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.

Observations on the turbulent fluctuations of a tidal current

1949 ◽  
Vol 199 (1058) ◽  
pp. 311-327 ◽  
Keyword(s):  
Time Scale ◽  
Tidal Current ◽  
Velocity Fluctuations ◽  
Turbulent Fluctuations ◽  
Long Period ◽  
Auto Correlation ◽  
Short Period ◽  
Wide Range ◽  
First Time ◽  
A Current

Records have been obtained of fluctuations in the speed of the tidal current in the Mersey estuary, using a current meter in a stand on the bottom, and compared with other records taken with the meter suspended freely at various depths. The fluctuations covered a wide range of periods but could be separated into two main types: ‘short period’, having periods of the order of a few seconds, and ‘long period’, with periods from 30 sec. to several minutes. The amplitudes, periods and auto-correlation of the short-period fluctuations have been examined in some detail, and it is concluded that the fluctuations observed near the bottom are evidence of the turbulence associated with bottom friction. It is believed to be the first time that the presence of turbulent velocity fluctuations of this time-scale in the sea has been established experimentally. The long-period fluctuations resemble those found in previous investigations and show features consistent with their being turbulent in origin also, although turbulence of the time-scale involved in their case would probably be mainly horizontal.

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 The terminus of Hubbard Glacier, Alaska

1992 ◽  
Vol 16 ◽  
pp. 151-157 ◽  
Author(s):  
Robert M. Krimmel ◽  
D. C. Trabant
Keyword(s):  
Seasonal Variation ◽  
Tidal Current ◽  
Time Lapse ◽  
Seasonal Fluctuations ◽  
Seasonal Differences ◽  
Long Period ◽  
Short Period ◽  
Length Changes ◽  
Detailed Record ◽  
Seasonal Length

Hubbard Glacier advanced across the entrance of Russell Fiord in May 1986, transforming the fiord into a lake, which began filling with fresh water. The dam failed in October 1986. The calving terminus of Hubbard Glacier has been mapped with increasing frequency for nearly a century. A mapping interval of a few years establishes that the terminus has made a slow, but accelerating, advance. Recently the terminus has been mapped several times per month using vertical photography, ground surveys, and time-lapse cameras. At this frequency of observation, the terminus position is found to fluctuate seasonally. These seasonal fluctuations are compared with those of Columbia Glacier, where a longer detailed record is available. Although Columbia Glacier is now undergoing a drastic retreat, it continues to have seasonal length changes similar to those it experienced before the retreat began. The lengths of both Columbia and Hubbard Glaciers are extended in the spring, and retracted in the fall. The relatively long period of record for Columbia Glacier shows consistent seasonal variation in length and, when compared with the short period of record for Hubbard Glacier, suggests that there are consistent seasonal differences in length at Hubbard also. The lower Hubbard Glacier diverges, feeding ice into Disenchantment Bay and Russell Fiord, and advances and retreats synchronously over most of its width. The tidal current, which passes through the 250–500 m wide entrance to Russell Fiord, does not affect the seasonal advance and retreat in that area significantly.

scholarly journals Internal tides in the strait of Denmark

2019 ◽  
Vol 55 (3) ◽  
pp. 78-84
Author(s):  
Е. G. Morozov ◽  
D. I. Frey ◽  
S. V. Gladyshev ◽  
А. А. Klyuvitkin ◽  
А. N. Novigatsky
Keyword(s):  
Numerical Model ◽  
Internal Waves ◽  
Field Measurements ◽  
Internal Tides ◽  
Denmark Strait ◽  
Vertical Displacements ◽  
The Mean ◽  
Temperature Records ◽  
The Waves ◽  
Mean Current

Six day temperature records carried out at the three mooring levels revealed isotherm fluctuations in the Denmark Strait sill in July 2018 caused by internal waves. In addition to the field measurements, fluctuations of isopycnals were estimated on the basis of a numerical model. It was shown that the vertical displacements of water particles caused by semidiurnal internal tides are approximately 50 m in the region of the sill crossing the strait. The displacements decrease to 30 m over a distance of 100 km from the sill. The internal waves in the northern part of the strait are more intense than in the southern part because the wave propagates in the opposite direction to the mean current. In the southern part the waves and the current propagate to the south, which increases the wavelength and decreases their amplitudes.

scholarly journals Mass Transport in the Stokes Edge Wave for Constant Arbitrary Bottom Slope in a Rotating Ocean

2014 ◽  
Vol 44 (4) ◽  
pp. 1161-1174 ◽  
Author(s):  
Peygham Ghaffari ◽  
Jan Erik H. Weber
Keyword(s):  
Mass Transport ◽  
Edge Wave ◽  
Stokes Drift ◽  
Future Application ◽  
Bottom Slope ◽  
The Mean ◽  
The Given ◽  
The Waves ◽  
Mean Current ◽  
Local Depth

Abstract The Lagrangian mass transport in the Stokes surface edge wave is obtained from the vertically integrated equations of momentum and mass in a viscous rotating ocean, correct to the second order in wave steepness. The analysis is valid for bottom slope angles β in the interval 0 &lt; β ≤ π/2. Vertically averaged drift currents are obtained by dividing the fluxes by the local depth. The Lagrangian mean current is composed of a Stokes drift (inherent in the waves) plus a mean Eulerian drift current. The latter arises as a balance between the radiation stresses, the Coriolis force, and bottom friction. Analytical solutions for the mean Eulerian current are obtained in the form of exponential integrals. The relative importance of the Stokes drift to the Eulerian current in their contribution to the Lagrangian drift velocity is investigated in detail. For the given wavelength, the Eulerian current dominates for medium and large values of β, while for moderate and small β, the Stokes drift yields the main contribution to the Lagrangian drift. Because most natural beaches are characterized by moderate or small slopes, one may only calculate the Stokes drift in order to assess the mean drift of pollution and suspended material in the Stokes edge wave. The main future application of the results for large β appears to be for comparison with laboratory experiments in rotating tanks.

scholarly journals WAVE BASIN EXPERIMENTS ON BOTTOM FRICTION DUE TO CURRENT AND WAVES

1986 ◽  
Vol 1 (20) ◽  
pp. 61 ◽  
Author(s):  
Paul J. Visser
Keyword(s):  
Laser Doppler Anemometer ◽  
Bottom Friction ◽  
Frictional Stress ◽  
Wave Basin ◽  
New Type ◽  
Mean Water Level ◽  
The Mean ◽  
The Waves ◽  
Mean Current ◽  
A Current

Results are presented of experiments in a wave basin on the increase of the mean bottom frictional stress in a flow when a wave field is superimposed on a current. The bottom friction was derived from the mean water level measured at various places. Measurements of wave orbital and mean current velocities were done both with a micro-propeller and with a new type immersible Laser Doppler Anemometer. The data indicate an increase of the mean bottom shear stress due to the presence of the waves, but less than predicted by Bijker (1967). A suggestion is made to improve the accuracy of this theory. The bottom stresses as predicted by Fredsoe (1984) are somewhat larger than the, experimental results.

A determination of the frictional forces in a tidal current

1952 ◽  
Vol 214 (1118) ◽  
pp. 371-392 ◽  
Keyword(s):  
Frictional Force ◽  
Tidal Current ◽  
Frictional Stress ◽  
Dynamical Equations ◽  
Average Value ◽  
Open Sea ◽  
Frictional Forces ◽  
The Mean ◽  
Mean Current

The frictional forces in a tidal current have been determined from simultaneous observations of the surface gradients and the currents at various depths. The observations were made a few miles from the coast, off Red Wharf Bay, Anglesey. The gradients were derived from measurements of the surface elevations obtained by a pair of open-sea tide-gauges of the Favé type, modified to give increased accuracy. The Doodson electrically recording current meter was used for the current measurements. Each set of observations extended over 24 h, and they were subjected to harmonic analysis for the semi-diurnal constituent. The data from these analyses were then used in the dynamical equations, giving the amplitudes and phases of the frictional force at the bottom, and of the internal shearing stress in the water at various depths. Five complete sets of records were obtained, three of which are considered to have given significant results. Expressing the amplitude of the frictional force at the bottom in the form F ═ kρU 2 , where U is the amplitude of the mean current from surface to bottom, and ρ is the density of the water, the results give the coefficient k an average value of 1⋅8 x 10 ─a . The internal frictional stress in the water was found to increase approximately linearly with depth from the surface to the bottom, and the corresponding values of the mean eddy viscosity have been derived.

scholarly journals The terminus of Hubbard Glacier, Alaska

1992 ◽  
Vol 16 ◽  
pp. 151-157 ◽  
Author(s):  
Robert M. Krimmel ◽  
D. C. Trabant
Keyword(s):  
Seasonal Variation ◽  
Tidal Current ◽  
Time Lapse ◽  
Seasonal Fluctuations ◽  
Seasonal Differences ◽  
Long Period ◽  
Short Period ◽  
Length Changes ◽  
Detailed Record ◽  
Seasonal Length

Hubbard Glacier advanced across the entrance of Russell Fiord in May 1986, transforming the fiord into a lake, which began filling with fresh water. The dam failed in October 1986. The calving terminus of Hubbard Glacier has been mapped with increasing frequency for nearly a century. A mapping interval of a few years establishes that the terminus has made a slow, but accelerating, advance. Recently the terminus has been mapped several times per month using vertical photography, ground surveys, and time-lapse cameras. At this frequency of observation, the terminus position is found to fluctuate seasonally. These seasonal fluctuations are compared with those of Columbia Glacier, where a longer detailed record is available. Although Columbia Glacier is now undergoing a drastic retreat, it continues to have seasonal length changes similar to those it experienced before the retreat began. The lengths of both Columbia and Hubbard Glaciers are extended in the spring, and retracted in the fall. The relatively long period of record for Columbia Glacier shows consistent seasonal variation in length and, when compared with the short period of record for Hubbard Glacier, suggests that there are consistent seasonal differences in length at Hubbard also. The lower Hubbard Glacier diverges, feeding ice into Disenchantment Bay and Russell Fiord, and advances and retreats synchronously over most of its width. The tidal current, which passes through the 250–500 m wide entrance to Russell Fiord, does not affect the seasonal advance and retreat in that area significantly.

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.

the effects of resonance with Jupiter in the system of short-period comets

1974 ◽  
Vol 22 ◽  
pp. 193-203
Author(s):  
L̆ubor Kresák
Keyword(s):  
Structural Effects ◽  
Order Resonance ◽  
Mean Motion ◽  
Short Period ◽  
The Mean ◽  
Compound Effect ◽  
Low Order

AbstractStructural effects of the resonance with the mean motion of Jupiter on the system of short-period comets are discussed. The distribution of mean motions, determined from sets of consecutive perihelion passages of all known periodic comets, reveals a number of gaps associated with low-order resonance; most pronounced are those corresponding to the simplest commensurabilities of 5/2, 2/1, 5/3, 3/2, 1/1 and 1/2. The formation of the gaps is explained by a compound effect of five possible types of behaviour of the comets set into an approximate resonance, ranging from quick passages through the gap to temporary librations avoiding closer approaches to Jupiter. In addition to the comets of almost asteroidal appearance, librating with small amplitudes around the lower resonance ratios (Marsden, 1970b), there is an interesting group of faint diffuse comets librating in characteristic periods of about 200 years, with large amplitudes of about±8% in μ and almost±180° in σ, around the 2/1 resonance gap. This transient type of motion appears to be nearly as frequent as a circulating motion with period of revolution of less than one half that of Jupiter. The temporary members of this group are characteristic not only by their appearance but also by rather peculiar discovery conditions.

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