Reflectionless propagation of acoustic waves in the solar atmosphere

The possibility that vertical acoustic waves with frequencies lower than the cutoff frequency corresponding to the temperature minimum pass this minimum is investigated. It is shown that the averaged temperature profile in the solar atmosphere can be approximated by several so-called reflectionless profiles on which the acoustic waves propagate without internal reflection. The possibility of the penetration of vertical acoustic waves, including low-frequency ones, into the solar corona is explained in this way.     

Scattering of surface waves in a basin with a statistically uneven bottom

The propagation of surface waves over a statistically uneven bottom is considered on the basis of equations of the linear potential theory. The expression which emphasizes the dispersion influence is obtained for the spatial decrement of the average field. The north-east Pacific is considered as an example.Translated by Mikhail M. Trufanov.     

A short cut numerical method for determination of periods of free oscillations for basins with irregular geometry and bathymetry

A short cut numerical method for evaluation of the modes of free oscillations of the basins which have irregular geometry and bathymetry is presented in this paper. In the method, a single wave is inputted to the basin as an initial impulse. The respective agitation in the basin is computed by using the numerical method solving the nonlinear form of long wave equations. The time histories of water surface fluctuations at different locations due to propagation of the waves in relation to the initial impulse are stored and analyzed by the fast Fourier transform technique (FFT) and energy spectrum curves for each location are obtained. The frequencies of each mode of free oscillations are determined from the peaks of the spectrum curves. The method is tested by using regular shaped flat bottom basins with different depths. The computed periods of free oscillations are compared with the theoretical values. The accuracy and performance of the method are discussed. As a case study for the application to the basins of irregular shape and bathymetry, the periods of free oscillations of the sea of Marmara is determined and discussed.     

Polynomial approximations of Berkhoff's model for waves in a basin of variable depth

On the basis of the polynomial approximation of the dispersion relation for gravity waves, a generalized version of Berkhoff's model for a non-stationary case has been obtained. The standard problem of the transition of a wave from deep water into shallow water in a basin with a slowly varying topography is applied to study analytically Berkhoff's model polynomial approximations. It has been demonstrated that all qualitative characteristics of wave transformation can be described in the framework of this model.Translated by V. Puchkin.     

Run-Up of a Nonlinear Monochromatic Wave on a Plane Beach in Presence of a Tide

Oceanology - Abstract—The nonlinear problem of run-up of a long wave on a plane beach in presence of a tide is solved within nonlinear shallow water theory using the Carrier–Greenspan...     

Influence of Nonlinear Interaction on the Evolution of Waves in a Shallow Basin

Izvestiya, Atmospheric and Oceanic Physics - The influence of nonlinear interaction of oppositely directed nonlinear waves in a shallow basin is studied theoretically and numerically within the...     

Nonreflected vertical propagation of acoustic waves in a strongly inhomogeneous atmosphere

Using the linear theory of waves in a compressible atmosphere located in a gravitational field, we found a family of sound speed profiles for which the wave field can be represented by a traveling wave with no reflection. The vertical flux of wave energy on these nonreflected profiles is retained, which proves that the energy transfer may occur over long distances.     

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.     

Non-reflective Propagation of Kink Waves in Coronal Magnetic Loops

Propagating kink waves are ubiquitously observed in solar magnetic wave guides. We consider the possibility that these waves propagate without reflection although there is some inhomogeneity. We briefly describe the general theory of non-reflective, one-dimensional wave propagation in inhomogeneous media. This theory is then applied to kink-wave propagation in coronal loops. We consider a coronal loop of half-circle shape embedded in an isothermal atmosphere, and assume that the plasma temperature is the same inside and outside the loop. We show that non-reflective kink-wave propagation is possible for a particular dependence of the loop radius on the distance along the loop. A viable assumption that the loop radius increases from the loop footpoint to the apex imposes a lower limit on the loop expansion factor, which is the ratio of the loop radii at the apex and footpoints. This lower limit increases with the loop height; however, even for a loop that is twice as high as the atmospheric scale height, it is small enough to satisfy observational constraints. Hence, we conclude that non-reflective propagation of kink waves is possible in a fairly realistic model of coronal loops.