time series measured in a zero pressure gradient boundary layer shows that phase coupling between longitudinal and vertical velocity components is strong at both large and small scales, but minimal in the middle of the inertial regime. The same general pattern is observed at all vertical positions studied, but there is stronger phase coherence as the vertical coordinate, y, increases. The phase difference histograms evolve from a unimodal shape at small scales to the development of significant bimodality at the integral scale and above. The asymmetry in the off-diagonal couplings changes sign at the midpoint of the inertial regime, with the small scale relation consistent with intense ejections followed by a more prolonged sweep motion. These results may be interpreted in a manner that is consistent with the action of low speed streaks and hairpin vortices near the wall, with large scale motions further from the wall, the effect of which penetrates to smaller scales. Hence, a measure of phase coupling, when combined with a scale-by-scale decomposition of perpendicular velocity components, is a useful tool for investigating boundary-layer structure and inferring process from single-point measurements
Self-binormal solutions of the Localized Induction Approximation: Singularity formation
We investigate the formation of singularities in a self-similar form of
regular solutions of the Localized Induction Approximation (also referred as to
the binormal flow). This equation appears as an approximation model for the
self-induced motion of a vortex filament in an inviscid incompressible fluid.
The solutions behave as 3d-logarithmic spirals at infinity.
The proofs of the results are strongly based on the existing connection
between the binormal flow and certain Schr\"odinger equations.Comment: 60 pages, 8 figure
Stability of parallel flows
Stability of Parallel Flows provides information pertinent to hydrodynamical stability. This book explores the stability problems that occur in various fields, including electronics, mechanics, oceanography, administration, economics, as well as naval and aeronautical engineering. Organized into two parts encompassing 10 chapters, this book starts with an overview of the general equations of a two-dimensional incompressible flow. This text then explores the stability of a laminar boundary layer and presents the equation of the inviscid approximation. Other chapters present the general equatio
- …