Search Results (4)

A two-dimensional time-dependent model is presented for upward-propagating internal gravity waves generated by an imposed thermal forcing in a layer of fluid with uniform background velocity and stable stratification under the anelastic approximation. The configuration studied is representative of a situation with deep or shallow latent heating in the lower atmosphere where the amplitude of the waves is small enough to allow linearization of the model equations. Approximate asymptotic time-dependent solutions, valid for late time, are obtained for the linearized equations in the form of an infinite series of terms involving Bessel functions. The asymptotic solution approaches a steady-amplitude state in the limit of infinite time. A weakly nonlinear analysis gives a description of the temporal evolution of the zonal mean flow velocity and temperature resulting from nonlinear interaction with the waves. The linear solutions show that there is a vertical variation of the wave amplitude which depends on the relative depth of the heating to the scale height of the atmosphere. This means that, from a weakly nonlinear perspective, there is a non-zero divergence of vertical momentum flux, and hence, a non-zero drag force, even in the absence of vertical shear in the background flow. Full article

The accurate and efficient simulation of seismic wave energy dissipation and phase dispersion during propagation in subsurface media due to inelastic attenuation is critical for the hydrocarbon-bearing distinction and improving the quality of seismic imaging in strongly attenuating geological media. The fractional viscoelastic equation, which quantifies frequency-independent anelastic effects, has recently become a focal point in seismic exploration. We have developed a novel hybrid staggered-grid Grünwald–Letnikov (HSGGL) finite difference method for solving the fractional viscoelastic equation in the time domain. The proposed method achieves accurate and computationally efficient solutions by using a staggered grid to discretize the first-order partial derivatives of the velocity–stress equations, combined with Grünwald–Letnikov finite difference discretization for the fractional-order terms. To improve the computational efficiency, we employ a preset accuracy to truncate the difference stencil, resulting in a compact fractional-order difference scheme. A stability analysis using the eigenvalue method reveals that the proposed method confers a relaxed stability condition, providing greater flexibility in the selection of sampling intervals. The numerical experiments indicate that the HSGGL method achieves a maximum relative error of no more than 0.17% compared to the reference solution (on a finely meshed domain) while being significantly faster than the conventional global FD method (GFD). In a 500 × 500 computational domain, the computation times for the proposed methods, which meet the specified accuracy levels used, are only approximately 4.67%, 4.47%, 4.44%, and 4.42% of that of the GFD method. This indicates that the novel HSGGL method has the potential as an effective forward modeling tool for understanding complex subsurface structures by employing a fractional viscoelastic equation. Full article

This paper is devoted to the dynamics of the propagation of non-planetary scale internal gravity waves (IGWs) in the stratified atmosphere. We consider the system of equations describing internal gravity waves in three approximations: (1) the incompressible fluid approximation, (2) the anelastic gas (compressible fluid) approximation, and (3) a new approximation called the non-Boussinesq gas approximation. For each approximation, a different dispersion relation is given, from which it follows that the oscillation frequency of internal gravity waves depends on the direction of propagation, the horizontal and vertical components of the wave vector, the vertical gradient of the background temperature, and the background wind shear. In each of the three cases, the maximum frequency of internal gravity waves is different. Moreover, in the anelastic gas approximation, the maximum frequency is equal to the Brunt–Väisälä buoyancy frequency, and in the incompressible fluid approximation, it is larger than the Brunt–Väisälä frequency by a factor of $\sqrt{7}\cong 2.6$. In the model proposed in this paper, the value of the maximum frequency of internal gravity waves occupies an intermediate position between the above limits. The question arises: which of the above fluid representations adequately describe the dynamics of internal gravity waves? This paper compares the above theories with observational data and experiments. Full article

New observational data and modeling of physical processes constantly appear in the young and rapidly developing branch of science of plasma astrophysics. However, there is a lack of theoretical studies in the field of plasma astrophysics, that could unite the physics of various objects in the Universe, explain the observed phenomena and contribute to the improvement of numerical modeling schemes efficiency. This article makes up for this shortcoming by introducing different models, taking into account the various properties of plasma objects. We present a review of the latest magnetohydrodynamic theories of wave processes in rotating astrophysical plasma, taking into account important and common properties of astrophysical objects as compressibility and stratification. Full article