Dissipation Of Gravity Waves Research Articles

A numerical model for gravity wave dissipation in the thermosphere

Two simplified models of internal gravity wave dissipation due to viscosity, thermal conduction and ion-drag, in a multilayered, isothermal thermosphere are developed. Each of these models uses the WKB approximation, ray theory and the time-averaged equation of energy conservation, but whereas one of the models (A) employs all of the gravity wave equations appropriate to a dissipative atmosphere, the other (B) does not. Results derived from these models for one particular wave are compared to each other and also to some previously published results of Klostermeyer, which employed a full-wave, model. A breakdown of the WKB approximation in the lower, non-isothermal thermosphere leads to models A and B underestimating the total dissipation there. In the middle thermosphere model A estimates the dissipation reasonably well, while model B grossly overestimates the dissipation. In the upper thermosphere model A underestimates the total upward energy flux, probably as a result of the neglect of coupling into the dissipative waves at these levels, while no energy remains in model B. Results from model A show that when dissipation due to viscosity and thermal conduction are included correctly and simultaneously, the dissipation due to viscosity can exceed that due to thermal conduction by a factor of three. It is argued that ray theory may either overestimate or underestimate the energy flux reaching the upper boundary of a thermospheric model depending on both its height and the particular thermospheric model used.

Influence of Marginal Ice Cover on Storm Surges

Observational evidence is provided to show that positive storm surges are damped more than negative surges by ice. Data on the influence of an ice layer on tides and circulation is reviewed as supportive evidence for dissipation of long waves by ice. A mechanism is suggested as to why positive surges are more strongly damped. The crest and trough of the surge wave (which is a long gravity wave) are respectively referred to as the positive and negative surge. The observations consisted of tide gage data from 23 locations in eastern Canadian water bodies for the period 1965–1975. Classical studies, while recognizing the dissipation of long gravity waves by ice, do not account for the asymmetric dissipation of the crests and troughs. Here, we suggest a mechanism involving surface contraction and dilation as responsible for the asymmetric damping. This asymmetric damping occurs during the propagation of the surge in the shallow coastal waters and not during the generation. Open water or leads play an important role in this asymmetric dissipation process.

Parameterization of IR cooling in a Middle Atmosphere Dynamics Model: 2. Non‐LTE radiative transfer and the globally averaged temperature of the mesosphere and lower thermosphere

An efficient technique for including non‐LTE radiative transfer effects has been added to our LTE IR cooling model. The physical processes of thermal and turbulent conduction, odd oxygen transport, gravity wave dissipation, and NO cooling are incorporated into the radiation model to calculate the globally averaged equilibrium temperature profile up to 120 km. The quantitative importance of each process is discussed. We find that gravity wave effects are crucial in cooling the lower thermosphere, which would otherwise be 15–100 K warmer. The magnitude of required gravity wave cooling provides a stringent upper limit on the globally averaged turbulent diffusion coefficient in the mesopause region of <106 cm2 s−1. In the 65‐ to 75‐km mesospheric region, IR cooling rates are uncertain primarily due to the lack of accurate CO2 hot band collisional activation rates. Without any gravity wave heating in this region, total IR cooling rates of 2 K d−1 are required for the computed equilibrium temperature profile to agree with observations, in contrast to the 3.5 K d−1 obtained with a two‐level‐atom non‐LTE source function. Gravity wave heating in this region is estimated at 0.5 K d−1.

Mesospheric Heating Due to Convectively Excited Gravity Waves—A Case Study

A series of at least daily rocket soundings of the mesosphere at Wallops Island, Virginia (37°50′N, 75°29′W), in August and September 1976 reveal near simultaneity between rapid temperature rises and tropospheric convection in the form of squall lines. A multilevel numerical model is developed to test the hypothesis that the convection and warnings are related via internal gravity waves. Some features of the model are: 1) the wave energy source is expressed in terms of cloud-base mass flux, plume diameter and buoyant updraft velocity; and 2) the turbulent-viscous gravity wave dissipation is limited to above 55 km and is parameterized on the basis of findings by Hines (1965). Significant findings are: 1) mesospheric heating rates of the same order as those observed result for reasonable values of the convective parameters and in situ dissipation time scales; 2) only gravity waves confined to a well-defined wavelength and frequency interval are able to propagate upward to mesospheric altitudes; 3) heating rates are strongly dependent on plume diameter and updraft velocity; and 4) for a given cloud-base mass flux, heating rates are optimized for a plume updraft velocity of 10 m s−1.

Energy transfer by gravity wave dissipation

This paper reviews the subject of the dissipation of internal gravity waves in the thermosphere and shows how this is related to propagation. Differences of dissipation and heating rates in quiet and disturbed atmospheres are discussed, and the ranges of waves for different source heights in these atmospheres are calculated. Despite heavy damping of the waves, they may explain T.I.D.'s and related airglow observations in middle and low latitudes.

On the dissipation of interfacial and internal long gravity waves

The Korteweg-deVries equations modified by viscosity for interfacial and internal long gravity waves between two parallel plates are derived in the paper. A method based on the inverse scattering method developed recently by Karpman and Maslov has been used to confirm the well-known inverse fourth power decay of the amplitude of a solitary wave on the one hand and to find the time evolution of its velocity on the other.

Large‐amplitude gravity wave energy production and dissipation in the thermosphere

This paper extends some of the analysis of gravity wave generation and dissipation in the thermosphere given in a previous paper [Richmond, 1978] by defining wave energy for gravity waves of arbitrary amplitude and by analyzing several numerical simulations. Wave energy as defined in this paper is closely related to the sum of kinetic energy and available potential energy of the atmosphere. In the absence of production or dissipation mechanisms, wave energy is approximately, but not strictly, conserved. Its dissipation is related to, but in general is not the same as, entropy generation. Numerical simulations substantiate the findings of Richmond (1978) that both the Lorentz force and the Joule heating of auroral currents can generate substantial gravity wave energy but that the waves produced by Joule heating are more capable of traveling to middle and low latitudes. The simulations also reveal that molecular dissipation of wave energy can be relatively less important, in comparison to daytime Joule dissipation, than the simple treatment of Richmond [1978] indicated.

Structure in the λ557.7 nm [OI] airglow

The application of a four field photometer for study of structure in the airglow is described. Records of the λ557.7 nm [OI] emission from the 95km level frequently show quasi periodic structures. Drift velocities of these structures, typically in the range 50 to 100 ms −1, differ in magnitude, and direction from wind velocities inferred from Doppler shift of the emission line measured with a Fabry-Perot interferometer. The power spectrum of the intensity fluctuations typically cuts off at a period of about 4 min, consistent with the hypothesis that gravity waves are a major cause of the structure. On one night much shorter periods were observed; these were attributed to turbulence generated in the dissipation of large amplitude gravity waves. It is suggested that the major fluctuations with periods of tens of minutes are due to gravity waves generated in the vicinity of tropospheric fronts.

Some properties of upper atmosphere dynamics

Composition and temperature data from satellite measurements and from radar backscatter observations show that dynamics is a major key in our understanding of the upper atmosphere. Individual gases are tracers of wind fields which in turn are driven by the energy and momentum sources of the complex magnetosphere‐thermosphere‐lower atmosphere system. As is shown with data from Ogo 6, ion drag effects on winds impose a magnetic field control on the thermospheric density structure. Differential heating manifests itself in day‐night and summer‐winter temperature contrasts and drives large‐scale circulation that redistributes the minor gases to account for the observed winter bulges in O and He (a factor of 40 larger in winter than in summer) and the large phase separations between atmospheric species in the diurnal tide. Large‐scale atomic oxygen transport within the thermosphere significantly enhances the annual temperature amplitude (by more than a factor of 2) and, through release of chemical energy, contributes to the mesospheric temperature anomaly. The latter phenomenon and the associated reversals in circulation are largely determined by the annual tide excited near 50 km and possibly by dissipation of gravity and planetary waves in the winter hemisphere. During magnetic storms, Joule heating and viscous dissipation drive winds that effectively deplete O and He in the auroral zones and accumulate them at lower latitudes. Mass transport of O amplifies and confines the temperature enhancement to high latitudes, compatible with the observed global response of mass density. The timing of wind and composition effects significantly contributes to the positive and negative phases in ionospheric storms. Owing to the rotational nature of ion drift momentum sources, their signatures in the atmosphere are comparatively weak and differ substantially from those associated with heat sources.

Gravity wave generation, propagation, and dissipation in the thermosphere

This is the first in a series of papers examining large‐scale gravity waves in the thermosphere and their ability to transfer energy from high to low latitudes during magnetic disturbances. The gravity wave source is assumed to be either the Lorentz force of auroral electrojet currents or else a heat input due to energetic particle precipitation or to Joule heating. It is pointed out that the characteristic vertical width of the gravity wave source should usually lie between 2 and 4 pressure scale heights, placing constraints on the vertical wavelengths and horizontal velocities of the generated waves. A simplified analytic model of small‐amplitude wave generation by a current source shows how wave energy production depends on the temporal and spatial dimensions of the source, on the electric field strength, and on the electron density enhancement. The steep thermospheric temperature gradient in the vicinity of the source altitude strongly influences the properties of upward and downward propagating waves compared with waves generated in an isothermal atmosphere. Waves produced by the Lorentz force of Hall currents, by the Lorentz force of Pedersen currents, and by Joule heating are influenced quite differently by this temperature gradient. Because upgoing waves above the source are combinations of waves originally launched upward and waves originally launched downward but reflected around 110 km altitude, the mean effective source altitude is about 110 km for the far field response in the thermosphere. Large‐scale traveling ionospheric disturbances observable at middle latitudes are most likely produced primarily by Pedersen, rather than Hall, currents. The temperature structure of the thermosphere generally causes gravity wave packets to refract upward; waves traveling with a horizontal component of velocity faster than 250 m/s and with an initial downward component of group velocity will always be reflected upward in the lower thermosphere. The effects of viscosity, heat conduction, and Joule dissipation tend to filter out shorter‐period and slower moving waves from observation points at some distance from the source, so that only long‐period fast moving waves can reach low latitudes from an auroral source. For example, a wave with a 94‐min period moving horizontally at 605 m/s is largely dissipated by the time it has traveled 4000 km from a typical auroral source. A numerical simulation using a fairly realistic thermospheric model illustrates many of the points described from analytic considerations.

Heating of the lower thermosphere by the dissipation of acoustic waves

Infrasound of 0.2 Hz known as microbaroms, generated by interfering ocean waves, propagates into the lower thermosphere where it is dissipated between 110 and 140 km. It is shown here that under average conditions in winter the energy input into this region is of the order of 0.33 W/kg, the same as that estimated for gravity wave dissipation, and capable of producing a heating of at least 30 K/day. To arrive at this result different dissipation mechanisms are discussed, with the calculated attenuation compared to previously published observations and observations of natural infrasound at Palisades N.Y. Increased acoustic attenuation due to the presence of turbulence is not, in general, in evidence.

Heating of the lower thermosphere by the dissipation of acoustic waves

Infrasound of 0.2 Hz known as microbaroms, generated by interfering ocean waves, propagates into the lower thermosphere where it is dissipated between 110 and 140 km. It is shown here that under average conditions in winter the energy input into this region is of the order of 0.33 W/kg, the same as that estimated for gravity wave dissipation, and capable of producing a heating of at least 30 K/day. To arrive at this result different dissipation mechanisms are discussed, with the calculated attenuation compared to previously published observations and observations of natural infrasound at Palisades N.Y. Increased acoustic attenuation due to the presence of turbulence is not, in general, in evidence.

On the structure of Mars' atmosphere at 120–220 km

Altitude dependences of [CO 2] and [CO 2 +] are deduced from Mariner 6 and 7 CO 2 + airglow measurements. CO 2 densities are also obtained from n e radio occultation measurements. Both [CO 2] profiles are similar and correspond to the model atmosphere of Barth et al. (1972) at 120 km, but at higher altitudes they diverge and at 200–220 km the obtained [CO 2] values are three times less the model. Both the airglow and radio occultation observations show that a correction factor of 2.5 should be included into the values for solar ionization flux given by Hinteregger (1970). The ratio of [CO 2 +]/ n e is 0.15–0.2 and, hence, [O]/[CO 2] is ∼3% at 135 km. An atmospheric and ionospheric model is developed for 120–220 km. The calculated temperature profile is characterized by a value of T ≈ 370°K at h ⩾ 220 km, a steep gradient (∼2°/km) at 200-160 km, a bend in the profile at 160 km, a small gradient (∼0.7°/km) below and a value of T ≈ 250°K at 120 km. The upper point agrees well with the results of the Lyman-α measurements; the steep gradient may be explained by molecular viscosity dissipation of gravity and acoustical waves (the corresponding energy flux is 4 × 10 −2 erg cm −2sec −1 at 180 km). The bend at 160 km may be caused by a sharp decrease of the eddy diffusion coefficient and defines K ≈ 2 × 10 8cm 2sec −1; and the low gradient gives an estimate of the efficiency of the atmosphere heating by the solar radiation as ϵ ≈ 0.1.