Lasing condition for trapped modes in subwavelength-wired PT-symmetric resonators

Notions of linear and nonlinear hydrodynamic (in)stability are explained and criteria of instability of plane-parallel flows are presented. Instabilities of jets are investigated by direct pseudospectral collocation method in various flow configurations, starting from the classical barotropic and baroclinic instabilities. Characteristic features of instabilities are displayed, as well as typical patterns of their nonlinear saturation. It is shown that in the Phillips model of Chapter 5, new ageostrophic Rossby–Kelvin and shear instabilities appear at finite Rossby numbers. These instabilities are interpreted in terms of resonances among waves counter-propagating in the flow. It is demonstrated that the classical inertial instability is a specific case of ageostrophic baroclinic instability. At the equator it appears also in the barotropic configuration, and is related to resonances of Yanai waves. The nature of the inertial instability in terms of trapped modes is established. A variety of instabilities of density fronts is displayed.

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Recent development of conception of trapped modes in low-loss all-dielectric metamaterials

2017 47th European Microwave Conference (EuMC) ◽

10.23919/eumc.2017.8230895 ◽

2017 ◽

Author(s):

Vladimir R. Tuz ◽

Vyacheslav V. Khardikov ◽

Natalia V. Sydorchuk ◽

Denis V. Novitsky ◽

Sergey L. Prosvirnin

Keyword(s):

Trapped Modes ◽

Low Loss

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Wave interaction with two-dimensional bodies floating in a two-layer fluid: uniqueness and trapped modes

Journal of Fluid Mechanics ◽

10.1017/s0022112003005354 ◽

2003 ◽

Vol 490 ◽

pp. 321-331 ◽

Cited By ~ 13

Author(s):

N. KUZNETSOV ◽

M. MCIVER ◽

P. MCIVER

Keyword(s):

Wave Interaction ◽

Two Dimensional ◽

Trapped Modes

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Double Kelvin waves with continuous depth profiles

Journal of Fluid Mechanics ◽

10.1017/s002211206800176x ◽

1968 ◽

Vol 34 (1) ◽

pp. 49-80 ◽

Cited By ~ 59

Author(s):

M. S. Longuet-Higgins

Keyword(s):

Group Velocity ◽

Transition Zone ◽

Kelvin Wave ◽

Trapped Modes ◽

Full Account ◽

Higher Modes ◽

Depth Profiles ◽

Different Depths ◽

Bounded Below ◽

Asymptotic Forms

The possibility of long waves in a rotating ocean being trapped along a straight discontinuity in depth was demonstrated in a recent paper (Longuet-Higgins 1968). The analysis is now extended to the situation where the depth varies continuously, in a zone separating two regions of different depths. The trapping of waves in the transition zone is investigated, taking full account of the horizontal divergence of the motion.If the profile of the depth is assumed to be monotonic, then it is shown that the trapped waves always travel along the transition zone with the shallower water to their right in the northern hemisphere and to their left in the southern hemisphere. The wave period must always exceed a pendulum-day. The period is also bounded below by a quantity depending inversely on the maximum bottom gradient.By allowing the width W of the transition zone to vary, asymptotic forms for the trapped modes are obtained, both as W → 0 and as W → ∞. In the limit as W → 0 the depth becomes discontinuous, and it is shown that the lowest mode then becomes a double Kelvin wave (Longuet-Higgins 1968) propagated along the discontinuity. The periods of the higher modes, on the other hand, all tend to infinity; these modes become steady currents.Numerical calculations of the trapped modes are presented for two different laws of depth in the transition zone. It is found that as W → 0 the lowest mode is insensitive to the form of the depth profile. Higher modes depend on the details of the profile. Hence the lowest mode is the most likely to be observed in the real ocean.The dispersion relation is also investigated. It is shown that the group-velocity of all modes must change sign at some point in the range of wave-numbers, if the divergence is taken into account. When the divergence was neglected the lowest mode appeared to be exceptional, in that the group-velocity was always in the same direction. This anomaly is now removed.

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Simple examples of perfectly invisible and trapped modes in waveguides

The Quarterly Journal of Mechanics and Applied Mathematics ◽

10.1093/qjmam/hby006 ◽

2018 ◽

Vol 71 (3) ◽

pp. 297-315 ◽

Cited By ~ 4

Author(s):

L Chesnel ◽

V Pagneux

Keyword(s):

Trapped Modes

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Trapped modes in a waveguide with a long obstacle

Journal of Fluid Mechanics ◽

10.1017/s0022112099007028 ◽

2000 ◽

Vol 403 ◽

pp. 251-261 ◽

Cited By ~ 8

Author(s):

N. S. A. KHALLAF ◽

L. PARNOVSKI ◽

D. VASSILIEV

Keyword(s):

Two Dimensional ◽

Trapped Modes ◽

Acoustic Waveguide ◽

Trapped Mode ◽

Rectangular Obstacle

Consider an infinite two-dimensional acoustic waveguide containing a long rectangular obstacle placed symmetrically with respect to the centreline. We search for trapped modes, i.e. modes of oscillation at particular frequencies which decay down the waveguide. We provide analytic estimates for trapped mode frequencies and prove that the number of trapped modes is asymptotically proportional to the length of the obstacle.

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Acoustic resonances and trapped modes in pipes and tunnels

Journal of Fluid Mechanics ◽

10.1017/s002211200800164x ◽

2008 ◽

Vol 605 ◽

pp. 401-428 ◽

Cited By ~ 41

Author(s):

STEFAN HEIN ◽

WERNER KOCH

Keyword(s):

Cross Sections ◽

High Speed ◽

Hard Spheres ◽

Cutoff Frequency ◽

Three Dimensional ◽

Absorbing Boundary Conditions ◽

Trapped Modes ◽

Absorbing Boundary ◽

Complex Scaling Method ◽

Acoustic Resonances

Acoustic resonances of simple three-dimensional finite-length structures in an infinitely long cylindrical pipe are investigated numerically by solving an eigenvalue problem. To avoid unphysical reflections at the finite grid boundaries placed in the uniform cross-sections of the pipe, perfectly matched layer absorbing boundary conditions are applied in the form of the complex scaling method of atomic and molecular physics. Examples of the structures investigated are sound-hard spheres, cylinders, cavities and closed side branches. Several truly trapped modes with zero radiation loss are identified for frequencies below the first cutoff frequency of the pipe. Such trapped modes can be excited aerodynamically by coherent vortices if the frequency of the shed vortices is close to a resonant frequency. Furthermore, numerical evidence is presented for the existence of isolated embedded trapped modes for annular cavities above the first cutoff frequency and for closed side branches below the first cutoff frequency. As applications of engineering interest, the acoustic resonances are computed for a ball-type valve and around a simple model of a high-speed train in an infinitely long tunnel.

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