Characteristics Of Long Waves Research Articles

N.D. Kondratiev Long Wave Models for Three Large European Countries

The purpose of this study is to analyze the similarities and differences in the structure of N. D. Kondratiev long waves in the economies of the three largest European countries: Germany, France and Great Britain. It is assumed that the main trend in the dynamics of the GDP of these countries – ​is the trend associated precisely with changes in technology, and not with the influence of ones or others exogenous factors – ​can be represented in the form of a superposition of long Kondratiev waves represented by a periodic function, the values of which at a given time determines the amount of value added produced over the previous time interval. Each wave is characterized by four parameters: time, length of its period, magnitude of the initial amplitude and rate of amplitude decrease. In addition, such characteristics of long waves as the duration of their latency period, the time of their entry into leading positions and duration of their leadership relative to the previous and subsequent technological waves are calculated. Five long Kondratiev waves are considered, the parameters of which are estimated in such a way as to obtain the best description of the dynamics of the GDP of a given country in terms of the deviation of the model from this dynamics. As an estimate of GDP, its values measured in international dollars (Geary–Khamis dollars) for the period from 1790 to 2020 are considered. The calculations showed that in some parameters there is a similarity in the structure of technological waves in these countries, while in others there are differences in the dynamics of their occurrence and development. In the final part of the article, the characteristics of long waves for three European countries are compared with the characteristics of long waves in the US economy over the same time period obtained in previous studies. It is also shown that the leadership durations of long waves obtained in these calculations coincide with the theoretical estimates of the periods of long waves by N. D. Kondratiev.

Statistical characteristics of long waves nearshore

The random long wave runup on a beach of constant slope is studied in the framework of the rigorous solutions of the nonlinear shallow water theory. These solutions are used for calculation of the statistical characteristics of the vertical displacement of the moving shoreline and its horizontal velocity. It is shown that probability characteristics of the runup heights and extreme values of the shoreline velocity coincide in the linear and nonlinear theory. If the incident wave is represented by a narrow-band Gaussian process, the runup height is described by a Rayleigh distribution. The significant runup height can also be found within the linear theory of long wave shoaling and runup. Wave nonlinearity nearshore does not affect the Gaussian probability distribution of the velocity of the moving shoreline. However the vertical displacement of the moving shoreline becomes non-Gaussian due to the wave nonlinearity. Its statistical moments are calculated analytically. It is shown that the mean water level increases (setup), the skewness is always positive and kurtosis is positive for weak amplitude waves and negative for strongly nonlinear waves. The probability of the wave breaking is also calculated and conditions of validity of the analytical theory are discussed. The spectral and statistical characteristics of the moving shoreline are studied in detail. It is shown that the probability of coastal floods grows with an increase in the nonlinearity. Randomness of the wave field nearshore leads to an increase in the wave spectrum width.

Longwave Measurements for the Coast of British Columbia and Improvements to the Tsunami Warning Capability

A few years ago the Canadian Hydrographic Service initiated a major upgrade toall tide gauges and tsunami stations on the coast of British Columbia (B.C.). Thisprogram was undertaken to address shortcomings of the earlier digital systems andwas driven by concerns about emergency response continuity in the year 2000. By1999, thirteen tide gauge stations had been installed and were operational. Three ofthese stations (Tofino, Winter Harbour, and Langara) were selected for use as tsunamiwarning stations. Several years of continuous, high quality data have now been collectedat these stations and used for analysis of long waves in the tsunami frequency band.Careful examination of these data revealed two weak tsunamis recorded by severalB.C. stations: a distant tsunami of June 23, 2001 generated by the Peru Earthquake(Mw = 8.4), and a local tsunami of October 12, 2001 induced by the Queen Charlotte Earthquake (Mw = 6.3$). Spectral characteristics of these two tsunamis are compared with the spectral characteristics of long waves generated by a strong storm (October, 2000) and of ordinary background oscillations. The topographic admittance functions (frequency responses) constructed for all stations showed that most of them (in particular, Winter Harbour, Tofino, Bamfield, Port Hardy, and Victoria) have strong resonance at periods from 2.5 to 20 min, indicating that these locations are vulnerable to relatively high-frequency tsunamis. The Winter Harbour station also has two strong resonant peaks with periods of 30 and 47 min and with amplification factors of about 7. The estimated source functions show very clear differences between long waves associated with the seismic source (typical periods 10–30 min) and those generated by a storm, which typically have shorter periods and strong energy pumping from high-frequencies due to non-linear interaction of wind waves.

Characteristics of Long Waves Trapped by Conical Island

Characteristics of Long Waves Trapped by Conical Island

Generation of long waves by random sources

A statistical approach is applied to solving the problem of long wave generation due to the ocean bottom shift. Various models of random sources are studied. The dependence of the amplitudinal characteristics of long waves on the time scale of random processes is considered. Results of the solution of the dynamic and random source problems are compared.

CNOIDAL WAVES IN SHALLOW WATER

The propagation of long waves of finite amplitude in water with depth to wavelength ratios less than about one-tenth and greater than about one-fiftieth can be described by cnoidal wave theory. To date little use has been made of the theory because of the difficulties involved in practical application. This paper presents the theory necessary for predicting the transforming characteristics of long waves based on cnoidal theory. Basically the method involves calculating the power transmission for a wave train m shallow water from cnoidal theory and equating this to the deep water power transmission assuming no reflections or loss of energy as the waves move into shoaling water. The equations for wave power have been programmed for the range of cnoidal waves, and the results are plotted in non-dimensional form.

Characteristics of Long Waves in Westerlies Related to Solar-Activity

Characteristics of Long Waves in Westerlies Related to Solar-Activity

Experimental investigations of very long waves reflected from the ionosphere

This paper is an account of experiments which have been carried out to determine the characteristic features (amplitude, height of reflexion, and polarization) of waves of very great length (18·8 km) reflected from the ionosphere at fairly small angles of incidence. The transmission characteristics of long waves have previously been studied by Holling-worth, Naismith, and Namba. In Hollingworth's pioneer experiment measurement were made on the space characteristics of the interference pattern produced at the ground by the superposition of the direct and the downcoming wave. the observations were made within the range 300-1000 bin from the sender, during the daytime, and one minimum and one maximum of the interference pattern were located. With the large distances to be covered the measurements extended over three months, and it was necessary to assume constancy of the conditions from day to day. The result demonstrate the presence of the interference system in a very beautiful manner, but cannot be used for an accurate determination of the height of reflexion at any one time. In §2 of the present paper we describe experiments, of the same type as Holling-worth's, carried out at shorter distances (70-140 km). The advantage of using shorter transmission distances are twofold. Firstly, it is possible to make sufficient measurements in the course of a single day (or night) to determine the reflexion height and the reflexion coefficient for a single day (or night), and, secondly, the information derived applies to the conditions of nearly vertical incidence, and so is more directly comparable with the detailed information which is now available concerning short waves. In the papers mentioned above muck attention has been given to the observation and explanation of the effects observed near sunset. It is pointed out that if the resultant signal strength on a single aerial system is alone observed, it is impossible to decide whether the changes are due to changes of amplitude, phase, or polarization of the downcoming wave. Assuming that the sunset variations are due entirely to phase variations, Hollingworth first deduced a change of reflexion height from 75 km to 90 km during sunset, but later believed that the variations were almost entirely explained by a rotation of the plane of polarization of the wave, and that the change of reflexion height was only about 2 km. Naismith states that no sunset variations are observable at short distances (100 km) from the sender, and suggests that at vertical incidence the waves are reflected from a higher level which does not exhibit changes at sunset.

On the rotation of the plane of polarization of long radio waves

The propagation of long waves at great distances has been studied in great detail by Austin, by Round, Eckersley, Tremellen, and Lunnon, by Espenschied, Anderson, and Bailey, and by Yokoyama and Nakai. Thus the propagational characteristics of long waves, considered merely as channels of communication, are well known. There have remained, however, a number of unexplained directional effects of which one might quote as an example the difficulty, noticed by Round, Eckersley, Tremellen, and Lunnon, of receiving signals whose great circle path traversed the earth’s magnetic poles. Pronounced directional effects at short distances have been reported by Naismith. He found that the intensity of the space wave from GKB, Northolt, was approximately twice as great at Manchester as at Exeter although both receiving points are at the same distance from the transmitter. At Manchester the receiver was north of the sender, while at Exeter the direction was west.