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.

Changes of the mean velocity profiles in the combined wave–current motion described in a GLM formulation

1998 ◽  
Vol 370 ◽  
pp. 271-296 ◽  
Author(s):  
J. GROENEWEG ◽  
G. KLOPMAN
Keyword(s):  
Velocity Profiles ◽  
Perturbation Series ◽  
Wave Crest ◽  
Mean Velocity ◽  
Initial Current ◽  
Eulerian Formulation ◽  
Waves And Currents ◽  
The Mean ◽  
The Waves ◽  
A Current

The generalized Lagrangian mean (GLM) formulation is used to describe the interaction of waves and currents. In contrast to the more conventional Eulerian formulation the GLM description enables splitting of the mean and oscillating motion over the whole depth in an unambiguous and unique way, also in the region between wave crest and trough. The present paper deals with non-breaking long-crested regular waves on a current using the GLM formulation coupled with a WKBJ-type perturbation-series approach. The waves propagate under an arbitrary angle with the current direction. The primary interest concerns nonlinear changes in the vertical distribution of the mean velocity due to the presence of the waves, but modifications of the orbital velocity profiles, due to the presence of a current, are considered as well. The special case of no initial current, where waves induce a so-called drift velocity or mass-transport velocity, is also studied.

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.

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 < 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 WATER WAVES ON A BILINEAR SHEAR CURRENT

1974 ◽  
Vol 1 (14) ◽  
pp. 36 ◽  
Author(s):  
Robert A. Dalrymple
Keyword(s):  
Water Waves ◽  
Perturbation Technique ◽  
Wave Theory ◽  
Interfacial Velocity ◽  
Shear Current ◽  
Irregular Form ◽  
Vertical Velocity Profile ◽  
Mean Water Level ◽  
The Waves ◽  
A Current

A water wave theory is presented to describe waves propagating on a bilinear shear current flowing in the direction of the waves. The theory is derived assuming an ideal fluid in which a current exists, having a vertical velocity profile which varies linearly from a mean water level velocity of Ug, an interfacial velocity Uj at depth, d, and a bottom velocity Uj$. The theory is developed first for small amplitude waves and then extended to any arbitrary order by a numerical perturbation technique for symmetric waves. For measured waves, an irregular form of the theory is presented to provide a representation of these waves for analysis.

Wave set-up, percolation and undertow in the surf zone

1983 ◽  
Vol 390 (1799) ◽  
pp. 283-291 ◽  
Keyword(s):  
Surf Zone ◽  
Bottom Current ◽  
Straight Tube ◽  
Mean Flow ◽  
Mean Water Level ◽  
The Mean ◽  
Run Up ◽  
Set Up ◽  
Sloping Beach ◽  
The Waves

Waves approaching a sloping beach induce a tilt in the mean water level within the surf zone. The existence of this ‘set-up’ is here demonstrated by observing the mean flow in a straight tube laid parallel to the incoming waves; also by showing that the waves induce a siphon in a U-tube laid on the sloping bottom. It is argued theoretically, and confirmed by experiment, that the set-up should help to drive an offshore bottom current (the undertow) between the shoreline and the breaker line. Seawards from the breaker line the bottom current is reversed. The consequent convergence of the bottom currents may contribute to building up the ‘breaker bar’. Further experiments show that the mean onshore pressure gradient drives a circulation of water within a porous beach. The associated pattern of streamlines also extends into the land, inshore from the run-up line. Theoretically, the injection of dye at the sediment-water interface might be used to probe the porosity of the beach material.

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.

Optimum Swimming Speeds in Fish: The Problem of Currents

1980 ◽  
Vol 37 (7) ◽  
pp. 1086-1092 ◽  
Author(s):  
Clifford L. Trump ◽  
William C. Leggett
Keyword(s):  
Energy Expenditure ◽  
Swimming Speed ◽  
Current Velocity ◽  
Migration Behavior ◽  
Fish Swimming ◽  
Retrograde Motion ◽  
The Mean ◽  
The Relationship ◽  
Mean Current ◽  
A Current

A model is presented describing the energetic consequences of various behavioral responses to currents. To minimize the energy cost of migration, when confronted with currents, fish must optimize both the mean swimming speed and the degree to which swimming speed is altered in response to changes in current velocity. The optimum swimming speed in a current is U0 + 1/b where U0 = mean current speed and b is a constant in the equation E(t) = a ebW(t) describing the relationship between specific energy expenditure per unit time E(t) and swimming speed W(t). In a variable current, such as might occur in estuaries and coastal areas, energy expenditure is minimized when these variations are ignored and a constant speed through the water is maintained. This is true even in conditions where occasional retrograde motion over the bottom may occur. The added energy costs of swimming at mean speeds ≠ U0 + 1/b or of varying swimming speeds in response to changes in current velocity are rigorously defined. Predictions of the model are in general agreement with empirical data on fish swimming behavior.Key words: swimming speeds, currents, fish, theoretical ecology, mathematical models, energetics, migration, behavior

scholarly journals Investigations on the Currents Influencing Iceberg Motion

1980 ◽  
Vol 1 ◽  
pp. 89-93 ◽  
Author(s):  
M. Dhalluin
Keyword(s):  
Southern Ocean ◽  
Surface Currents ◽  
The Mean ◽  
Natural Drift ◽  
Mean Current ◽  
A Current

Several factors contribute to the natural drift of an iceberg, and among these, currents play an important part on the translation and rotation. Some information exists on surface currents in sub-Antarctic areas, but an iceberg behaves as a current integrator due to its draught and it is assumed to drift under the action of a “mean” current. In order to measure the mean current, five drogued buoys were launched in July–August 1979. These buoys were located by Argos satellite transponders. The drift of the buoys gives the mean current from 0 to 230 m depth in the Southern Ocean. Some corrections must be made on the measured drifting speed of the drogued buoys, due to the influence of the wind on the above-water portion of the buoys.

Stability and Stabilization for Discrete System With Probabilistic Nonlinearities

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Xia Zhao ◽  
Engang Tian
Keyword(s):  
Sufficient Conditions ◽  
Discrete Systems ◽  
System Model ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Mean Square Stability ◽  
New Type ◽  
Stability And Stabilization ◽  
The Mean ◽  
Varying Delay

This paper investigates stability and stabilization of discrete systems with probabilistic nonlinearities and time-varying delay. New characters of the nonlinearities, the probability of the nonlinearities happening between different bounds, are used to build new type of system model, which can help us make a full use of the inner variation information of the nonlinearities. With the help of the new characters, new system model is proposed. Then, sufficient conditions for the mean square stability of the system can be obtained by using the Lyapunov functional approach and linear matrix inequalities technique. An example is proposed to illustrate the efficiency of the proposed method.

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