Transition in Homogeneously Heated Inclined Plane Parallel Shear Flows

2003 ◽  
Vol 125 (5) ◽  
pp. 795-803 ◽  
Author(s):  
S. Generalis ◽  
M. Nagata
Keyword(s):  
Shear Flows ◽  
Numerical Study ◽  
Fluid Layer ◽  
Travelling Wave ◽  
Inclined Plane ◽  
Vertical Orientation ◽  
Plane Parallel ◽  
Wide Range ◽  
Parallel Shear Flows ◽  
Roll Type

The transition of internally heated inclined plane parallel shear flows is examined numerically for the case of finite values of the Prandtl number Pr. We show that as the strength of the homogeneously distributed heat source is increased the basic flow loses stability to two-dimensional perturbations of the transverse roll type in a Hopf bifurcation for the vertical orientation of the fluid layer, whereas perturbations of the longitudinal roll type are most dangerous for a wide range of the value of the angle of inclination. In the case of the horizontal inclination transverse roll and longitudinal roll perturbations share the responsibility for the prime instability. Following the linear stability analysis for the general inclination of the fluid layer our attention is focused on a numerical study of the finite amplitude secondary travelling-wave solutions (TW) that develop from the perturbations of the transverse roll type for the vertical inclination of the fluid layer. The stability of the secondary TW against three-dimensional perturbations is also examined and our study shows that for Pr=0.71 the secondary instability sets in as a quasi-periodic mode, while for Pr=7 it is phase-locked to the secondary TW. The present study complements and extends the recent study by Nagata and Generalis (2002) in the case of vertical inclination for Pr=0.

Transition in plane parallel shear flows heated internally

2004 ◽  
Vol 332 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Masato Nagata ◽  
Sotos Generalis
Keyword(s):  
Shear Flows ◽  
Plane Parallel ◽  
Parallel Shear Flows

scholarly journals On the role of vortex stretching in energy optimal growth of three-dimensional perturbations on plane parallel shear flows

2012 ◽  
Vol 707 ◽  
pp. 369-380 ◽  
Author(s):  
H. Vitoshkin ◽  
E. Heifetz ◽  
A. Yu. Gelfgat ◽  
N. Harnik
Keyword(s):  
Shear Flows ◽  
Plane Waves ◽  
Three Dimensional ◽  
Energy Growth ◽  
Plane Parallel ◽  
Optimal Energy ◽  
Parallel Shear Flows ◽  
Spanwise Vorticity ◽  
Background Shear

AbstractThe three-dimensional linearized optimal energy growth mechanism, in plane parallel shear flows, is re-examined in terms of the role of vortex stretching and the interplay between the spanwise vorticity and the planar divergent components. For high Reynolds numbers the structure of the optimal perturbations in Couette, Poiseuille and mixing-layer shear profiles is robust and resembles localized plane waves in regions where the background shear is large. The waves are tilted with the shear when the spanwise vorticity and the planar divergence fields are in (out of) phase when the background shear is positive (negative). A minimal model is derived to explain how this configuration enables simultaneous growth of the two fields, and how this mutual amplification affects the optimal energy growth. This perspective provides an understanding of the three-dimensional growth solely from the two-dimensional dynamics on the shear plane.

scholarly journals NUMERICAL STUDY OF THE ROSENSWEIG INSTABILITY IN A MAGNETIC FLUID SUBJECT TO DIFFUSION OF MAGNETIC PARTICLES

2010 ◽  
Vol 15 (2) ◽  
pp. 223-233 ◽  
Author(s):  
Olga Lavrova ◽  
Viktor Polevikov ◽  
Lutz Tobiska
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Magnetic Fluid ◽  
Magnetic Particles ◽  
Numerical Study ◽  
Fluid Layer ◽  
Classical Problem ◽  
Parametric Representation ◽  
Field Configuration ◽  
Wide Range

The present study is devoted to the classical problem on stability of a magnetic fluid layer under the influence of gravity and a uniform magnetic field. A periodical peak‐shaped stable structure is formed on the fluid surface when the applied magnetic field exceeds a critical value. The mathematical model describes a single peak in the pattern assuming axial symmetry of the peak shape. The field configuration in the whole space, the magnetic particle concentration inside the fluid and the free surface structure are unknown quantities in this model. The unknown free surface is treated explicitly, using a parametric representation with respect to the arc length. The nonlinear problem is discretized by means of a finite element method for the Maxwell's equations and a finite‐difference method for the free surface equations. Numerical modelling allows to get over‐critical equilibrium free surface shapes in a wide range of applied field intensities. Our numerical results show a significant influence of the particle diffusion on the overcritical shapes.

scholarly journals Comoving frames and symmetry-related motions in parallel shear flows

2014 ◽  
Vol 751 ◽  
pp. 685-697 ◽  
Author(s):  
Tobias Kreilos ◽  
Stefan Zammert ◽  
Bruno Eckhardt
Keyword(s):  
Shear Flows ◽  
Travelling Waves ◽  
Edge State ◽  
Travelling Wave ◽  
Laboratory Frame ◽  
Frame Of Reference ◽  
Parallel Shear Flows ◽  
Continuous Symmetries ◽  
Fast Oscillations ◽  
Flow States

AbstractParallel shear flows have continuous symmetries of translation in the downstream and spanwise directions. As a consequence, flow states that differ in their spanwise or downstream location but are otherwise identical are dynamically equivalent. In the case of travelling waves, this trivial degree of freedom can be removed by going to a frame of reference that moves with the state, thereby turning the travelling wave in the laboratory frame into a fixed point in the comoving frame of reference. We here discuss a general approach, the method of comoving frames, by which the symmetry related motions can also be removed for more complicated and dynamically active states and demonstrate its application for several examples. For flow states in the asymptotic suction boundary layer (ASBL) we show that in the case of the long-period oscillatory edge state we can find local phase speeds which remove the fast oscillations and reveal the slow vortex dynamics underlying the burst phenomenon. For spanwise translating states we show that the method removes the drift but not the dynamical events that cause the big spanwise displacement. For a turbulent case we apply the method to the spanwise shifts and find slow components that are correlated over very long times. Calculations for plane Poiseuille flow show that the long correlations in the transverse motions are not specific to the ASBL.

scholarly journals Strain Sensor via Wood Anomalies in 2D Dielectric Array

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 1022
Author(s):  
Rashid G. Bikbaev ◽  
Ivan V. Timofeev ◽  
Vasiliy F. Shabanov
Keyword(s):  
Higher Plants ◽  
Numerical Study ◽  
Reciprocal Lattice ◽  
Strain Sensing ◽  
Photonic Materials ◽  
Sensing Applications ◽  
Wide Range ◽  
Sensor Structure ◽  
Optical Behavior ◽  
Chlorophyll Absorption

Optical sensing is one of many promising applications for all-dielectric photonic materials. Herein, we present an analytical and numerical study on the strain-responsive spectral properties of a bioinspired sensor. The sensor structure contains a two-dimensional periodic array of dielectric nanodisks to mimic the optical behavior of grana lamellae inside chloroplasts. To accumulate a noticeable response, we exploit the collective optical mode in grana ensemble. In higher plants, such a mode appears as Wood’s anomaly near the chlorophyll absorption line to control the photosynthesis rate. The resonance is shown persistent against moderate biological disorder and deformation. Under the stretching or compression of a symmetric structure, the mode splits into a couple of polarized modes. The frequency difference is accurately detected. It depends on the stretch coefficient almost linearly providing easy calibration of the strain-sensing device. The sensitivity of the considered structure remains at 5 nm/% in a wide range of strain. The influence of the stretching coefficient on the length of the reciprocal lattice vectors, as well as on the angle between them, is taken into account. This adaptive phenomenon is suggested for sensing applications in biomimetic optical nanomaterials.

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