On the trapping of long-period waves round islands

1969 ◽  
Vol 37 (4) ◽  
pp. 773-784 ◽  
Author(s):  
M. S. Longuet-Higgins
Keyword(s):  
Gravity Waves ◽  
Pressure Field ◽  
Critical Radius ◽  
Wave Number ◽  
Coriolis Parameter ◽  
Long Period ◽  
Short Period ◽  
Zero Radius ◽  
Inertial Currents ◽  
The Waves

The trapping of short-period gravity waves by islands and seamounts has been studied by Chambers (1965) and by Longuet-Higgins (1967). It was shown by the latter that in the absence of rotation, or when the wave frequency σ is large compared with the Coriolis parameter f, these waves cannot be perfectly trapped; some energy must always leak away to infinity. Very long-period oscillations in the presence of a sloping shelf surrounding an island, with σ [Lt ] f, have been studied by Mysak (1967) and Rhines (1967, 1969). Here perfect trapping is possible. However, as pointed out in Longuet-Higgins (1968), the rotation itself exerts a strong trapping effect not only when |σ| [Lt ] f, but also whenever a |σ| < f. It seems not to have been noticed that this effect is capable of trapping waves round an island in an ocean of uniform depth, in the absence of any shelf or sloping region offshore.The existence of such waves is demonstrated for a circular island in § 1 of the present paper. It is shown that the waves exist only when the azimuthal wave-number n is at least 1. The waves always progress round the island in a clockwise sense in the northern hemisphere. At large distances r from the island, the wave amplitude decays exponentially, but this exponential trapping occurs only if the radius a of the island exceeds the critical value (n(n − 1)gh)½/f. When n = 1, this critical radius is zero, so that in theory the waves exist for any island of non-zero radius.The application of these results to the ocean is discussed in § 2. Except possibly for baroclinic motions, it appears that only the waves corresponding to n = 1 could exist in fact, and that their frequency would be nearly equal to the inertial frequency f. It is unlikely that f could be regarded as constant over a sufficiently wide area for the model to apply without qualification. Nevertheless, the oscillations may be regarded as the local adjustment of the pressure field to inertial currents in the neighbourhood of the island. It is possible that the peak at about 0·73 c.p.d. in the spectrum of sea-level at Oahu, as found by Miyata & Groves (1968), can be interpreted in this way.

scholarly journals Internal wave breaking and the fate of planets around solar-type stars

2010 ◽  
Vol 6 (S271) ◽  
pp. 363-364
Author(s):  
Adrian J. Barker ◽  
Gordon I. Ogilvie
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Internal Gravity Waves ◽  
Amplitude Dependence ◽  
Tidal Dissipation ◽  
Short Period ◽  
Central Regions ◽  
Solar Type ◽  
The Waves ◽  
Solar Type Star

AbstractInternal gravity waves are excited at the interface of convection and radiation zones of a solar-type star, by the tidal forcing of a short-period planet. The fate of these waves as they approach the centre of the star depends on their amplitude. We discuss the results of numerical simulations of these waves approaching the centre of a star, and the resulting evolution of the spin of the central regions of the star and the orbit of the planet. If the waves break, we find efficient tidal dissipation, which is not present if the waves perfectly reflect from the centre. This highlights an important amplitude dependence of the (stellar) tidal quality factor Q′, which has implications for the survival of planets on short-period orbits around solar-type stars, with radiative cores.

Inertia–Gravity Waves Generated within a Dipole Vortex

2007 ◽  
Vol 64 (12) ◽  
pp. 4417-4431 ◽  
Author(s):  
Chris Snyder ◽  
David J. Muraki ◽  
Riwal Plougonven ◽  
Fuqing Zhang
Keyword(s):  
Gravity Waves ◽  
Initial Conditions ◽  
Initial Period ◽  
Potential Temperature ◽  
Leading Edge ◽  
Vertical Shear ◽  
Coriolis Parameter ◽  
Dipole Vortex ◽  
The Waves ◽  
Inertia Gravity Waves

Abstract Vortex dipoles provide a simple representation of localized atmospheric jets. Numerical simulations of a synoptic-scale dipole in surface potential temperature are considered in a rotating, stratified fluid with approximately uniform potential vorticity. Following an initial period of adjustment, the dipole propagates along a slightly curved trajectory at a nearly steady rate and with a nearly fixed structure for more than 50 days. Downstream from the jet maximum, the flow also contains smaller-scale, upward-propagating inertia–gravity waves that are embedded within and stationary relative to the dipole. The waves form elongated bows along the leading edge of the dipole. Consistent with propagation in horizontal deformation and vertical shear, the waves’ horizontal scale shrinks and the vertical slope varies as they approach the leading stagnation point in the dipole’s flow. Because the waves persist for tens of days despite explicit dissipation in the numerical model that would otherwise damp the waves on a time scale of a few hours, they must be inherent features of the dipole itself, rather than remnants of imbalances in the initial conditions. The wave amplitude varies with the strength of the dipole, with waves becoming obvious once the maximum vertical vorticity in the dipole is roughly half the Coriolis parameter. Possible mechanisms for the wave generation are spontaneous wave emission and the instability of the underlying balanced dipole.

scholarly journals Kelvin wake pattern at large Froude numbers

2013 ◽  
Vol 738 ◽  
Author(s):  
Alexandre Darmon ◽  
Michael Benzaquen ◽  
Elie Raphaël
Keyword(s):  
Gravity Waves ◽  
Water Surface ◽  
Pressure Field ◽  
Maximum Amplitude ◽  
Specific Pattern ◽  
Surface Form ◽  
Wake Region ◽  
Strong Hypothesis ◽  
Lord Kelvin ◽  
The Waves

AbstractGravity waves generated by an object moving at constant speed at the water surface form a specific pattern commonly known as the Kelvin wake. It was proved by Lord Kelvin that such a wake is delimited by a constant angle ${\simeq }19. 4{7}^{\circ } $. However a recent study by Rabaud and Moisy based on the observation of airborne images showed that the wake angle seems to decrease as the Froude number $Fr$ increases, scaling as $F{r}^{- 1} $ for large Froude numbers. To explain such observations they make the strong hypothesis that an object of size $b$ cannot generate wavelengths larger than $b$. Without the need of such an assumption and modelling the moving object by an axisymmetric pressure field, we analytically show that the angle corresponding to the maximum amplitude of the waves scales as $F{r}^{- 1} $ for large Froude numbers, whereas the angle delimiting the wake region outside which the surface is essentially flat remains constant and equal to the Kelvin angle for all $Fr$.

scholarly journals Some observations of waves and other fluctuations in a tidal current

1948 ◽  
Vol 192 (1030) ◽  
pp. 403-425 ◽  
Keyword(s):  
Tidal Current ◽  
Time Pressure ◽  
Pressure Gauge ◽  
Experimental Conditions ◽  
Long Period ◽  
Short Period ◽  
The Mean ◽  
Particle Velocities ◽  
The Waves ◽  
Mean Current

Observations have been made of fluctuations in the speed of a tidal current with periods of about 2 sec. upwards. At the same time pressure-gauge records were obtained, showing oscillations due to the wave motion. Both current and pressure measurements were made at various depths between the surface and the bottom. From the pressure records, the rate of attenuation of wave pressures with depth has been shown to follow the theoretical equation, within the limits set by the experimental conditions. The current variations have been classified into short-period and long-period fluctuations. The short-period fluctuations correspond approximately in period to the waves, and their amplitudes are of the same order of magnitude as the calculated wave-particle velocities. The correspondence is not complete, however, and, while it appears probable that the current fluctuations are largely due to the particle velocities of the waves, the possibility of other fluctuations of similar or shorter periods being present is not excluded. The periods of the long-period fluctuations vary from 30 sec. to several minutes, and their amplitude, which increases with the mean current and with depth, sometimes attains 0-4 of the mean current.

Climatological monthly characteristics of middle atmosphere gravity waves (10 min-10 h) during 1979-1993 at Saskatoon

1995 ◽  
Vol 13 (3) ◽  
pp. 285-295 ◽  
Author(s):  
N. M. Gavrilov ◽  
A. H. Manson ◽  
C. E. Meek
Keyword(s):  
Gravity Waves ◽  
Middle Atmosphere ◽  
Radar Data ◽  
Internal Gravity Waves ◽  
Annual Variations ◽  
Long Period ◽  
Short Period ◽  
Annual Component ◽  
Band Pass ◽  
Summer Minimum

Abstract. Saskatoon (52° N, 107°W) medium frequency (MF) radar data from 1979 to 1993 have been analyzed to investigate the climatology of irregular wind components in the height region 60-100 km. This component is usually treated in terms of internal gravity waves (IGW). Three different band-pass filters have been used to separate the intensities of IGWs having periods 0.2-2.5; 1.5-6 and 2-10 h, respectively. Height, seasonal and inter-annual variations of IGW intensities, anisotropy and predominant directions of propagation are investigated. Mean over 14 years' seasonal variation of the intensity of long-period IGWs shows a dominant annual component with winter maximum and summer minimum. Seasonal variations of the intensity of short-period waves have a strong semi-annual component as well, which forms a secondary maximum in summer. Predominant azimuths of long-period IGWs are generally zonal, though they vary with season. For short-period IGWs, the predominant azimuth is closer to the meridional direction. Anisotropy of IGW intensity is larger in summer, winter and at lower altitudes. The IGW intensity shows apparent correlation with both solar and geomagnetic activity. In most cases, this correlation appears to be negative. The variations versus solar activity is larger for longer-period IGW. Possible reasons and consequences of the observed climatological variations of IGW intensity are discussed.

scholarly journals Statistical analysis of thermospheric gravity waves from Fabry-Perot Interferometer measurements of atomic oxygen

2008 ◽  
Vol 26 (1) ◽  
pp. 29-45 ◽  
Author(s):  
E. A. K. Ford ◽  
A. L. Aruliah ◽  
E. M. Griffin ◽  
I. McWhirter
Keyword(s):  
Gravity Waves ◽  
Time Resolution ◽  
Atomic Oxygen ◽  
Source Region ◽  
Auroral Oval ◽  
Wave Activity ◽  
Similar Proportion ◽  
Short Period ◽  
Fabry Perot ◽  
The Waves

Abstract. Data from the Fabry-Perot Interferometers at KEOPS (Sweden), Sodankylä (Finland), and Svalbard (Norway), have been analysed for gravity wave activity on all the clear nights from 2000 to 2006. A total of 249 nights were available from KEOPS, 133 from Sodankylä and 185 from the Svalbard FPI. A Lomb-Scargle analysis was performed on each of these nights to identify the periods of any wave activity during the night. Comparisons between many nights of data allow the general characteristics of the waves that are present in the high latitude upper thermosphere to be determined. Comparisons were made between the different parameters: the atomic oxygen intensities, the thermospheric winds and temperatures, and for each parameter the distribution of frequencies of the waves was determined. No dependence on the number of waves on geomagnetic activity levels, or position in the solar cycle, was found. All the FPIs have had different detectors at various times, producing different time resolutions of the data, so comparisons between the different years, and between data from different sites, showed how the time resolution determines which waves are observed. In addition to the cutoff due to the Nyquist frequency, poor resolution observations significantly reduce the number of short-period waves (<1 h period) that may be detected with confidence. The length of the dataset, which is usually determined by the length of the night, was the main factor influencing the number of long period waves (>5 h) detected. Comparisons between the number of gravity waves detected at KEOPS and Sodankylä over all the seasons showed a similar proportion of waves to the number of nights used for both sites, as expected since the two sites are at similar latitudes and therefore locations with respect to the auroral oval, confirming this as a likely source region. Svalbard showed fewer waves with short periods than KEOPS data for a season when both had the same time resolution data. This gives a clear indication of the direction of flow of the gravity waves, and corroborates that the source is the auroral oval. This is because the energy is dissipated through heating in each cycle of a wave, therefore, over a given distance, short period waves lose more energy than long and dissipate before they reach their target.

Nonlinear dynamic pressure beneath waves in water of large and intermediate depth

2021 ◽  
Author(s):  
Anna Kokorina ◽  
Alexey Slunyaev ◽  
Marco Klein
Keyword(s):  
Gravity Waves ◽  
Pressure Field ◽  
Dynamic Pressure ◽  
Surface Displacement ◽  
Weakly Nonlinear ◽  
Pressure Fields ◽  
Component Theory ◽  
Theoretical Predictions ◽  
Weakly Nonlinear Waves ◽  
The Waves

&lt;p&gt;The data of simultaneous measurements of the surface displacement produced by propagating planar waves in experimental flume and of the dynamic pressure fields beneath the waves are compared with the theoretical predictions based on different approximations for modulated potential gravity waves. The performance of different theories to reconstruct the pressure field from the known surface displacement time series (the direct problem) is investigated. A new two-component theory for weakly modulated weakly nonlinear waves is proposed, which exhibits the best capability among the considered. Peculiarities of the vertical modes of the nonlinear pressure harmonics are discussed.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;The work was supported by the RFBR projects 19-55-15005 and 20-05-00162 (AK).&lt;/p&gt;

Discussion following the presentation by F. Deubner

1977 ◽  
Vol 36 ◽  
pp. 69-74
Keyword(s):  
List Type ◽  
The Sun ◽  
Type Number ◽  
Harmonic Motion ◽  
Locally Excited ◽  
Long Period ◽  
Coherent Wave ◽  
Short Period ◽  
Global Modes

The discussion was separated into 3 different topics according to the separation made by the reviewer between the different periods of waves observed in the sun :1) global modes (long period oscillations) with predominantly radial harmonic motion.2) modes with large coherent - wave systems but not necessarily global excitation (300 s oscillation).3) locally excited - short period waves.

scholarly journals Influence of the cloud-level neutral layer on the vertical propagation of topographically generated gravity waves on Venus

2019 ◽  
Vol 71 (1) ◽  
Author(s):  
Takeru Yamada ◽  
Takeshi Imamura ◽  
Tetsuya Fukuhara ◽  
Makoto Taguchi
Keyword(s):  
Layer Thickness ◽  
Gravity Wave ◽  
Local Time ◽  
Gravity Waves ◽  
Analytical Approach ◽  
Wave Activity ◽  
Neutral Layer ◽  
Low Latitudes ◽  
Vertical Propagation ◽  
The Waves

AbstractThe reason for stationary gravity waves at Venus’ cloud top to appear mostly at low latitudes in the afternoon is not understood. Since a neutral layer exists in the lower part of the cloud layer, the waves should be affected by the neutral layer before reaching the cloud top. To what extent gravity waves can propagate vertically through the neutral layer has been unclear. To examine the possibility that the variation of the neutral layer thickness is responsible for the dependence of the gravity wave activity on the latitude and the local time, we investigated the sensitivity of the vertical propagation of gravity waves on the neutral layer thickness using a numerical model. The results showed that stationary gravity waves with zonal wavelengths longer than 1000 km can propagate to the cloud-top level without notable attenuation in the neutral layer with realistic thicknesses of 5–15 km. This suggests that the observed latitudinal and local time variation of the gravity wave activity should be attributed to processes below the cloud. An analytical approach also showed that gravity waves with horizontal wavelengths shorter than tens of kilometers would be strongly attenuated in the neutral layer; such waves should originate in the altitude region above the neutral layer.

scholarly journals Isolation and Analysis of Six timeless Alleles That Cause Short- or Long-Period Circadian Rhythms in Drosophila

Genetics ◽  
2000 ◽  
Vol 156 (2) ◽  
pp. 665-675
Author(s):  
Adrian Rothenfluh ◽  
Marla Abodeely ◽  
Jeffrey L Price ◽  
Michael W Young
Keyword(s):  
Nuclear Translocation ◽  
Phase Response Curve ◽  
Fixed Number ◽  
Constant Darkness ◽  
Genetic Screens ◽  
Protein Levels ◽  
Long Period ◽  
Short Period ◽  
Molecular Oscillation ◽  
New Alleles

Abstract In genetic screens for Drosophila mutations affecting circadian locomotion rhythms, we have isolated six new alleles of the timeless (tim) gene. Two of these mutations cause short-period rhythms of 21–22 hr in constant darkness, and four result in long-period cycles of 26–28 hr. All alleles are semidominant. Studies of the genetic interactions of some of the tim alleles with period-altering period (per) mutations indicate that these interactions are close to multiplicative; a given allele changes the period length of the genetic background by a fixed percentage, rather than by a fixed number of hours. The timL1 allele was studied in molecular detail. The long behavioral period of timL1 is reflected in a lengthened molecular oscillation of per and tim RNA and protein levels. The lengthened period is partly caused by delayed nuclear translocation of TIML1 protein, shown directly by immunocytochemistry and indirectly by an analysis of the phase response curve of timL1 flies.

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