The Role of Nonnormality in Overreflection Theory

2010 ◽  
Vol 67 (8) ◽  
pp. 2547-2558 ◽  
Author(s):  
Nikolaos A. Bakas ◽  
Brian F. Farrell
Keyword(s):  
Shear Layer ◽  
Gravity Waves ◽  
Finite Depth ◽  
Stimulated Emission ◽  
Incoming Wave ◽  
Propagating Waves ◽  
Three Stages ◽  
Orr Mechanism ◽  
Weak Stratification

Abstract The role of nonnormality in the overreflection of gravity waves is investigated. In the limit of weak stratification, wave packets having a critical level inside a shear layer of finite depth are reflected with amplified energy. This process, which exhibits the characteristics of stimulated emission, occurs in three stages: first, the incoming wave enters the shear layer and excites nonpropagating perturbations leaning with and against the shear. Subsequently, the energy of perturbations leaning against the shear grows in a manner similar to energy growth of perturbations in constant shear flows, indicating that the Orr mechanism that is slightly modified by stratification underlies the observed growth. Finally, the amplified perturbations excite propagating waves originating from the vicinity of the shear layer boundary. The role of nonnormality in this process is also investigated from the perspective of the associated nonorthogonality of the modes of the dynamical system. It is found that the incident wave packet projects on nonorthogonal analytic modes having the structure of a downward propagating wave in the far field below the shear layer and overreflection expressed by the interaction among these nonorthogonal modes.

scholarly journals Unique Slow Crack Growth Behavior of Isotactic Polypropylene: The Role of Shear Layer-Spherulites Layer Alternated Structure

Polymers ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 2746
Author(s):  
Mingjin Liu ◽  
Jiaxu Luo ◽  
Jin Chen ◽  
Xueqin Gao ◽  
Qiang Fu ◽  
...  
Keyword(s):  
Shear Layer ◽  
Crack Growth ◽  
Isotactic Polypropylene ◽  
Slow Crack Growth ◽  
Crack Growth Behavior ◽  
Polymer Science ◽  
The Past ◽  
Propagation Behavior ◽  
Crack Propagation Behavior

With the development of polymer science, more attention is being paid to the longevity of polymer products. Slow crack growth (SCG), one of the most important factors that reveal the service life of the products, has been investigated widely in the past decades. Here, we manufactured an isotactic polypropylene (iPP) sample with a novel shear layer–spherulites layer alternated structure using multiflow vibration injection molding (MFVIM). However, the effect of the alternated structure on the SCG behavior has never been reported before. Surprisingly, the results showed that the resistivity of polymer to SCG can be enhanced remarkably due to the special alternated structure. Moreover, this sample shows unique slow crack propagation behavior in contrast to the sample with the same thickness of shear layer, presenting multiple microcracks in the spherulites layer, which can explain the reason of the resistivity improvement of polymer to SCG.

scholarly journals Resonance in Optimal Perturbation Evolution. Part II: Effects of a Nonzero Mean PV Gradient

2007 ◽  
Vol 64 (3) ◽  
pp. 695-710 ◽  
Author(s):  
H. de Vries ◽  
J. D. Opsteegh
Keyword(s):  
Potential Vorticity ◽  
Propagation Speed ◽  
Building Blocks ◽  
Joint Effect ◽  
Optimal Perturbation ◽  
Orr Mechanism ◽  
Nonzero Mean ◽  
Low Levels ◽  
Pv Gradient

Abstract Optimal perturbations are constructed for a two-layer β-plane extension of the Eady model. The surface and interior dynamics is interpreted using the concept of potential vorticity building blocks (PVBs), which are zonally wavelike, vertically confined sheets of quasigeostrophic potential vorticity. The results are compared with the Charney model and with the two-layer Eady model without β. The authors focus particularly on the role of the different growth mechanisms in the optimal perturbation evolution. The optimal perturbations are constructed allowing only one PVB, three PVBs, and finally a discrete equivalent of a continuum of PVBs to be present initially. On the f plane only the PVB at the surface and at the tropopause can be amplified. In the presence of β, however, PVBs influence each other’s growth and propagation at all levels. Compared to the two-layer f-plane model, the inclusion of β slightly reduces the surface growth and propagation speed of all optimal perturbations. Responsible for the reduction are the interior PVBs, which are excited by the initial PVB after initialization. Their joint effect is almost as strong as the effect from the excited tropopause PVB, which is also negative at the surface. If the optimal perturbation is composed of more than one PVB, the Orr mechanism dominates the initial amplification in the entire troposphere. At low levels, the interaction between the surface PVB and the interior tropospheric PVBs (in particular those near the critical level) takes over after about half a day, whereas the interaction between the tropopause PVB and the interior PVBs is responsible for the main amplification in the upper troposphere. In all cases in which more than one PVB is used, the growing normal mode configuration is not reached at optimization time.

scholarly journals Theoretical Studies of Convectively Forced Mesoscale Flows in Three Dimensions. Part II: Shear Flow with a Critical Level

2010 ◽  
Vol 67 (3) ◽  
pp. 694-712 ◽  
Author(s):  
Ji-Young Han ◽  
Jong-Jin Baik
Keyword(s):  
Shear Flow ◽  
Gravity Waves ◽  
Wind Direction ◽  
Critical Level ◽  
Deep Convection ◽  
Vertical Wind Shear ◽  
Finite Depth ◽  
Vertical Displacement ◽  
Two Dimensions ◽  
Three Dimensions

Abstract Convectively forced mesoscale flows in a shear flow with a critical level are theoretically investigated by obtaining analytic solutions for a hydrostatic, nonrotating, inviscid, Boussinesq airflow system. The response to surface pulse heating shows that near the center of the moving mode, the magnitude of the vertical velocity becomes constant after some time, whereas the magnitudes of the vertical displacement and perturbation horizontal velocity increase linearly with time. It is confirmed from the solutions obtained in present and previous studies that this result is valid regardless of the basic-state wind profile and dimension. The response to 3D finite-depth steady heating representing latent heating due to cumulus convection shows that, unlike in two dimensions, a low-level updraft that is necessary to sustain deep convection always occurs at the heating center regardless of the intensity of vertical wind shear and the heating depth. For deep heating across a critical level, little change occurs in the perturbation field below the critical level, although the heating top height increases. This is because downward-propagating gravity waves induced by the heating above, but not near, the critical level can hardly affect the flow response field below the critical level. When the basic-state wind backs with height, the vertex of V-shaped perturbations above the heating top points to a direction rotated a little clockwise from the basic-state wind direction. This is because the V-shaped perturbations above the heating top is induced by upward-propagating gravity waves that have passed through the layer below where the basic-state wind direction is clockwise relative to that above.

scholarly journals The role of constant vorticity on weakly nonlinear surface gravity waves

Wave Motion ◽  
2020 ◽  
pp. 102702
Author(s):  
M.A. Manna ◽  
S. Noubissie ◽  
J. Touboul ◽  
B. Simon ◽  
R.A. Kraenkel
Keyword(s):  
Gravity Waves ◽  
Surface Gravity ◽  
Weakly Nonlinear ◽  
Surface Gravity Waves ◽  
Constant Vorticity ◽  
Nonlinear Surface

Effect of a single bout of exercise and chronic exercise training on insulin sensitivity in racing sled dogs

2014 ◽  
Vol 10 (3) ◽  
pp. 167-172 ◽  
Author(s):  
S.E. Pratt-Phillips ◽  
R.J. Geor ◽  
M. Buser ◽  
A. Zirkle ◽  
A. Moore ◽  
...  
Keyword(s):  
Insulin Sensitivity ◽  
Exercise Training ◽  
Exercise Bout ◽  
Post Exercise ◽  
Exercise Challenge ◽  
Sled Dogs ◽  
Significant Difference ◽  
Single Bout ◽  
Three Stages

Two experiments were designed to investigate the role of exercise on insulin sensitivity (IS) in Alaskan racing sled dogs. In both experiments, IS was quantified with an isoglycemic-hyperinsulinemic clamp (IHC), whereby IS was defined as the glucose infusion rate (GIR) divided by the mean insulin concentration during the clamp. In Experiment 1, IS was quantified in 12 racing sled dogs during three stages of exercise training: unexercised for 4 months over the summer (deconditioned), and after two and four months of exercise conditioning. At each stage IS was assessed in unexercised dogs (n=6) and 60 h following a standard exercise challenge (n=6) consisting of a 35.4 km run completed in 2.5 h. In Experiment 2, IS was assessed in deconditioned dogs (n=6) and in well-conditioned dogs that had either completed a 708 km race 5-days prior (n=3) or were unraced for the previous month (n=3). In Experiment 1, there were no significant differences (Pã0.05) in GIR or IS between the three levels of conditioning, nor were there any effects of the exercise bout 60 h prior to the IHC. In Experiment 2 there was no significant difference in IS between well-conditioned dogs and untrained dogs (Pã0.05). However, dogs that completed a 708 km race 5-days prior to the IHC had a significantly higher IS than dogs that were deconditioned and those that were conditioned but unraced. These results suggest that the workload of an exercise challenge is a factor in post-exercise changes in IS but that exercise conditioning has little impact on IS in Alaskan sled dogs.

Uniformly travelling water waves from a dynamical systems viewpoint: some insights into bifurcations from Stokes’ family

1992 ◽  
Vol 241 ◽  
pp. 333-347 ◽  
Author(s):  
C. Baesens ◽  
R. S. Mackay
Keyword(s):  
Gravity Waves ◽  
Water Waves ◽  
Travelling Waves ◽  
Hamiltonian Formulation ◽  
Inviscid Fluid ◽  
Centre Manifold ◽  
Numerical Work ◽  
Bifurcation Tree ◽  
Area Preserving

Numerical work of many people on the bifurcations of uniformly travelling water waves (two-dimensional irrotational gravity waves on inviscid fluid of infinite depth) suggests that uniformly travelling water waves have a reversible Hamiltonian formulation, where the role of time is played by horizontal position in the wave frame. In this paper such a formulation is presented. Based on this viewpoint, some insights are given into bifurcations from Stokes’ family of periodic waves. It is demonstrated numerically that there is a ‘fold point’ at amplitude A0 ≈ 0.40222. Assuming non-degeneracy of the fold and existence of an associated centre manifold, this explains why a sequence of p/q-bifurcations occurs on one side of A0, with 0 < p/q [les ] ½, in the order of the rationals. Secondly, it explains why no symmetry-breaking bifurcation is observed at A0, contrary to the expectations of some. Thirdly, it explains why the bifurcation tree for periodic uniformly travelling waves looks so much like that for the area-preserving Hénon map. Fourthly, it leads to predictions of a rich variety of spatially quasi-periodic, heteroclinic and chaotic waves.

scholarly journals On the role of dust storms in triggering atmospheric gravity waves observed in the middle atmosphere

2011 ◽  
Vol 29 (9) ◽  
pp. 1647-1654 ◽  
Author(s):  
S. K. Das ◽  
A. Taori ◽  
A. Jayaraman
Keyword(s):  
Gravity Waves ◽  
Dust Storm ◽  
Hot Spots ◽  
Middle Atmosphere ◽  
Thermal Structure ◽  
Dust Storms ◽  
Storm Events ◽  
Atmospheric Perturbations ◽  
Atmospheric Gravity

Abstract. Lower atmospheric perturbations often produce measurable effects in the middle and upper atmosphere. The present study demonstrates the response of the middle atmospheric thermal structure to the significant enhancement of the lower atmospheric heating effect caused by dust storms observed over the Thar Desert, India. Our study from multi-satellite observations of two dust storm events that occurred on 3 and 8 May 2007 suggests that dust storm events produce substantial changes in the lower atmospheric temperatures as hot spots which can become sources for gravity waves observed in the middle atmosphere.

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