Steady wave patterns on a non-uniform steady fluid flow

1960 ◽  
Vol 9 (3) ◽  
pp. 333-346 ◽  
Author(s):  
F. Ursell
Keyword(s):  
Wave Length ◽  
Present Theory ◽  
Wave Pattern ◽  
Wave Crest ◽  
Stream Velocity ◽  
List Type ◽  
Mathematical Form ◽  
Local Wave ◽  
Pass Through ◽  
The Waves

A steady slightly non-uniform flow with a free surface is subject to a concentrated surface pressure which gives rise to a pattern of surface waves. (For gravity waves on deep water this is the well-known Kelvin ship-wave pattern.) The motion is assumed inviscid, and the waves are assumed small. A theory is developed for the wave pattern, based on the following assumptions: The stream velocity component normal to a wave crest is equal to the phase velocity based on the local wavelength;the separation between consecutive crests is equal to the local wave-length. These assumptions are expressed in mathematical form, and the existence of a set of characteristic curves (associated with the group velocity) is deduced from them. These characteristics are not identical with the crests. Let the additional assumption be made thatthe characteristics all pass through the point disturbance; the characteristics are then completely defined and may be constructed by a step-by-step process starting at the point disturbance. The same construction gives the direction of the wave crests at all points. The wave crests can then be deduced.Assumptions of the same type as (1) and (2) have long been familiar in various applications of ray tracing. For uniform flows the present theory gives the same pattern as the method of stationary phase.

Shearing flow over a wavy boundary

1959 ◽  
Vol 6 (2) ◽  
pp. 161-205 ◽  
Author(s):  
T. Brooke Benjamin
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Boundary Layers ◽  
Wave Train ◽  
Present Theory ◽  
Wave Crest ◽  
Mean Velocity ◽  
Dimensional Boundary ◽  
The Waves ◽  
As If

A theoretical study is made of shearing flows bounded by a simple-harmonic wavy surface, the main object being to calculate the normal and tangential stresses on the boundary. The type of flow considered is approximately parallel in the absence of the waves, being exemplified by two-dimensional boundary layers over a plane. Account is taken of viscosity; but, as the Reynolds number is assumed to be large, its effects are seen to be confined within narrow ‘friction layers’, one of which adjoins the wave and another surrounds the ‘critical point’ where the velocity of flow equals the wave velocity. The boundary conditions are made as general as possible by including the three cases where respectively the boundary is rigid, flexible yet still solid, or completely mobile as if it were the interface with a second fluid.The theory is developed on the model of stable laminar flow, although it is proposed that the same theory may usefully be applied also to examples of turbulent flow considered as ‘pseudo-laminar’ with velocity profiles corresponding to the mean-velocity distribution. Use is made of curvilinear co-ordinates which follow the contour of the wave-train. This admits a linearized form of the problem whose validity requires only that the wave amplitude be small in comparison with the wavelength, even when large velocity gradients exist close to the boundary. The analysis is made largely without restriction to particular forms of the velocity profile; but eventually consideration is given to the example of a linear profile and the example of a boundary-layer profile approximated by a quarter-period sinusoid. In § 7 some general methods are set out for the treatment of disturbed boundary-layer proses: these apply with greatest precision to thin boundary layers, but are also useful for the initially very steep but on the whole fairly diffuse profiles which occur in most practical instances of turbulent flow over waves.The phase relationships found between the stresses and the wave elevation are discussed for several examples, and their interest in connexion with problems of wave generation by wind is pointed out. It is shown that in most circumstances the stresses are distributed in much the same way as if the leeward slopes of the waves were sheltered. For instance, the pressure distribution often has a substantial component in phase with the wave slope, just as if a wake were formed behind each wave crest—although of course actual separation effects are outside the scope of the present theory. In this aspect, the analysis amplifies the work of Miles (1957).

Wave Forces on a Stationary Platform of Elliptical Shape

1973 ◽  
Vol 17 (02) ◽  
pp. 61-71
Author(s):  
H. S. Chen ◽  
C. C. Mei
Keyword(s):  
Diffraction Problem ◽  
Wave Length ◽  
Practical Interest ◽  
Vertical Cylinder ◽  
Present Theory ◽  
Wave Forces ◽  
Mathieu Functions ◽  
Body Type ◽  
Elliptical Cross ◽  
Long Wave

Exciting forces and moments due to plane incident waves on a stationary platform are studied in this paper. The platform is a vertical cylinder with a finite draft and elliptical cross section. The mathematical solution to the diffraction problem is obtained on the basis of the linearized long wave approximation. Numerical results via Mathieu functions are presented for a shiplike body with beam-to-length ratio Various draft-to-depth ratios and angles of incidence are considered. Results have been checked with the limiting case of a circular cylinder for the long-wave length range. Aside from its own practical interest, the present theory provides a basis for comparison with other approximate theories of slender-body type and serves as a prelude to the corresponding calculations for arbitrary wavelengths.

An experimental investigation of the nature and origin of microseisms at St. Louis, Missouri

1940 ◽  
Vol 30 (2) ◽  
pp. 139-178
Author(s):  
J. Emilio Ramirez
Keyword(s):  
Wave Length ◽  
Vertical Axis ◽  
The Other ◽  
Wave Form ◽  
Stationary Waves ◽  
Retrograde Motion ◽  
Time Signals ◽  
Group Form ◽  
Triangular Network ◽  
The Waves

Summary Over a period of six months, from July to December, 1938, an investigation on microseismic waves has been carried out in the Department of Geophysics of St. Louis University. Four electromagnetic seismographs, specially designed for recording microseisms, were installed in the city of St. Louis in the form of a triangular network. Two of these were E-W components, one at the St. Louis University Gymnasium and the other 6.4 km. due west at Washington University. The other two were arranged as N-S components, one at the St. Louis University Gymnasium and one 6.3 km. due south at Maryville College. The speed of the photographic paper was 60 mm/min., and time signals were recorded automatically and simultaneously on each paper from the same clock every minute and at shorter intervals from a special pendulum and “tickler” combination by means of telephone wires. The results have demonstrated beyond doubt that microseismic waves are traveling and not stationary waves. The same waves have been identified at each one of the stations of the network, and also at Florissant, 21.8 km. away from St. Louis University. The speed of microseismic waves at St. Louis was determined from several storms of microseisms and it was found to be 2.67±0.03 km/sec. The direction of microseisms was also established for most of the storms and it was found that about 80 per cent of incoming microseisms at St. Louis were from the northeast quadrant during the interval from July to December, 1938. No microseisms were recorded from the south, west, or southwest. The period of the waves varied between 3.5 and 7.5 sec. The average period was about 5.4 sec. The microseismic wave length was therefore of the order of 14¼ km. A study of the nature of microseismic waves from the three Galitzin-Wilip components of the Florissant station reveals in the waves many of the characteristics of the Rayleigh waves; that is, the particles in the passage of microseismic waves move in elliptical orbits of somewhat larger vertical axis and with retrograde motion. A comparison carried over a period of more than a year between microseisms and microbarometric oscillations recorded by specially designed microbarographs showed no direct relationship between the two phenomena in wave form, group form, period, or duration of storms. The source of microseisms is to be found not over the land, but rather out over the surface of the ocean. The amplitudes of microseisms depend only on the intensity and widespread character of barometric lows traveling over the ocean. Several correlations between the two phenomena seem to make this conclusion rather evident. Special emphasis is laid on the fact that all the determined directions of incoming microseisms at St. Louis point to a deep barometric low over the ocean. The period of microseisms seems to be a function of the distance between the station and the source of microseisms. The exact mechanism by which barometric lows over the ocean water result in the production of microseisms needs further investigation. Large microseisms have been produced without any indication of surf near the coasts, or with winds blowing from the land toward the ocean.

The flow past a rapidly rotating circular cylinder

1957 ◽  
Vol 242 (1228) ◽  
pp. 108-115 ◽  
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Present Theory ◽  
Stream Velocity ◽  
Two Dimensional ◽  
Rotating Circular Cylinder ◽  
Flow Past ◽  
Separating Flow ◽  
Two Dimensional Flow ◽  
Uniform Stream

This paper considers the two-dimensional flow past a circular cylinder immersed in a uniform stream, when the cylinder rotates about its axis so fast that separation in suppressed. The solution of the flow in the boundary layer on the cylinder is obtained in the form of a power series in the ratio of the stream velocity to the cylinder's peripheral velocity, and expressions are deduced for the value of the circulation and the torque on the cylinder. The terms calculated explicitly are sufficient to give reliable numerical values over the whole range of rotational speeds for which the postulate of non-separating flow is justifiable. The previously accepted theory, due to Prandtl, predicted that the circulation should not exceed a certain limit, while the present theory indicates that the circulation increases indefinitely with increase of rotaional speed. Strong arguments against the older theory are put forward, but the experimental evidence available is inconclusive.

scholarly journals The effect of junctions on the propagation of electric waves along conductors

1913 ◽  
Vol 88 (601) ◽  
pp. 103-110
Keyword(s):  
Cylindrical Shell ◽  
Wave Length ◽  
General Character ◽  
Original Form ◽  
Annular Space ◽  
Approximate Methods ◽  
Positive Direction ◽  
Positive Side ◽  
The Waves ◽  
Electric Waves

Some interesting problems in electric wave propagation are suggested by an experiment of Hertz. In its original form waves of the simplest kind travel in the positive direction (fig. 1), outside an infinitely thin conducting cylindrical shell, AA, which comes to an end, say, at the plane z = 0. Co-axial with the cylinder a rod or wire BB (of less diameter) extends to infinity in both directions. The conductors being supposed perfect, it is required to determine the waves propagated onwards beyond the cylinder on the positive side of z , as well as those reflected back outside the cylinder and in the annular space between the cylinder and the rod. So stated, the problem, even if mathematically definite, is probably intractable; but if we modify it by introducing an external co-axial con­ducting sheath CC (fig. 2), extending to infinity in both directions, and if we further suppose that the diameter of this sheath is small in comparison with the wave-length (λ) of the vibrations, we shall bring it within the scope of approximate methods. It is under this limitation that I propose here to consider the present and a few analogous problems. Some considerations of a more general character are prefixed.

scholarly journals A SIMILARITY PARAMETER FOR BREAKWATERS: THE MODIFIED IRIBARREN NUMBER

2018 ◽  
pp. 28
Author(s):  
Maria Clavero ◽  
Pedro Folgueras ◽  
Pilar Diaz-Carrasco ◽  
Miguel Ortega-Sanchez ◽  
Miguel A. Losada
Keyword(s):  
Incident Wave ◽  
Wave Length ◽  
Slope Angle ◽  
Wave Pattern ◽  
Relative Width ◽  
Scattering Parameter ◽  
Wave Regime ◽  
Similarity Parameter ◽  
Mean Water Level ◽  
Run Up

In the 14th ICCE, Battjes (1974) showed that a single similarity parameter only, embodying both the effects of slope angle and incident wave steepness, was important for many aspects of waves breaking on impermeable slopes, and suggested to call it the "Iribarren number", denoted by "Ir". Ahrens and McCartney (1975) verified the usefulness of Ir to describe run-up and stability on rough permeable slopes. Since then, many researchers applied Ir to characterize and to develop formulae for the design of breakwaters and to verify their stability. On the other hand, depending on their typology, breakwaters reflect, dissipate, transmit, and radiate incident wave energy. Partial standing wave patterns are likely to occur at all types of breakwater, thus playing an important role in defining the wave regime in front of, near (seaward and leeward), and inside the breakwater. The characteristics of the porous medium, relative grain size D/L and relative width, Aeq/L2, are relevant magnitudes in that wave pattern (Vilchez et al. 2016), being D the grain diameter, L the wave length and Aeq the porous area per unit section under the mean water level. Aeq/L2 is a scattering parameter controlling the averaged transformation of the wave inside the porous section of the structure. For a vertical porous breakwater (Type A), Aeq is simply B · h, and for a constant depth, the scattering parameter is reduced to B/L, which is the relative breakwater width.

scholarly journals APPLICATIONS ON NONLINEAR WAVE COMBINATION

1986 ◽  
Vol 1 (20) ◽  
pp. 26
Author(s):  
J.T. Juang
Keyword(s):  
Wave Height ◽  
Taiwan Strait ◽  
Western Coast ◽  
Linear Wave ◽  
Wave System ◽  
Height Distribution ◽  
Wave Height Distribution ◽  
Local Wave ◽  
Source Wave ◽  
The Waves

Due to the special bathymetry in Taiwan Strait, the waves off the western coast of Taiwan are considered to be composed of two-source wave system. One propagates from the central part of the Strait named main wave, and the other is generated by the local wind known as local wave which occurs along the shore. After the combination and the transformation procedure from these two-nonlinear-source wave system, the wave height distribution in Taiwan Strait should be modified. A comparison of the wave height distributions based on the present proposed method with the field data indicates that the present method yields a better result than other theorems. Furthermore, the result of application of two non-linear wave theorem to wave prediction are also presented.

Application of Ship-Wave Theory to the Hydrofoil of Finite Span

1957 ◽  
Vol 1 (02) ◽  
pp. 27-55
Author(s):  
John P. Breslin
Keyword(s):  
Wave Theory ◽  
Wave Pattern ◽  
Wave Drag ◽  
Test Results ◽  
Dimensional Theory ◽  
Ship Hydrodynamics ◽  
Finite Span ◽  
Induced Drag ◽  
Load Distributions ◽  
The Waves

It is demonstrated in this paper2 that the deepwater wave drag of a hydrofoil of finite span can be found directly from the theory developed largely for ship hydrodynamics by Havelock and others. The wave drag is then studied at high Froude numbers and from the observed behavior the induced drag of the hydrofoil can be deduced from existing aerodynamic formulas. Evaluation of the resulting formulas is effected for two arbitrary load distributions and a comparison with some model test results is made. A practical approximation which gives the influence of gravity over a range of high Froude numbers is found and from this one can deduce a Froude number beyond which the effects of gravity may be ignored. It is also shown that an expression for the waves at some distance aft of the hydrofoil can be deduced from the general formulas developed for ship hydrodynamics. A discussion of the wave pattern is given with particular emphasis on the centerline profile at high Froude numbers and a contrast is pointed out in regard to the results of the two-dimensional theory for the hydrofoil waves and wave resistance.

scholarly journals I. On the waves produced by a single impulse in water of any depth, or in a dispersive medium

1887 ◽  
Vol 42 (251-257) ◽  
pp. 80-83 ◽  
Keyword(s):  
Wave Velocity ◽  
Dispersive Medium ◽  
Wave Length ◽  
Periodic Waves ◽  
Two Dimensional ◽  
Group A ◽  
Two Sides ◽  
The Waves

For brevity and simplicity consider only the case of two-dimensional motion . All that it is necessary to know of the medium is the relation between the wave-velocity and the wave-length of an endless procession of periodic waves. The result of our work will show us that the velocity of progress of a zero, or maximum, or minimum, in any part of a varying group of waves, is equal to the velocity of progress of periodic waves of wave-length equal to a certain length, which may be defined as the wave-length in the neighbourhood of the particular point looked to in the group (a length which will generally be intermediate between the distances from the point considered to its next-neighbour corresponding points on its two sides).

Wave Impact Load and Corresponding Nonlinear Response of a Semi-Submersible

2019 ◽  
Author(s):  
Yinghao Guo ◽  
Longfei Xiao ◽  
Handi Wei ◽  
Lei Li ◽  
Yanfei Deng
Keyword(s):  
Spatial Distribution ◽  
Structural Integrity ◽  
Impact Load ◽  
Wave Crest ◽  
Impulsive Effect ◽  
Offshore Platforms ◽  
Wave Impact ◽  
Global Response ◽  
Local Wave ◽  
Incident Waves

Abstract Offshore platforms operating in harsh ocean environments often suffer from severe wave impacts which threaten the structural integrity and staffs safety. An experimental study was carried out to investigate the wave impact load and its effect on the global response of a semi-submersible. First, two typical wave impact events occurring successively in the wave test run are analyzed, including the characteristics of incident waves, relative wave elevations and the spatial distribution of the wave impact load. Subsequently, the corresponding global response of the semi-submersible under these two wave impacts are investigated in time domain. It reveals that compared with the incident wave, the relative wave elevation has a more straightforward relationship with the wave impact load. The relative wave crest height is associated with the spatial distribution of the wave impact load, while the local wave steepness matters more in the magnitude of the wave impact load. The impulsive effect of the wave impact load on the motion behaviors is not obvious. But severe wave impacts can introduce excessive horizontal accelerations and nonlinear behaviors like ringing in the acceleration response.

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