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Frequencies of intermediate-degree f-modes of the Sun seem to indicate that the solar radius is smaller than what is normally used in constructing solar models. We investigate the possible consequences of an error in radius on results for…
We consider a classical problem of linear stability of convective rolls in a plane layer with stress-free horizontal boundaries near the onset of convection. The problem has been studied by a number of authors, who have shown that rolls of…
In the present paper we consider convection and cracking instabilities as well as their interplay. We develop a simple criterion to identify equations of state unstable to convection, and explore the influence of buoyancy on cracking (or…
Since the first observations of solar oscillations in 1962, helioseismology has probably been one of the most successful fields of astrophysics. Besides the improvement of observational data, solar seismologists developed sophisticated…
In this article, we derive and compute the sensitivity of measurements of coupling between normal modes of oscillation in the Sun to underlying flows. The theory is based on first-Born perturbation theory, and the analysis is carried out…
We analyze spectral properties of solar convection in the range of depths from 0 to 19~Mm using subsurface flow maps obtained by the time-distance heiioseismology analysis of solar-oscillation data from the Helioseismic and Magnetic Imager…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
We present numerical simulations of penetrative convection and gravity wave excitation in the Sun. Gravity waves are self-consistently generated by a convective zone overlying a radiative interior. We produce power spectra for gravity waves…
Modelling the base of the solar convective envelope is a tedious problem. Since the first rotation inversions, solar modellers are confronted with the fact that a region of very limited extent has an enormous physical impact on the Sun.…
In the last decade, much work in atmospheric science has focused on spatial verification (SV) methods for gridded prediction, which overcome serious disadvantages of pixelwise verification. However, neural networks (NN) in atmospheric…
We consider a dynamo wave in the solar convective shell for the kinematic $\alpha\omega$-dynamo model. The spectrum and eigenfunctions of the corresponding equations are derived analytically with the aid of the WKB method. Our main aim here…
The tilt angle, current helicity and twist of solar magnetic fields can be observed in solar active regions. We carried out estimates of these parameters by two ways. Firstly, we consider the model of turbulent convective cells…
Steady-state solutions to the Navier-Stokes equations are known to admit solutions that are singular at the sonic point. Consequently, inviscid solar wind models require special treatment of the solution near the sonic points, and this has…
Solar models computed with mass loss, microscopic diffusion of helium and heavy elements and with updated physics have been evolved from the pre-main sequence to present days; they are compared to the observational constraints including…
Wave propagation through sunspots involves conversion between waves of acoustic and magnetic character. In addition, the thermal structure of sunspots is very different than that of the quiet Sun. As a consequence, the interpretation of…
Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. Here, we study a broad class of bistable models subject to self-activation, degradation and spatially inhomogeneous activating agents. We…
Helioseismology has allowed us to study the structure of the Sun in unprecedented detail. One of the triumphs of the theory of stellar evolution was that helioseismic studies had shown that the structure of solar models is very similar to…
The basic equations, concepts, and modes of linear, ideal, MHD waves -- slow, Alfv\'en and fast -- are set out and generalised to gravitationally-stratified atmospheres. Particular attention is devoted to mode conversion, wherein the local…
Time-distance helioseismology is the method of the study of the propagation of waves through the solar interior via the travel times of those waves. The travel times of wave packets contain information about the conditions in the interior…
We discuss current advances in forward and inverse modeling for local helioseismology. We report theoretical uniqueness results, in particular the Novikov-Agaltsov reconstruction algorithm, which is relevant to solving the non-linear…