Modeling internal gravity waves in a range-dependent medium

The dispersion relation of small amplitude waves in an isothermal saturated atmosphere with constant specific humidity is derived. The propagation of internal gravity waves is found to be severely inhibited while the effect on acoustic gravity waves is small.

UDC 550.388.2+551.510.536 We present for the first time the experimental data on the frequency of ion–neutral collisions at the altitudes of the ionospheric E layer, which were obtained by the method of resonance scattering of the radio waves by artificial periodic irregularities of the ionospheric plasma. The measurements were carried out in different time periods from 1990 to 2012. Time and altitude dependences of the collision frequency are given. The dependence of the collision frequency on the solar and geomagnetic activity has been analyzed. Collisions of electrons and ions with atoms and molecules play an important role in physics of the ionosphere and atmosphere. In particular, they determine the friction force and should be taken into account in the equations of motion of a medium when its viscosity increases. The frequency of ion–neutral collisions affects the energy and momentum transfer processes [1–4]. When propagation of internal gravity waves above 100 km is considered, it is needed to allow for dissipation due to increasing viscosity of the medium [4–7], which is directly related to collisions. The frequency νin of collisions between ions and neutral molecules should also be taken into account when the low-frequency processes associated with the plasma conductivity are analyzed (see, e. g., [8]). However, the experimental data on νin are fairly scarce. Meanwhile, considerable variations in the ion–neutral collision frequency can be observed in the upper ionosphere. These variations are due most frequently to the neutral atmosphere density variations caused by the transmission of internal gravity and tidal waves. Variations from day to day can be due to propagation of planetary waves. At the altitudes of the upper mesosphere and lower thermosphere, the neutral atmosphere density variations according to the lidar data can exceed 20%, while the temperature variations can reach 70 K [9, 10]. Observations suggest that during propagation of gravity waves the collision frequency can be changed by a factor of 1.5–2 for half an hour [9, 11]. The collision frequency variations can also be a consequence of variations in the composition of both the ion component and the neutral atoms and molecules. In particular, in the ionospheric E region, variations in the ion–neutral collision frequency can be caused by the penetration of metal meteor particles and ions that contribute to the formation of both the sporadic layers of the electron density and the layer with increased content of Na, K, Fe, etc. atoms [12–15]. In this paper, we present the results of determining the ion–molecule collision frequency obtained by the method of resonant scattering of radio waves by artificial periodic irregularities of the plasma at the altitudes of the ionospheric E region.

The generation of internal gravity waves from an initially geostrophically balanced flow is diagnosed in nonhydrostatic numerical simulations of shear instabilities for varied dynamical regimes. A nonlinear decomposition method up to third order in the Rossby number (Ro) is used as the diagnostic tool for a consistent separation of the balanced and unbalanced motions in the presence of their nonlinear coupling. Wave emission is investigated in an Eady-like and a jet-like flow. For the jet-like case, geostrophic and ageostrophic unstable modes are used to initialize the flow in different simulations. Gravity wave emission is in general very weak over a range of values for Ro. At sufficiently high Ro, however, when the condition for symmetric instability is satisfied with negative values of local potential vorticity, significant wave emission is detected even at the lowest order. This is related to the occurrence of fast ageostrophic instability modes, generating a wide spectrum of waves. Thus, gravity waves are excited from the instability of the balanced mode to lowest order only if the condition of symmetric instability is satisfied and ageostrophic unstable modes obtain finite growth rates. Significance Statement We aim to understand the generation of internal gravity waves in the atmosphere and ocean from a flow field that is initially balanced, i.e., free from any internal gravity waves. To examine this process, we use simulations from idealized numerical models and nonlinear flow decomposition method to identify waves. Our results show that a prominent mechanism by which waves can be generated is related to symmetric or ageostrophic instabilities of the balanced flow possibly occurring during frontogenesis. This process can be a significant mechanism to dissipate the energy of the geostrophic flow in the ocean.

A high-resolution nonlinear numerical model is used to simulate propagation of internal gravity waves (IGWs) from the troposphere to the upper atmosphere. This simulation takes into account background wind profiles containing critical levels at which the horizontal wind velocity becomes equal to the horizontal phase speed of IGW. According to traditional linear theories of atmospheric waves, near critical levels the vertical wavelength approaches zero, which should lead to a strong dissipation of IGWs propagating from the troposphere and may significantly decrease their ampli-tudes in the upper atmosphere. The wave sources in the model are defined as vertical velocity perturbations propagating along the Earth surface. The mean horizontal wind in the atmosphere is approximated by the Gaussian profile with a maximum at an altitude of 50 km. We analyze the spectra of wave fields near criti-cal levels and at a distance from them. It has been found that the instability of waves near critical levels intensifies the energy transition from primary IGWs propagating from surface sources to secondary wave modes. This causes an increase in spectral peaks at wavelengths shorter than the horizontal length of primary IGW. Therefore, above critical levels, spectral modes with shorter horizontal wavelengths begin to prevail with increasing altitude, and the amplitudes of these secondary waves at the same altitudes can exceed the amplitudes of analogous primary IGW propagating in the absence of critical levels in the middle atmosphere.

Laboratory experiments were conducted to study the motion of miscible buoyant fluid parcels in both homogeneous and stratified media, and were complemented with numerical experiments using the model of Orlanski & Ross (1973). Parcel motion in the homogeneous case was found to be shape-preserving, in agreement with the large body of data for such motion. The stratified medium experiments were such that the parcel attained equilibrium positions. It was found that the time for the parcel to reach maximum depth was approximately 0·7 times the buoyancy period, independent of that depth. The subsequent collapse of the parcel and generation of internal gravity waves was observed. Ray-like patterns of waves propagated out from the collapse region, and wave frequencies near 0·7 times the Brunt-Väisälä frequency were predominant. The internal wave energy radiated away from the collapsed parcel was estimated and found to be 20 to 25% of the change in the system potential energy.

The parabolic equation (PE) method is widely used in radiowave propagation predictions. It has the advantages of high efficiency and stability, but it will lead to greater predicting errors in some situations, because the effects of transverse terrain gradients are not modeled. This problem can be solved by extending the 2D PE to the three-dimensional (3D) PE. However, the computing efficiency will degrade because of large scale matrix operations. In this paper, a new method is presented, in which the 3D PE is decomposed into two 2D PEs. It increases the computational efficiency and accuracy effectively. To verify the capability of the proposed method in radiowave propagation prediction, an experiment platform was set up. The computational results using this new method are compared with the experimental and Method of Moment (MoM) numerical computational results. Good agreements are achieved in the comparison. The study of radiowave propagation under complex environments is vitally important for improving the effective signal coverage in wireless communication and television broadcasting with plenty of urban buildings as well as mountainous terrains. It presents a big challenge due to the multiple wave propagation mechanisms involving the line of sight, diffraction and scattering propagation and the characteristic of large scale computation. The major issues refer to how to keep the computational accuracy and conducting the large scale computation at the same time. To meet the request for large scale computation of actual engineering problems, the modified empirical formulas are often used for analysis and computation with the drawback of poor computational accuracy, and the variance of the predicted propagation loss is generally 2 to 5 dB for the flat terrain, but for the complex terrain, the variance of the predicted propagation loss is usually about 5 to 10 dB. Many computational methods have been developed to improve the predicted accuracy. The commonly used methods are geometric diffraction methods, path integration methods and FDTD. It is hard to meet the requirement of engineering computation because these methods are computationally expensive and require high data accuracy of the terrain database at the same time (1). The Parabolic Equation (PE) method is a computational method for radiowave propagation loss besides the full wave method and ray tracing method, and has become a research focus. The PE method has high potential in radiowave propagation of mobile communication and broadcasting and television signal coverage as it can not only deal with complex terrain boundary conditions accurately, but also deal with complex atmosphere waveguide structure. Compared with the full wave method, the PE method deals with an unidirectional wave propagation, in which the equation can be solved by the step marching method in the propagation direction. The PE method can reduce the computational complexity of the full wave equation.

Context. The Tayler-Spruit dynamo (TSD) is capable of generating a small-scale magnetic field in the differentially rotating, stably stratified layers of stars. Its activity was recently observed in numerical simulations. In parallel, the propagation of internal gravity waves in stars can be modified in the presence of a magnetic field. Aims. We want to estimate the interaction between a magnetic field generated by the TSD and internal gravity waves in the radiative cores of low-mass stars. This allows us to characterise the effect of this interplay on the observed standing mode spectrum and on the internal transport of angular momentum via progressive waves. Methods. We used the STAREVOL evolution code to compute the structure of low-mass rotating stars with various transport and mixing mechanisms along their evolution. We implemented the formalism to describe the TSD and estimate regions where the magnetic field generated by TSD is strong enough to change the identity of internal gravity waves to magneto-gravity waves. In addition, we evaluated the possible limitation of angular momentum transport via the combined action of rotation and magnetism. Results. Along the pre-main sequence and main sequence evolution of low-mass stars, the lowest frequencies of the excited gravity wave spectrum should be converted to magneto-gravity waves by the magnetic field generated by the TSD. On the red giant branch, we find that most of the excited spectrum of progressive internal gravity waves could be converted into magneto-gravity waves.

The generation of acoustic-gravity waves by meteorological heat sources in the troposphere and the propagation of these waves to the heights of the upper atmosphere are studied theoretically. Equations that describe separately the generation and propagation of acoustic and gravity waves by a local heat source are derived. The heat source of the waves is divided into partial sources of gravity and acoustic waves (AWs). The power of these partial sources is estimated and it is shown that the power of the sources differs by about a factor of two, regardless of the shape, size, and frequency of the heat source. It is shown that in the case of heat sources of the waves, the generation of gravity waves cannot occur without the corresponding generation of AWs: these waves are generated only in pairs. The splitting of the problem of waves from a heat source into problems of waves from gravity and acoustic sources is illustrated by the direct modeling of these waves. The application of the obtained results to the problem of parametrization of acoustic-gravity waves in general circulation and climate models is discussed.

Convective generation and vertical propagation of fast gravity waves on Mars: One- and two-dimensional modeling

The suppression of stationary planetary waves by internal gravity waves in the mesosphere is treated using a quasi-geostrophic model on a midlatitude beta-plane. The drag forces due to internal gravity waves are parameterized based on the wave breaking assumption recently proposed by Lindzen. In the present model the vertical propagation of internal gravity waves is affected not only by mean zonal wind distribution but also by eastward and northward velocity perturbations associated with stationary planetary waves, viz., the total local velocity. Numerical mulls show that the drag force due to breaking internal gravity waves acts like a Rayleigh friction, and the amplitudes of stationary planetary waves in the mesosphere are much reduced by this effect. Equivalent Rayleigh friction coefficients are also presented.

We describe a series of fixed Froude number numerical simulations of the generation of internal gravity waves by the flow of stably stratified fluid over an isolated obstacle. Upstream of the obstacle the parallel flow is shear free and the Brunt-Vaisala frequency is independent of height. Under these conditions the nonhydrostatic model which we employ does not support resonance modes. In this model the nonlinear lower boundary condition is treated via a general tensor transformation which maps the domain with an irregular lower boundary into a rectangle. We explore the characteristics of the wave field as a function of the aspect ratio of the topography and show that there exists a critical aspect ratio which, if exceeded, results in the generation of internal waves which are subject to a local convective instability. In the long time limit we compare the numerically determined wave drag, the vertical profile of Reynolds stress and the downslope wind amplification to the corresponding prediction...

Elevated stratopauses formed at ~80–90 km altitude during the recovery phase of stratospheric sudden warmings in February 2006 and 2009. These likely occurred in response to changes in the downward circulation due to gravity waves (GWs) and/or planetary waves in the mesosphere and the lower thermosphere (MLT). However, the physical mechanisms are not fully understood, due in part to the lack of global GW observations in the MLT. This study presents global‐scale GW observations in the MLT during elevated stratopause events using Thermosphere, Ionosphere, Mesosphere Energetics Dynamics (TIMED)‐Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) temperature observation, which provide a better insight into the formation of an elevated stratopause. During the downward movement of elevated stratopause events in 2006 and 2009, GWs were suppressed below ~60 km and enhanced above ~60 km at high latitudes compared to non‐elevated stratopause years (2005 and 2007). Global SABER GW observations indicate that the regions of GW enhancement propagate from low‐mid latitudes to high latitudes in association with the equatorward shift of the polar night jet during elevated stratopause events. Ray‐tracing simulations show enhancements of the poleward propagation of GWs during elevated stratopause events as well as continuous propagation of non‐orographic GWs within high latitudes. Therefore, our results suggest that meridional propagation of GWs from lower to higher latitudes, which is typically not included in global‐scale models, plays an important role in determining GW variations and thus the downward movement of an elevated stratopause, in addition to non‐orographic GWs originating at high latitudes.

The dispersion relation for internal waves in a fluid is generalized from the barotropic approximation to the baroclinic case to allow for the inclination of surfaces of constant density to surfaces of constant pressure. This generalization allows the barotropic approximation to be tested in a variety of situations. The dispersion relation applies to both acoustic waves and internal gravity waves propagating in either the ocean or the atmosphere. Imaginary terms in the dispersion relation proportional to the baroclinic vector indicate energy exchange between the wave and the mean flow, a result of buoyancy being a nonconservative force in a baroclinic fluid. A buoyancy calculation shows that the baroclinic generalization of the Brunt–Väisälä frequency N is given by N2=∇ρθ⋅∇p/ρ2, where ρ is density, ρθ is potential density, and p is pressure. The baroclinicity in a weather front or cyclonic ring can sometimes have as large an effect as the Earth’s rotation on the propagation of internal gravity waves.

The parabolic equation method is an accurate and efficient approach for solving nonseparable problems in ocean acoustics in which there are horizontal variations in the environmental parameters. Many range-dependent problems may be solved using 2-D parabolic equation models that ignore coupling of energy between planes of constant azimuth. When azimuthal coupling must be taken into account, the splitting method may be used to efficiently solve a 3-D parabolic equation that handles the depth operator to higher order but handles the azimuth operator only to leading order. Despite the fact that this approximation provides a favorable combination of accuracy and efficiency for 3-D problems, run times have generally been regarded as prohibitive for the long-range problems that are often of interest in ocean acoustics. It is demonstrated here that, when propagation paths from source to receiver are confined to a relatively narrow neighborhood of the vertical plane containing the source and receiver, it is practical to solve 3-D problems out to long ranges by using nonuniform azimuthal sampling, with fine sampling near the vertical plane and extremely coarse sampling elsewhere.

The effects of viscosity and heat conduction on the propagation of internal gravity waves are examined. These waves propagate in a stably stratified, parallel shear flow with one critical level. The Boussinesq approximation is adopted. For large Reynolds number the governing sixth-order differential equation is solved by analytical methods. In the limit of large Reynolds number it is found that the reflection and transmission coefficients for a wave incident in a viscous fluid are the same as in the inviscid case. Hence over-reflection can also occur in a viscous fluid. For the perturbed velocity components at the critical level, asymptotic expressions are derived. The results we obtain are valid for smooth, but otherwise arbitrary, shear-flow and density profiles.