On near resonances and symmetry breaking in forced rotating flows at moderate Rossby number

The behaviour of clean and contaminated bubbles in solid-body rotating flows is compared in terms of drag and lift forces. Both spherical and deformed bubbles are considered. For that comparison, we have completed the data published in Rastello et al. (J. Fluid Mech., vol. 624, 2009, pp. 159–178; J. Fluid Mech., vol. 682, 2011, pp. 434–459) by a new series of measurements. When they are contaminated, bubbles are subject to an additional lift force due to the spinning of their surfaces, while the clean ones are not. A detailed description of this spinning motion is presented and an expression for the Magnus-like lift it induces is given in the light of the new information. The component of the lift induced by flow rotation depends on the Rossby number $Ro$, contrary to the case of clean bubbles. Including the ‘spin’ induced lift component in the dynamical equations provides a better prediction of the bubble’s trajectory in contaminated fluid. The presence of contaminants immobilizes the rear part of the bubble and reduces significantly the deformation. The laws of deformation according to the nature of the surface are presented. The way deformation influences the drag and lift coefficients in pure and contaminated fluids is quantified and discussed. Expressions for these various coefficients are proposed.

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The effects of obstacle shape and viscosity in deep rotating flow over finite-height topography

Journal of Fluid Mechanics ◽

10.1017/s0022112082002808 ◽

1982 ◽

Vol 120 ◽

pp. 359-383 ◽

Cited By ~ 6

Author(s):

E. R. Johnson

Keyword(s):

Reynolds Number ◽

Strong Dependence ◽

Finite Depth ◽

Reynolds Numbers ◽

Rotating Flows ◽

Rotating Flow ◽

Rossby Number ◽

Ridge Width ◽

Inertial Wave ◽

Finite Slope

The limiting process introduced by Stewartson & Cheng (1979) is used to obtain solutions in the limit of vanishing Rossby number for deep rotating flows at arbitrary Reynolds number over cross-stream ridges of finite slope. Examination of inviscid solutions for infinite-depth flow shows strong dependence on obstacle shape of not only the magnitudes but also the positions of disturbances in the far field. In finite-depth flow there is present the Stewartson & Cheng inertial wave wake, which may be expressed as a sum of vertical modes whose amplitudes depend on the obstacle shape but are independent of distance downstream; the smoother the topography and the shallower the flow, the fewer the number of modes required to describe the motion. For abrupt topography the strength of the wake does not, however, decrease monoton- ically with decreasing container depth (or Rossby number). In very deep flows viscosity causes the wake to decay on a length scale of order the Reynolds number times the ridge width. In shallower flows, where only a few modes are present, the decay of the wake is more rapid. For Reynolds numbers and depths of the order of those in the experiments of Hide, Ibbetson & Lighthill (1968)) viscosity causes the disturbance to take on the appearance of a leaning column.

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Instability of rigidly rotating flows to non-axisymmetric disturbances

Journal of Fluid Mechanics ◽

10.1017/s0022112074002412 ◽

1974 ◽

Vol 64 (2) ◽

pp. 307-318 ◽

Cited By ~ 21

Author(s):

S. A. Maslowe

Keyword(s):

Growth Rates ◽

Axial Flow ◽

Maximum Growth ◽

Swirling Flows ◽

Rotating Flows ◽

Necessary Condition ◽

Rossby Number ◽

Instability Mechanism ◽

Wave Numbers ◽

Axisymmetric Disturbances

An investigation of the hydrodynamic stability of swirling flows having arbitrary Rossby numbers is described. A necessary condition for instability is derived for rigidly rotating flows and this condition is further refined in the specific case of a parabolic axial flow. Numerical results are presented for two azimuthal wave-numbers corresponding to the maximum growth rates of unstable perturbations as a function of Rossby number. It is found that the largest growth rates occur when the Rossby number is O(1) and that instability persists for surprisingly large values of this parameter. Previous explanations of the instability mechanism are discussed and it is concluded that these are only adequate in the limit of small Rossby number.

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WKB thresholds of standard, helical, and azimuthal magnetorotational instability

Proceedings of the International Astronomical Union ◽

10.1017/s1743921312019771 ◽

2012 ◽

Vol 8 (S290) ◽

pp. 233-234 ◽

Cited By ~ 2

Author(s):

Oleg Kirillov ◽

Frank Stefani

Keyword(s):

Magnetic Field ◽

External Magnetic Field ◽

Prandtl Number ◽

Local Stability ◽

Rotating Flows ◽

Rossby Number ◽

Magnetorotational Instability ◽

Electrically Conducting ◽

Magnetic Prandtl Number ◽

Wavelength Approximation

AbstractWe consider rotating flows of an electrically conducting, viscous and resistive fluid in an external magnetic field with arbitrary combinations of axial and azimuthal components. Within the short-wavelength approximation, the local stability of the flow is studied with respect to perturbations of arbitrary azimuthal wavenumbers. In the limit of vanishing magnetic Prandtl number (Pm) we find that the maximum critical Rossby number (Ro) for the occurrence of the magnetorotational instability (MRI) is universally governed by the Liu limit ${\rm Ro}_{Liu}=2-2\sqrt{2}\approx -0.828$ which is below the value for Keplerian rotation RoKepler = −0.75.

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Symmetry breaking in convergent-beam diffraction

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100154378 ◽

1989 ◽

Vol 47 ◽

pp. 480-481

Author(s):

D.J. Eaglesham

Keyword(s):

Symmetry Breaking ◽

Point Group ◽

X Ray Diffraction ◽

Multiple Diffraction ◽

Space Groups ◽

Atomic Displacements ◽

Small Probe ◽

Phase Sensitive ◽

Convergent Beam

Convergent Beam Electron Diffraction is now almost routinely used in the determination of the point- and space-groups of crystalline samples. In addition to its small-probe capability, CBED is also postulated to be more sensitive than X-ray diffraction in determining crystal symmetries. Multiple diffraction is phase-sensitive, so that the distinction between centro- and non-centro-symmetric space groups should be trivial in CBED: in addition, the stronger scattering of electrons may give a general increase in sensitivity to small atomic displacements. However, the sensitivity of CBED symmetry to the crystal point group has rarely been quantified, and CBED is also subject to symmetry-breaking due to local strains and inhomogeneities. The purpose of this paper is to classify the various types of symmetry-breaking, present calculations of the sensitivity, and illustrate symmetry-breaking by surface strains.CBED symmetry determinations usually proceed by determining the diffraction group along various zone axes, and hence finding the point group. The diffraction group can be found using either the intensity distribution in the discs

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Centrosome Aurora A gradient ensures single polarity axis in C. elegans embryos

Biochemical Society Transactions ◽

10.1042/bst20200298 ◽

2020 ◽

Vol 48 (3) ◽

pp. 1243-1253 ◽

Cited By ~ 1

Author(s):

Sukriti Kapoor ◽

Sachin Kotak

Keyword(s):

Symmetry Breaking ◽

Cell Fate ◽

Cell Cortex ◽

Axis Formation ◽

Aurora A Kinase ◽

Aurora A ◽

C Elegans ◽

Cell Embryo ◽

Polarity Establishment

Cellular asymmetries are vital for generating cell fate diversity during development and in stem cells. In the newly fertilized Caenorhabditis elegans embryo, centrosomes are responsible for polarity establishment, i.e. anterior–posterior body axis formation. The signal for polarity originates from the centrosomes and is transmitted to the cell cortex, where it disassembles the actomyosin network. This event leads to symmetry breaking and the establishment of distinct domains of evolutionarily conserved PAR proteins. However, the identity of an essential component that localizes to the centrosomes and promotes symmetry breaking was unknown. Recent work has uncovered that the loss of Aurora A kinase (AIR-1 in C. elegans and hereafter referred to as Aurora A) in the one-cell embryo disrupts stereotypical actomyosin-based cortical flows that occur at the time of polarity establishment. This misregulation of actomyosin flow dynamics results in the occurrence of two polarity axes. Notably, the role of Aurora A in ensuring a single polarity axis is independent of its well-established function in centrosome maturation. The mechanism by which Aurora A directs symmetry breaking is likely through direct regulation of Rho-dependent contractility. In this mini-review, we will discuss the unconventional role of Aurora A kinase in polarity establishment in C. elegans embryos and propose a refined model of centrosome-dependent symmetry breaking.

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