14,117 research outputs found
On a model of forced axisymmetric flows
In this work, we consider a model of forced axisymmetric flows which is
derived from the inviscid Boussinesq equations. What makes these equations
unusual is the boundary conditions they are expected to satisfy and the fact
that the boundary is part of the unknown. We show that these flows give rise to
an unusual Monge-Ampere equations for which we prove the existence and the
uniqueness of a variational solution. We take advantage of these Monge-Ampere
equations and construct a solution to the model
Mean flow stability analysis of oscillating jet experiments
Linear stability analysis is applied to the mean flow of an oscillating round
jet with the aim to investigate the robustness and accuracy of mean flow
stability wave models. The jet's axisymmetric mode is excited at the nozzle lip
through a sinusoidal modulation of the flow rate at amplitudes ranging from 0.1
% to 100 %. The instantaneous flow field is measured via particle image
velocimetry and decomposed into a mean and periodic part utilizing proper
orthogonal decomposition. Local linear stability analysis is applied to the
measured mean flow adopting a weakly nonparallel flow approach. The resulting
global perturbation field is carefully compared to the measurements in terms of
spatial growth rate, phase velocity, and phase and amplitude distribution. It
is shown that the stability wave model accurately predicts the excited flow
oscillations during their entire growth phase and during a large part of their
decay phase. The stability wave model applies over a wide range of forcing
amplitudes, showing no pronounced sensitivity to the strength of nonlinear
saturation. The upstream displacement of the neutral point and the successive
reduction of gain with increasing forcing amplitude is very well captured by
the stability wave model. At very strong forcing (>40%), the flow becomes
essentially stable to the axisymmetric mode. For these extreme cases, the
prediction deteriorates from the measurements due to an interaction of the
forced wave with the geometric confinement of the nozzle. Moreover, the model
fails far downstream in a region where energy is transferred from the
oscillation back to the mean flow. This study supports previously conducted
mean flow stability analysis of self-excited flow oscillations in the cylinder
wake and in the vortex breakdown bubble and extends the methodology to
externally forced convectively unstable flows.Comment: submitted to the Journal of Fluid Mechanic
Nonlinear dynamo in a short Taylor-Couette setup
It is numerically demonstrated by means of a magnetohydrodynamics code that a
short Taylor-Couette setup with a body force can sustain dynamo action. The
magnetic threshold is comparable to what is usually obtained in spherical
geometries. The linear dynamo is characterized by a rotating equatorial dipole.
The nonlinear regime is characterized by fluctuating kinetic and magnetic
energies and a tilted dipole whose axial component exhibits aperiodic reversals
during the time evolution. These numerical evidences of dynamo action in a
short Taylor-Couette setup may be useful for developing an experimental device
Precession-driven flows in non-axisymmetric ellipsoids
We study the flow forced by precession in rigid non-axisymmetric ellipsoidal
containers. To do so, we revisit the inviscid and viscous analytical models
that have been previously developed for the spheroidal geometry by,
respectively, Poincar\'e (Bull. Astronomique, vol. XXVIII, 1910, pp. 1-36) and
Busse (J. Fluid Mech., vol. 33, 1968, pp. 739-751), and we report the first
numerical simulations of flows in such a geometry. In strong contrast with
axisymmetric spheroids, where the forced flow is systematically stationary in
the precessing frame, we show that the forced flow is unsteady and periodic.
Comparisons of the numerical simulations with the proposed theoretical model
show excellent agreement for both axisymmetric and non-axisymmetric containers.
Finally, since the studied configuration corresponds to a tidally locked
celestial body such as the Earth's Moon, we use our model to investigate the
challenging but planetary-relevant limit of very small Ekman numbers and the
particular case of our Moon
Weakly nonlinear modelling of a forced turbulent axisymmetric wake
A theory is presented where the weakly nonlinear analysis of laminar globally unstable flows in the presence of external forcing is extended to the turbulent regime. The analysis is demonstrated and validated using experimental results of an axisymmetric bluff-body wake at high Reynolds numbers, Re_D âŒ1.88Ă10^5, where forcing is applied using a zero-net-mass-flux actuator located at the base of the blunt body. In this study we focus on the response of antisymmetric coherent structures with azimuthal wavenumbers m = ±1at a frequency St_D = 0.2 S, responsible for global vortex shedding. We found experimentally that axisymmetric forcing (m = 0) couples nonlinearly with the global shedding mode when the flow is forced at twice the shedding frequency, resulting in parametric subharmonic resonance through a triadic interaction between forcing and shedding. We derive simple weakly nonlinear models from the phase-averaged NavierâStokes equations and show that they capture accurately the observed behaviour for this type of forcing. The unknown model coefficients are obtained experimentally by producing harmonic transients. This approach should be applicable in a variety of turbulent flows to describe the response of global modes to forcing
Two-dimensionalization of the flow driven by a slowly rotating impeller in a rapidly rotating fluid
We characterize the two-dimensionalization process in the turbulent flow
produced by an impeller rotating at a rate in a fluid rotating at a
rate around the same axis for Rossby number down to
. The flow can be described as the superposition of a large-scale
vertically invariant global rotation and small-scale shear layers detached from
the impeller blades. As decreases, the large-scale flow is subjected to
azimuthal modulations. In this regime, the shear layers can be described in
terms of wakes of inertial waves traveling with the blades, originating from
the velocity difference between the non-axisymmetric large-scale flow and the
blade rotation. The wakes are well defined and stable at low Rossby number, but
they become disordered at of order of 1. This experiment provides insight
into the route towards pure two-dimensionalization induced by a background
rotation for flows driven by a non-axisymmetric rotating forcing.Comment: Accepted for publication in Physical Review Fluid
Dynamics and thermodynamics of axisymmetric flows: I. Theory
We develop new variational principles to study stability and equilibrium of
axisymmetric flows. We show that there is an infinite number of steady state
solutions. We show that these steady states maximize a (non-universal)
-function. We derive relaxation equations which can be used as numerical
algorithm to construct stable stationary solutions of axisymmetric flows. In a
second part, we develop a thermodynamical approach to the equilibrium states at
some fixed coarse-grained scale. We show that the resulting distribution can be
divided in a universal part coming from the conservation of robust invariants
and one non-universal determined by the initial conditions through the fragile
invariants (for freely evolving systems) or by a prior distribution encoding
non-ideal effects such as viscosity, small-scale forcing and dissipation (for
forced systems). Finally, we derive a parameterization of inviscid mixing to
describe the dynamics of the system at the coarse-grained scale
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