scholarly journals The Motion of a Point Vortex near Large-Amplitude Topography in a Two-Layer Fluid

2004 ◽  
Vol 34 (12) ◽  
pp. 2808-2824 ◽  
Author(s):  
Andrew J. White ◽  
N. Robb McDonald
Keyword(s):  
Dispersion Relation ◽  
Linear Theory ◽  
Large Amplitude ◽  
Small Amplitude ◽  
Lower Layer ◽  
Point Vortex ◽  
Step Change ◽  
Wave Radiation ◽  
Contour Dynamics ◽  
Analytic Expression

Abstract This work examines the dynamics of point vortices in a two-layer fluid near large-amplitude, sharply varying topography like that which occurs in continental shelf regions. Topography takes the form of an infinitely long step change in depth, and the two-layer stratification is chosen such that the height of topography in the upper layer is a small fraction of the overall depth, enabling quasigeostrophic theory to be used in both layers. An analytic expression for the dispersion relation of free topographic waves in this system is found. Weak vortices are studied using linear theory and, if located in the lower layer, propagate mainly because of their image in the topography. Depending on their sign, they are able to produce significant topographic wave radiation in their wakes. Upper-layer vortices propagate much slower and produce relatively small amplitude topographic wave radiation. Contour dynamics results are used to investigate the nonlinear regions of parameter space. For lower-layer vortices, linear theory is a good approximation, but for upper-layer vortices complicated features evolve and linear theory is only valid for weak vortices.

Radiation Hydrodynamics of a Surface Effect Ship

2013 ◽  
Author(s):  
Palaniswamy Ananthakrishnan
Keyword(s):  
Free Surface ◽  
Large Amplitude ◽  
Small Amplitude ◽  
Stokes Equations ◽  
Surface Effect ◽  
Wave Radiation ◽  
Absolute Pressure ◽  
Radiation Hydrodynamics ◽  
Surface Effect Ship ◽  
Air Cushion

The radiation hydrodynamics of a heaving surface effect ship (SES) is examined including the effect of air compressibility on the hydrodynamic forces and surface waves. Of particular focus of the study has been on determining the nonlinear viscous and air compressibility effects at natural frequencies corresponding to the piston and sloshing wave modes between the hulls and at the natural frequency corresponding to the heave motion of a surface effect ship with the restoring force dominated by the compressibility of the air cushion. In the present paper, the air cushion pressure is assumed to be uniform with its variation due to change of volume modeled using the adiabatic gas law pVγ = constant, where p denotes the absolute pressure of the air, V the air volume bounded by the side hulls, the free surface and the wet deck, and γ the ratio of specific heats Cp/Cv which is about 1.4 for air. The incompressible Navier-Stokes equations governing the nonlinear viscous wave-air-body interaction problem is solved in the time domain using a finite-difference method based on boundary fitted coordinates. New results presented in this paper show that air cushion compressibility affects the generation of waves and wave radiation forces significantly even at small amplitude of hull motion. As already well known, the free surface nonlinearity due to hull motion is significant for large amplitude of oscillation. At small amplitude of body oscillation, significant nonlinearity can be caused by air compressibility resulting in the generation of higher harmonic waves and forces. The results also highlight the significance of viscosity and flow separation, in conjunction with air compressibility, in the case of large amplitude hull motion with a small draft.

scholarly journals Bragg resonances in a two-layer fluid

1996 ◽  
Vol 37 (3) ◽  
pp. 334-345 ◽  
Author(s):  
W. D. McKee
Keyword(s):  
Surface Wave ◽  
Large Amplitude ◽  
Small Amplitude ◽  
Lower Layer ◽  
Interaction Effects ◽  
Interfacial Waves ◽  
Interfacial Wave ◽  
Bragg Resonances

AbstractEquations are derived to approximately describe the propagation of small amplitude surface and interfacial waves across small irregularities in depth in a two-layer fluid. When the irregularities are sinusoidal, Bragg interaction effects between an incident surface wave and the bottom corrugations can lead to a large-amplitude reflected interfacial wave or a large-amplitude transmitted interfacial wave if the incident surface wave is relatively long and the lower layer shallow in comparison with the upper layer.

scholarly journals The motion of a singular vortex near an escarpment

2001 ◽  
Vol 448 ◽  
pp. 335-365 ◽  
Author(s):  
D. C. DUNN ◽  
N. R. McDONALD ◽  
E. R. JOHNSON
Keyword(s):  
Linear Theory ◽  
Drift Velocity ◽  
Time Scale ◽  
Large Time ◽  
Wave Radiation ◽  
Moderate Intensity ◽  
Leading Order ◽  
Asymptotic Results ◽  
Contour Dynamics ◽  
Singular Vortex

McDonald (1998) has studied the motion of an intense, quasi-geostrophic, equivalent-barotropic, singular vortex near an infinitely long escarpment. The present work considers the remaining cases of the motion of weak and moderate intensity singular vortices near an escarpment. First, the limit that the vortex is weak is studied using linear theory. For times which are short compared to the advective time scale associated with the vortex it is found that topographic waves propagate rapidly away from the vortex and have no leading-order influence on the vortex drift velocity. The vortex propagates parallel to the escarpment in the sense of its image in the escarpment. The mechanism for this motion is identified and is named the pseudoimage of the vortex. Large-time asymptotic results predict that vortices which move in the same direction as the topographic waves radiate non-decaying waves and drift slowly towards the escarpment in response to wave radiation. Vortices which move in the opposite direction to the topographic waves reach a steadily propagating state. Contour dynamics results reinforce the linear theory in the limit that the vortex is weak, and show that the linear theory is less robust for vortices which move counter to the topographic waves. Second, contour dynamics results for a moderate intensity vortex are given. It is shown that dipole formation is a generic feature of the motion of moderate intensity vortices and induces enhanced motion in the direction perpendicular to the escarpment.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

Solitary Filaments of Coupled Electromagnetic Wave and Finite Amplitude Ion Fluctuations

1976 ◽  
Vol 31 (12) ◽  
pp. 1517-1519 ◽  
Author(s):  
P. K. Shukla ◽  
M. Y. Yu ◽  
S. G. Tagare
Keyword(s):  
Electromagnetic Wave ◽  
Electromagnetic Radiation ◽  
Plasma Density ◽  
Large Amplitude ◽  
Small Amplitude ◽  
Finite Amplitude ◽  
Nonlinear Coupling ◽  
Incoming Radiation

Abstract We show analytically that the nonlinear coupling of a large amplitude electromagnetic wave with finite amplitude ion fluctuations leads to filamentation. The latter consists of striations of the electromagnetic radiation trapped in depressions of the plasma density. The filamentation is found to be either standing or moving normal to the direction of the incoming radiation. Criteria for the existence of localized filaments are obtained. Small amplitude results are discussed.

Air‐gun source instabilities

Geophysics ◽  
1987 ◽  
Vol 52 (9) ◽  
pp. 1229-1251 ◽  
Author(s):  
Bill Dragoset ◽  
Neil Hargreaves ◽  
Ken Larner
Keyword(s):  
Large Amplitude ◽  
Small Amplitude ◽  
Ocean Surface ◽  
Data Interpretation ◽  
Central Portion ◽  
Air Gun ◽  
Individual Signature ◽  
Band Limited ◽  
Zero Phase

The signature of an air‐gun array can change over a period of time or even from one shot to the next. If the signature variations are large, then deterministic deconvolution, with an operator designed from a single signature or from an average signature, could produce errors significant enough to affect data interpretation. Possible sources of air‐gun instability include changes in gun positions, firing times, and pressures, gun failures, and scattering from the fluctuating rough ocean surface. If an air‐gun array were perfectly stable, after application of signature deconvolution the residual signatures for a sequence of shots would be identically shaped, broadband, zero‐phase wavelets. In practice, air‐gun instabilities lead to two major defects in band‐ limited residual signatures: the central portion of the wavelet can become asymmetrical, and unsuppressed energy can occur in the residual bubble region. Processing experiments done with synthesized air‐gun array signatures show that of all types of air‐gun instabilities likely to occur, only gun dropouts cause signature variations severe enough to affect data interpretation. Gun dropouts produce unsuppressed residual bubble energy that can show up as phantom events on a stacked section or that can obscure small‐amplitude events following large‐amplitude events. Neither gun dropouts nor any other kind of air‐gun instability has a significant effect on resolution within the seismic band. Since gun dropouts do not happen on a shot‐to‐shot basis and other instabilities are unimportant, there is no practical benefit to be gained by deriving and applying individual signature deconvolution operators for each shot. The influence of gun dropouts can be minimized through other actions taken in acquisition and processing.

Pathway-Specific Targeting of GABAA Receptor Subtypes to Somatic and Dendritic Synapses in the Central Amygdala

2001 ◽  
Vol 86 (2) ◽  
pp. 717-723 ◽  
Author(s):  
Andrew J. Delaney ◽  
Pankaj Sah
Keyword(s):  
Gaba Receptors ◽  
Large Amplitude ◽  
Gaba Receptor ◽  
Small Amplitude ◽  
Inhibitory Synapses ◽  
Receptor Subtypes ◽  
Central Amygdala ◽  
Low Concentrations ◽  
Gabaa Receptor Subtypes ◽  
Minimal Stimulation

Neurons in the central amygdala express two distinct types of ionotropic GABA receptor. One is the classical GABAA receptor that is blocked by low concentrations of bicuculline and positively modulated by benzodiazepines. The other is a novel type of ionotropic GABA receptor that is less sensitive to bicuculline but blocked by the GABAC receptor antagonist (1,2,5,6-tetrohydropyridine-4-yl) methylphosphinic acid (TPMPA) and by benzodiazepines. In this study, we examine the distribution of these two receptor types. Recordings of GABAergic miniature inhibitory postsynaptic currents (mIPSCs) showed a wide variation in amplitude. Most events had amplitudes of <50 pA, but a small minority had amplitudes >100 pA. Large-amplitude events also had rise times faster than small-amplitude events. Large-amplitude events were fully blocked by 10 μM bicuculline but unaffected by TPMPA. Small amplitude events were partially blocked by both bicuculline and TPMPA. Focal application of hypertonic sucrose to the soma evoked large-amplitude mIPSCs, whereas focal dendritic application of sucrose evoked small-amplitude mIPSCs. Thus inhibitory synapses on the dendrites of neurons in the central amygdala express both types of GABA receptor, but somatic synapses expressed purely GABAA receptors. Minimal stimulation revealed that inhibitory inputs arising from the laterally located intercalated cells innervate dendritic synapses, whereas inhibitory inputs of medial origin innervated somatic inhibitory synapses. These results show that different types of ionotropic GABA receptors are targeted to spatially and functionally distinct synapses. Thus benzodiazepines will have different modulatory effects on different inhibitory pathways in the central amygdala.

scholarly journals A Survey for Red Variables in the Magellanic Clouds

1984 ◽  
Vol 108 ◽  
pp. 217-218 ◽  
Author(s):  
T. Lloyd Evans
Keyword(s):  
Large Amplitude ◽  
Small Amplitude ◽  
Magellanic Clouds ◽  
Carbon Stars

One LMC and two SMC fields of 0.3 sq. deg. have been searched for red variables. Carbon stars of V ~ 16–17 are common and are usually of small amplitude, while the LMC alone contains numerous faint M type variables of small amplitude. M giants of small amplitude generally have much shorter periods than carbon stars. The LMC contains numerous Miras with a P-L relation similar to that of galactic Miras, while the SMC has few Miras but many bright red variables of large amplitude which have a steeper P-L relation.

scholarly journals Optical Variability of Twenty-Two Quasi-Stellar Objects

1972 ◽  
Vol 44 ◽  
pp. 171-178 ◽  
Author(s):  
R. J. Angione ◽  
H. J. Smith
Keyword(s):  
Large Amplitude ◽  
Small Amplitude ◽  
Secular Trends ◽  
Apparent Magnitude ◽  
Optical Variability ◽  
Stellar Objects ◽  
Light Fluctuations ◽  
Quasi Stellar Objects ◽  
One Year

Light fluctuations have been found in all 22 QSOs studied by measurement of plates from the Harvard collection, which cover the last eighty years. The conclusions of this study are: (i) There appear to be at least three general classes of variation: (a) erratic, small-amplitude variations, (b) erratic, large-amplitude variations, and (c) slow quasi-periodic variations, e.g. as in 3C 273; (ii) No significant differences were detected between the rates of rise and decline of luminosity; (iii) Definite secular trends over at least 50 years were found in 5 QSOs; (iv) No simple clearcut periods greater than one year have been found; (v) There may be a trend of decreasing amplitude of fluctuations in apparent magnitude with increasing luminosity.

Sign in / Sign up

Export Citation Format

Share Document