A note on the general concept of wave breaking for Rossby and gravity waves

A recently proposed general definition of wave breaking is further discussed, in order to deal with some points on which misunderstanding appears to have arisen. As with surface and internal gravity waves, the classification of Rossby waves into breaking and not breaking is a generic classification based on dynamical considerations, and not a statement about any unique signature or automatically recognizable shape. Nor is it a statement about passive tracers uncorrelated with potential vorticity on isentropic surfaces. A strong motivation for the definition is that proofs of the nonacceleration theorem of wave, mean-flow interaction theory rely, explicitly or implicitly, on a hypothesis that the waves do not break in the sense envisaged.The general definition refers to the qualitative behaviour of a certain set of material contours, namely those, and only those, which would undulate reversibly, with small slopes, under the influence of the waves' restoring mechanism, in those circumstances for which linearized, nondissipative wave theory is a self-consistent approximation to nonlinear reality. The waves' restoring mechanism depends upon the basic-state vertical potential density gradient in the case of gravity waves, and upon the basic-state isentropic gradient of potential vorticity in the case of Rossby waves. In the usual linearized theory of planetary scale Rossby waves on a zonal shear flow, the relevant material contours lie along latitude circles when undisturbed.     

Traveling planetary waves in the stratosphere

This paper reviews the theory and observations of some traveling planetary waves in the stratosphere. Two categories of waves which appear prominently in the literature are discussed: westward propagating waves of periods in the range 3–7 days (the 5-day wave) and in the range 10–20 days (the 16-day wave). Although the observations seem to indicate that these waves are waves of the Rossby type (planetary waves), the evidence is less clear regarding (1) the question of whether these waves are forced internal waves or free (resonant) external waves, and (2) the identification of the observed waves with specific theoretical waves of the Rossby type. When recent observations are compared with theory, the evidence seems to favor the notion that the 5-day and 16-day waves of longitudinal wave number 1 may be identified, respectively, with the gravest and next gravest symmetric free Rossby modes. However, the observational evidence seems to be less clear regarding the nature of the 16-day wave than the 5-day wave.     

The gross features of the lithosphere-asthenosphere system in Europe from seismic surface waves and body waves

Long-period recordings of dispersive Rayleigh waves along numerous station lines, or profiles, in Europe have for the first time permitted a uniform inversion of these observations based on a new method of phase velocity regionalization.Regional dispersion relations obtained by this method have then been subjected to a complete inversion procedure commonly known as the hedgehog method. The results are presented in a map outlining the thickness of the lower lithosphere (lid) and the shear (S) velocities in both the lid and the asthenosphere channel.A comparison of these results with the minimum compressional (P) wave velocities in the asthenosphere and their corresponding depths provides an estimate of theV _p /V _s ratio for the asthenosphere in the European area.Contribution No. 314, Institute of Geophysics, ETH-Zürich, Switzerland.     

Characteristics of the mid-latitude ionosphere suitable for modelling ionospheric filtration of ULF waves

Summary An approximate method of one-dimensional modelling of the plasma of the Earth's ionosphere is demonstrated for purposes of studying the ionospheric filtration of ULF waves (micropulsations). Apart from the basic local parameters, characterizing the plasma, also derived local characteristics have been defined, i.e. the mass of the so-called effective ion and its effective collision frequency . Drawing on existing empirical models of the mid-latitude ionosphere, vertical profiles (50 km h 1000 km) were determined of the characteristics N_e N_i, v_e, and for the daytime and nighttime mid-latitude ionosphere under low and enhanced solar activity, which can be used to study the ionospheric ULF filter.

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aa nu uum m¶rt; ¶rt;a ¶rt;uau na ¶rt; u ¶rt; nmm uu u umauu (unau). ¶rt; u mu naamau na n¶rt; mu m aamumuu — aa m. a. mu ua, , u mua amma mu, . a mu nuuu ¶rt; ¶rt;um u u n¶rt; mua nuu (50 h 1000 ) aamumu N_e N_i, v_e, u ¶rt; u u ¶rt;u um nu u u amumu. ¶rt;u nam nu uuu u uma.

     

The relation between the magnitude derived from surface and from body waves for station průhonice

auam aum¶rt;, m u n¶rt; n a¶rt;u u nm a anu, umua a u mauu u 1964–1976 . ¶rt; aum¶rt; ma auau aum¶rt;, n¶rt; uu m .     

Low frequency waves in plasmas with spatially varying electron temperature

Low frequency electrostatic waves are studied in magnetized plasmas with an electron temperature which varies with position in a direction perpendicular to the magnetic field. For wave frequencies below the ion cyclotron frequency, the waves need not follow any definite dispersion relation. Instead a band of phase velocities is allowed, with a range of variation depending on the maximum and minimum values of the electron temperature. Simple model equations are obtained for the general case which can be solved to give the spatial variation of a harmonically time varying potential. A simple analytical model for the phenomenon is presented and the results are supported by numerical simulations carried out in a 2.5-dimensional particle-in-cell numerical simulation. We find that when the electron temperature is striated along B₀ and low frequency waves (_ci) are excited in this environment, then the intensity of these low frequency waves will be striated in a manner following the electron temperature striations. High frequency ion acoustic waves (_ci) will on the other hand have a spatially more uniform intensity distribution.     

The Earth's structure in the region of the crimea according to the Rayleigh waves observations

Summary The Earth's crust and mantle structure in the region Crimea are investigated on the surface waves observations. For this investigation the long-period seismographs have been installed for the triangle of the seismic stations Simferopol, Alushta, Theodosiya. The phase velocities dispersion has been determined on the base of surface waves for the 8 earthquakes. The observed dispersion curves agree with the theoretical ones for the Earth's model with the crust's thickness of 36–40 km and with (in the mantle) the low velocity layer (V _s =4.3 km/sec at the depth of about 120 km). . , , . 8 . 36–40 . (V _s=4.3 /) 120 .Presented to the IASPEI General Assembly, Madrid, 1969.     

The computation of the elastic constants of an anisotropic medium from the velocities of body waves

¶rt;m n¶rt;u nu nm n m . m¶rt; n¶rt;am nuuu am uma au muna (6) u (10). amua aumnu m m nn unam u u, m nmu ama mm (u. 2). uu nu nm ¶rt;u am mu n¶rt; uua 15mu anau u mu u nn uua mu anau. u unauu m nn ¶rt;u am mu n¶rt; uua ¶rt; 21 anau.

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Dedicated to 90th Birthday of Professor Frantiek Fiala     

On the further generalization of trochoidal frontal waves

Summary A non-linear model of trochoidal waves is presented which represents a geometrical and kinematical generalization of Gerstner's waves and of the results of[2–4].

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¶rt;aam ¶rt; mu¶rt;a , ma m u ma u am[2–4] mu umuu u uamu mm ¶rt;u.

     

On surface seismic waves formation

Summary The interpretation of surface seismic waves records is rather complicated as they include a superposition of oscillations of the fundamental mode and higher modes. Besides recorded oscillations depend on spectral characteristics of motions in earthquakes sources. The consideration of these problems is based on results of surface waves two-dimensional modelling [1]³. Some physical ideas about their formation deals with the change of the nature of the oscillation propagating with dispersion. This report represents a condensate of several independent works. , , . , . , . () . .Scientific communication presented to the IASPEI Assembly, Madrid, 1969.     

Equations of motion of the moon retaining higher harmonics in the force function

u u u u uu smu um ¶rt;um ¶rt; a, s¶rt;a ¶rt;a ¶rt;u suu (n — mn, k — n¶rt;): saumauo n u: n=2, k=0; n=2, k=2; n=3, k=0, 1, 2, 3; n=4, k=0; n=4, k=3; saumau n : n=2, k=0; n=2, k=2; saumau n a: n=2, k=0.

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Dedicated to Prof. RNDr. Emil Buchar, DrSc., Corresponding Member of the Czechoslovak Academy of Sciences, on the Occasion of His 75^th Birthday     

On the propagation of certain types of surface waves in a non-homogeneous elastic layer

Summary The propagation of a certain type of surface waves in a non-homogeneous elastic layer of finite thickness lying in welded contact with a semi-infinite homogeneous elastic medium has been investigated in this paper. The surface wave is characterised by the fact that the dilatation and the vertical displacement component are both zero. It has been proved that such disturbance can propagate only when the phase velocity of the wave is greater than the shear wave velocity and the group velocity is inversely proportional to the phase velocity.     

On the possibility of combining functional optimality criteria in a geodetic net

Summary The procedure of computing the optimum plan, satisfying the conditions of the criterion generated by a convex linear combination of two convex functional optimality criteria is discussed. A numerical example of computing the optimum plan of a geodetic positional net combining criteria of L-optimality and D-optimality is given.

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m¶rt; uu nmua naa, n u umu, ¶rt;a n n u uauu ¶rt; n ua umu nmuamu. u nu ama nmua naa¶rt;u na mu nu uauu umu L-nmuamu u D-nmuamu.

     

On the problem of sudden commencements of geomagnetic storms as manifestations of shock waves

nma nu SS u nmau u nau a¶rt;a ¶rt;u nma u u a au 11-mu ua. u ¶rt; nm ¶rt; n. a¶rt;am nuu nu SS u.     

Some possibilities of predicting radio wave absorption in the lower ionosphere

Summary An attempt is made to show possible ways of predicting radio wave absorption in the midlatitude lower ionosphere using relations between absorption and the intensity of solar ionizing radiation and/or common solar activity indices, and between absorption and f₀F2.

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aa mu nuau nu a¶rt;u ¶rt;um u u a mu ¶rt; nu u umum uuu uu (uu uu u¶rt;au amumu) u ¶rt; nu u f₀F2.

     

Palaeointensity of the geomagnetic field during upper cainozoic derived from palaeo-slags and porcellanites in north Bohemia

Summary Porcellanites and palaeo-slags from North Bohemia are natural materials which can be used to derive the palaeomagnetic directions and palaeointensity of the geomagnetic field active at the time of caustic alteration. The origin of these rocks, called erdbrands, was due to the caustic alteration of predominantly pelitic sediments as a result of underground fires conditioned by spontaneous ignition of coal seams. The caustic alteration occurred during the Upper Pliocene to the Quaternary. Three procedure based on the methods by Thellier and Nagata are presented in the paper. The newly developed apparatus MAVACS (Magnetic Vacuum Control System) was used for the thermal demagnetization of samples. A procedure based on multi-component analysis was also proposed and tested. Besides some methodic results, it was found that the geomagnetic field intensity varied during the respective period within the limits of 48%±4% to 154%±32% of the present geomagnetic field intensity.

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aum u na au a mumuu uu n¶rt;mam nu¶rt; amua, m n¶rt;¶rt;um ¶rt; ¶rt;u naaum anau u naumumuaum n, ¶rt;m amu uu. mu n¶rt;, aa ¶rt;a¶rt;, uu n¶rt; uu amu uu num num a¶rt; n¶rt; ¶rt;mu aau . amu uu u m nu¶rt; m nua ¶rt; mmu nu¶rt;a. am n¶rt; mu umnmau nua, n¶rt;¶rt;u ¶rt; ¶rt;u naumumu, nuau a m¶rt; u aama. a aamaa annaama MAVACS (Magnetic Vacuum Control System) a unaa ¶rt; mu aauuau ¶rt; amu aa. n¶rt; u n n¶rt;¶rt;, a a munm aau amuauu. nu m¶rt;uu au, ma ma, m umumaum n u¶rt; nu¶rt; a n¶rt;a 48%±4%-154%±32% au umumu aum n.

     

Deep structure of the bohemian massif from phase velocities of Rayleigh and Love waves

Summary Phase velocities of Rayleigh and Love waves have been measured between the broadband seismic stations KHC (Kaperské Hory, South Bohemia) and KSP (Ksi, Lower Silesia), a profile that nearly coincides with the Interactional DSS Profile VII. The data for both wave types were separately inverted into models of shear-wave velocity versus depth. Novotný's model KHKS 82[1] for the DSS Profile VII was used as a start model. While the crustal section of Novotný's model is compatible with both of our data sets, our Rayleigh-wave data require smaller shear-wave velocities, on the average by 0.24 km/s, in the top 180 km of the mantle. The average difference between Novotný's model and our Love-wave model in that depth range is only 0.06 km/s. If our identification of the observed Love waves as the fundamental mode is correct, this result indicates the presence of polarization anisotropy in the uppermost mantle.

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u a mu u a ¶rt; unu uuu mauu (an , a u) u S (, ua uu). u - S nuuum mmmm ¶rt;a¶rt; nu VII . a ¶rt; u mun m¶rt; umua ¶rt;u auumu mu nn mu. am mam¶rt;u a unaa ¶rt; S 82 m[1] ¶rt; nu VII . a am ¶rt;u m aua uu aau au ¶rt;a, ¶rt;a au ¶rt;a ¶rt; mm uu m nn — ¶rt; a 0,24 / 180 uma amuu. ¶rt;a aua ¶rt; ¶rt; m u a ¶rt; ¶rt; a m ¶rt;uanau n¶rt;mam 0,06 /. u aa u¶rt;muuau a¶rt;a a a ¶rt;ama ¶rt;a m nau, m mm mam u¶rt;ummm numuu nuau aumnuu amuu.

     

Velocities of seismic waves propagating through the Bohemian massif from foci in Poland

mam mm ua a na Pn, Pg, Sn u Sg nu¶rt;u u au -ma. aa, m ¶rt; amu 5° m numa ua¶rt;a ¶rt;am mu a na n au ma¶rt;amu u mu anmau , uu m n u ma¶rt;am¶rt;a. am nmau a uu m anmau mmu aua.     

Effects of the interplanetary magnetic field sector structure in the winter ionosphere

Summary The ionospheric effects of the interplanetary magnetic field (IMF) sector boundary crossings are studied for the winters of 1963–69. They are considerably stronger for proton than for non-proton sector boundaries. There are two different types of effects. The geomagnetic type is a disturbance, observed in geomagnetic activity, the night-time ionosphere and the day-time F2 region near the geomagnetic equator. The effect in the ionosphere is interpreted in terms of the IMF sector boundary crossing related changes in geomagnetic activity. The tropospheric type is aquietening, observed in tropospheric vorticity and in the day-time mid-and low-latitude ionosphere (except the geomagnetic equator region). The mechanism of this effect remains unexplained.

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¶rt;m u m nu mau nam aum n () ¶rt; u 1963–69. u m u ¶rt; nm ¶rt; a mau. mm ¶rt;a m¶rt; muna m. aum m u, a¶rt;a aum amumu, u u ¶rt; F2 amu uuaum ama. mu u m ¶rt;mu uu aum amumu, m a nu mau . n mun m nu, a¶rt; aumu mn u ¶rt; ¶rt;- u uum u (a uu amuaum ama). au m ma um.

     

Some results of investigating the electric field with the interkosmos 10 satellite

¶rt; aau ua au u¶rt;a, umu a nmu m-10 n uum mau mu n (). am au ¶rt;uana amm. aa ¶rt;¶rt;auma umnmau uuu u, auau nu ua au u¶rt;a.