Damping Of Gravity Waves Research Articles

Response of the Thermosphere‐Ionosphere System to an X‐Class Solar Flare: 30 March 2022 Case Study

AbstractThe response of the thermosphere ionosphere system to an X1.3 class solar flare is studied using observations of the total electron content (TEC) and the Global Ionosphere Thermosphere Model (GITM) simulations. The solar flare erupted from the active region AR12975 on 30 March 2022. Owing to the absence of accompanying severe geomagnetic activity, it was possible to isolate the effects of the flare on the upper atmosphere. TEC data are processed for Continental USA (CONUS), employing filtering and binning techniques to create 2D variation maps. The spectral content of the TEC variations is analyzed using a wavelet coherence method. The immediate response of the solar flare exhibited broad similarities, while notable differences were observed during the recovery period between the East and West sides of the CONUS. GITM is used to explore the East–West asymmetry of the key T‐I parameters. Simulation results reveal that the coinciding interplanetary magnetic field southward turning had a greater influence on these parameters compared to the solar flare, while their nonlinear interaction introduced complex variations. Additional investigation reveals gravity wave damping also contributes to the asymmetric solar flare response.

Исследование затухания гравитационных волн на фрагментированном льду

Исследование затухания гравитационных волн на фрагментированном льду

Wave damping of a sloshing wave by an interacting turbulent vortex flow.

We report on the enhancement of the hydrodynamic damping of gravity waves at the surface of a fluid layer as they interact with a turbulent vortex flow in a sloshing experiment. Gravity surface waves are excited by oscillating horizontally a square container holding our working fluid (water). At the bottom of the container, four impellers in a quadrupole configuration generate a vortex array at moderate to high Reynolds number, which interact with the wave. We measure the surface fluctuations using different optical nonintrusive methods and the local velocity of the flow. In our experimental range, we show that as we increase the angular velocity of the impellers, the gravity wave amplitude decreases without changing the oscillation frequency or generating transverse modes. This wave dissipation enhancement is contrasted with the increase of the turbulent velocity fluctuations from particle image velocimetry measurements via a turbulent viscosity. To rationalize the damping enhancement a periodically forced shallow water model including viscous terms is presented, which is used to calculate the sloshing wave resonance curve. The enhanced viscous dissipation coefficient is found to scale linearly with the measured turbulent viscosity. Hence, the proposed scheme is a good candidate as an active surface gravity wave dampener via vortex flow reconfiguration.

A k–ε Turbulence Model for the Stable Atmosphere

AbstractA realizable k–ε turbulence model of incompressible fluid is extended for the stable atmosphere after taking account of the buoyancy damping of gravity waves. The new model is consistent with the Monin–Obukhov similarity theory on the stable atmospheric boundary layer (ABL) over a horizontally uniform surface. The model is incorporated into an ABL model to simulate mean flow against observations. Its ABL-model output is compared with the Leipzig dataset, showing the turbulence model works well for a stable ABL. Specifically, the ABL model properly replicates 1) the mixing length, turbulent viscosity, and mean wind; 2) a significant decrease of the mixing length with height in the upper ABL and thus a reasonable altitude of the ABL top; and 3) a sensitivity of the mixing length and turbulent viscosity to atmospheric stability.

Damping of gravity waves by kinetic processes in Jupiter's thermosphere

We employ a linearized full-wave model to show that the rovibrational damping (hereafter, RV damping) of gravity waves is an important source of atmospheric heating, which needs to be taken into account when modeling the wave processes in the jovian thermospheres. We find that RV damping of internal gravity waves becomes strong when the wave frequencies approach the thermal collision frequency. RV damping, compared to the damping by molecular viscosity and thermal diffusivity, can effectively lower the damping altitudes for waves with large frequencies, and requires larger upward wave energy fluxes to produce prescribed wave amplitudes for these waves. Particularly, the energy deposited by RV damping, viscous and thermal dissipation of the two waves identified in measurements by the Atmospheric Structure Instrument (ASI) on the Galileo Probe can produce a maximum temperature about 40 K higher than those in previous studies. We further demonstrate RV damping effect on the mesoscale gravity wave observed during the New Horizons flyby on Jupiter. Under the influence of RV damping, this wave has the vertical wavelength and damping altitude comparable to those of wave 2 retrieved from the ASI observations. The energy dissipation of these three observed waves, if coexist, should provide sufficient heating to produce the observed mean temperature between 357 km and 700 km above 1 bar.

Star-planet interactions

Context. When planets are formed from the protoplanetary disk and after the disk has dissipated, the evolution of their orbits is governed by tidal interactions, friction, and gravitational drag, and also by changes in the mass of the star and planet. These interactions may change the initial distribution of the distances between the planets and their host star by expanding the original orbit, by contracting it (which may cause an engulfment of the planet by the star), or by destroying the planet. Aims. We study the evolution of the orbit of a planet orbiting its host star under the effects of equilibrium tides, dynamical tides, drag (frictional and gravitational), and stellar mass loss. Methods. We used the Geneva stellar evolution code to compute the evolution of stars with initial masses of 1 and 1.5 M⊙ with different rotation rates at solar metallicity. The star is evolved from the pre-main-sequence (PMS) up to the tip of the red giant branch. We used these models as input for computing the evolution of the planetary orbits. We explored the effects of changing the planet masses (of 1 Earth mass up to 20 Jupiter masses), the distance between the planet and the star (of 0.015 and more than 3 au), the mass, and the spin of the star. We present results when only the equilibrium tide was accounted for and when both equilibrium and dynamical tides were accounted for. The expression for the dynamical tide is a frequency-averaged dissipation of tidally excited inertial waves, obtained from a piecewise homogeneous two-layer stellar model. Gravity wave damping was neglected. Results. Dynamical tides in convective zones have a significant effect on planetary orbits only during the PMS phase and only for fast-rotating stars. They have no significant effects during the PMS phase for initially slow-rotating stars and during the red giant branch phase, regardless of the initial rotation. In the plots of initial orbital distance versus planetary mass, we show the regions that lead to engulfment or any significant changes in the orbit. As a result of orbital evolution, a region near the star can become devoid of planets after the PMS phase. We call this zone the planet desert, and its extent depends sensitively on stellar rotation. An examination of the planet distribution as a function of distance to the host star and mass can provide constraints on current computations.

Consistent Scale Interaction of Gravity Waves in the Doppler Spread Parameterization

Abstract The standard Doppler spread parameterization of gravity waves, which was proposed by C.-O. Hines and has been applied in a number of middle atmosphere general circulation models, is extended by the inclusion of all effects associated with vertical diffusion. Here the Wentzel–Kramers–Brillouin (WKB) approximation is employed to calculate the vertical propagation of the wave spectrum in the presence of wave damping. According to the scale interaction between quasi-stationary turbulence and the larger nonturbulent flow, all vertical diffusion applied to the resolved flow should damp the parameterized gravity waves as well. Hence, the unobliterated part of the gravity wave spectrum is subject to diffusive damping by the following processes: 1) the background diffusion derived from the model’s boundary layer vertical diffusion scheme, which may extend into the middle atmosphere, 2) molecular diffusion, and 3) the turbulent diffusion resulting from the truncation of the gravity wave spectrum by Doppler spreading, which thus feeds back on the unobliterated gravity waves. The extended Doppler spread parameterization is examined using perpetual July simulations performed with a mechanistic general circulation model. For reasonable parameter settings, the convergence of the potential temperature flux cannot be neglected in the sensible heat budget, especially in the thermosphere. Less gravity wave flux enters the model thermosphere when vertical diffusion is included, thus avoiding the need for artificial means to control the parameterized gravity waves in the upper atmosphere. The zonal wind in the tropical middle and upper atmosphere is found to be especially sensitive to gravity wave damping by diffusion.

Oscillatory eddy structure in a container

We consider the periodic, two-dimensional motion of a viscous, incompressible liquid which fills a rectangular container. The motion is due to the periodic motion of the lid which moves in its own plane. If the velocities are sufficiently small the motion will be governed by the linearized Navier–Stokes equations and consequently the dimensionless stream function -plane. This fact has an important bearing on the damping of gravity waves at high Reynolds numbers. The eigenfunctions derived above are used to write down a formal expansion for the stream function and the coefficients are determined from the boundary conditions using a least-squares procedure. An examination of the resulting streamline patterns reveals interesting inertial effects even at low Reynolds numbers. In particular we examine the mechanism by which the flow field reverses its direction when the lid stops and reverses its direction of motion. If inertial effects are completely negelected, as has been done till now, one would infer an immediate response of the fluid to the changes in the lid motion; for example, one would conclude, wrongly, that when the lid is at rest so is the fluid. Our analysis shows, in fact, a very intricate and beautiful mechanism, involving among other things an apparent engulfing of the corner eddy by the new primary eddy, by which the direction of the circulation is reversed in the fluid. These results should be of importance in the analysis of mixing, where such effects appear to have been ignored till now.

High frequency atmospheric gravity wave damping in the mesosphere

Correlative measurements of temperature and winds by Na lidar and brightness in OH and O 2 Atmospheric band airglow have been made at Albuquerque, NM and Maui, HI for a study of high frequency (period less than 30 minutes) Atmospheric Gravity Waves. Wave studies from four nights have been made and the correlative information describes the intrinsic wave properties with altitude, their damping characteristics, and resulting accelerations to the large scale circulation in the 85–100 km altitude region. Generally, saturated to super-saturated conditions were observed below 95 km. Above this altitude, they were less saturated to freely propagating.

Damping of large‐scale traveling ionospheric disturbances detected with GPS networks during the geomagnetic storm

Large‐scale traveling ionospheric disturbances (LSTIDs) during the geomagnetic storm on 22 September 1999 were studied using total electron content (TEC) data from the GPS Earth Observation Network (GEONET) in Japan, International GPS Service (IGS), and Continuously Operating Reference Stations (CORS) in the United States. The damping rates of the LSTIDs were precisely derived in several local time sectors and were found to depend on values of the background TEC. This indicates that the dominant physical mechanism of the LSTIDs' damping is the ion‐drag effect by the background ionosphere. The high‐resolution TEC data from GEONET revealed that two successive LSTIDs were damped significantly as they traveled equatorward in the dawn sector. The ratio of the perturbation component of TEC to the background component (ΔI/I0) decreased exponentially with the damping rate of 0.89/1000 km and 0.77/1000 km. We studied also the amplitude of ΔI/I0 at high latitudes using IGS data and found that the damping rates of LSTIDs at high latitudes tended to be smaller than those at midlatitudes. Global TEC observations during this geomagnetic storm by the IGS and CORS networks detected that several LSTIDs propagated also equatorward in the afternoon sector and in the night sector. The LSTIDs in the afternoon sector were most damped with the damping rate of 1.04/1000 km, which corresponds to the e‐folding length of 961 km. The damping rate of LSTIDs in the night sector was found to be small. The LSTIDs had a tendency to be damped rapidly in the regions where background TEC was large. This dependence of the damping rate on latitude and local time indicates that this intense damping of LSTIDs was caused mainly by the ion‐drag effect that is proportional to the ion collision frequency. The relation between the damping rates and the background TEC derived from the observation are consistent with those estimated with a theoretical calculation of the gravity wave damping by the ion‐drag effect. The worldwide distribution of GPS receivers enabled us to estimate the longitudinal extent of these LSTIDs. The zonal width of LSTIDs in the dawn sector was narrower than 45° in longitude (2,900 km) around 55°N and wider than 20° in longitude (1,800 km) around 40°N. These widths were narrower than those reported in previous studies.

A fully nonlinear model for sloshing in a rotating container

In this paper a theoretical and experimental analysis of sloshing in 2D and 3D free-surface configurations is performed. In particular, the case of a tank rotating around a horizontal axis has been considered. The fluid is assumed to be incompressible and inviscid. A fully nonlinear mathematical model is defined by applying the variational method to the sloshing. The damping of gravity waves has been accounted by introducing a suitable dissipation function from which generalized dissipative forces are derived. A modal decomposition is then adopted for the unknowns and a dynamical system is derived to describe the evolution of the physical system. An experimental technique has been applied to select the leading modes, whose evolution characterizes the physical process, i.e. captures the most of the kinetic energy of the process. A very good agreement between experimental and numerical results confirms the validity of the methodological approach followed.

A simplified approach to internal gravity wave damping by viscous dissipation

Internal gravity wave perturbation velocity subject to constant dynamic viscosity and constant kinematic viscosity are approximately derived based on an energy conservation principle. When the dynamic viscosity is assumed to be a constant, the velocity at any height relative to the velocity at the saturation height, Z sat, is found to be solely dependent on the number of scale heights measured from Z sat. Gravity wave energy dissipation due to constant dynamic viscosity primarily occurs from one scale height below to one scale height above the saturation height. When the kinematic viscosity is assumed to be a constant, the perturbation amplitude either increases or decreases monotonically with height depending on whether the energy dissipation rate due, to viscosity, can offset the effect of the decreasing atmospheric density with increasing height. The derivations are made simple by assuming that the non-dissipative dispersion relation is applicable to the dissipative situation. The condition for the assumption to be approximately valid is also given.

Radiative damping of gravity waves in the terrestrial planetary atmospheres

We investigated the scale‐dependent radiative damping of internal gravity waves on the limit of amplitude growth with height in the altitude region 60–120 km of the terrestrial planetary atmospheres. The radiative damping due to the CO2 15 µm radiation limits wave propagation much more effectively in the Mars atmosphere than in the Earth's atmosphere. Though radiative damping is as effective in the Venus atmosphere as in the Mars atmosphere at ∼120 km altitude, it is not so effective below ∼100 km altitude. The damping due to molecular diffusion is significant compared to radiative damping above ∼80 km altitude on the Earth and above ∼120 km altitude on Mars, whereas on Venus it is not significant even above ∼120 km altitude.

Capillarity effects on surface gravity waves in a cylindrical container: wetting boundary conditions

Surface capillary–gravity waves are experimentally investigated in a cylindrical basin subjected to a horizontal oscillation by using a high-sensitivity optical method. We study the low-oscillation-amplitude regimes for a fluid which wets the vertical walls and we show that the presence of the capillary meniscus can effect greatly the main properties of the system. Both the free decay and the forced oscillations of surface oscillations are investigated. The amplitude, the phase and the damping of gravity waves are investigated in detail. The damping of the fundamental surface mode is found to exhibit nonlinear behaviour which is in qualitative agreement with the predictions of the Miles (1967) theory of capillary damping. The amplitude and the phase of gravity waves with respect to the oscillation of the container exhibit unusual behaviour which is strictly connected with the presence of the wetting boundary condition for the fluid at the vertical walls.

Effect of surface-active material on the damping of gravity waves: A reappraisal

Calculations on wave properties for gravity waves have shown that their damping coefficient can be considerably increased by the presence of surface-active material. The potential increase in damping is larger than that for short wavelength capillary waves, but the surface dilational modulus required to give a noticeable effect increases with increasing wavelength of the gravity waves. In practice-with a proper choice of surface-active material-effects on waves of up to 1 m wavelength can be expected. A reassessment of the old technique of wave calming by spreading of oil is advocated and some instances are mentioned in which it is expected to have a beneficial effect.

A study of the dynamics of four-dimensional data assimilation

The problem of four-dimensional data assimilation is investigated on the inviscid linearized shallow-water equations. The conditions under which an assimilation of mass data, performed according to a simple updating scheme, will reconstruct the complete mass and velocity fields are studied. On the basis of a mathematical result proved elsewhere, it is shown that energy conservation ensures exact convergence towards any given solution, irrespective of geostrophy or lack of geostrophy, under the only condition that the available observations define a unique solution of the model equations. For most values of the relevant parameters, the divergent part of the wind field is reconstructed much more rapidly than the rotational part. The effect of a damping of gravity waves is considered, and shown to accelerate the reconstruction of the wind field only for scales which are large compared to the Rossby radius of deformation.These results are generalized to the inviscid linearized multi-level primitive equations. The case of wind observations is also considered, and shown to lead to reconstitution of the complete mass field. Finally, comparison with numerical results obtained with non-linear equations shows that the main features deduced from the linearized theory are preserved, but also suggests that the non-linear advection can, at least in some cases, accelerate the process of reconstruction.

Radiative Damping of Gravity Waves in the Solar Atmosphere

AbstractThe nonlocal character of the radiation field sinnificantly modifies the radiative damping of perturbations in the solar photosphere. Gravity waves are not usually considered to exist in the solar photosphere because the radiative damping time, when based on the Newtonian approximation, is too short. However, this restriction does not apply to low order gravity waves. In fact, with the inclusion of nonlocal effects, the radiative damping for low order gravity waves becomes negative for some region in the photosphere and thus acts as a driving mechanism for gravity waves there.

Damping of Gravity Waves Over Porous Bed

The damping of gravity waves over the contaminated free surface of a viscous layer of fluid that is bounded below by a porous bed is investigated. It is assumed that the bed is saturated with the same fluid. The coupled system of linearized equations appropriate to the fluid layer and the porous bed is solved to study the damping of a progressive wave on the surface of the fluid. The dispersion relation yielding the dependence of the frequency on the viscosity on the parameters related to the porous bed, and on the free surface film, is derived. The effect of the latter on the damping of the waves is found to be very significant. The results obtained subsume the hitherto known results of other authors.

Radiative damping of gravity waves in the solar atmosphere

The nonlocal character of the radiation field sianificantly modifies the radiative damping of perturbations in the solar photosphere. Gravity waves are not usually considered to exist in the solar photosphere because the radiative damping time, when based on the Newtonian approximation, is too short. However, this restriction does not apply to low order gravity waves. In fact, with the inclusion of nonlocal effects, the radiative damping for low order gravity waves becomes negative for some region in the photosphere and thus acts as a driving mechanism for gravity waves there.

Viscous damping of gravity waves over a permeable bed

The damping of gravity waves over the surface of a layer of viscous fluid which overlies a porous bed saturated with the same fluid is studied. It is shown that viscosity may not be the dominant influence in the damping mechanism; the damping effects due to percolation in the fixed bed may be of the same or even higher order than those due to viscosity.