Wave-induced temporal fluctuations in the intensity of the OH nightglow are related to the temperature oscillations of the wave field by a model that incorporates a five-reaction photochemical scheme and the complete dynamics of linearized acoustic-gravity waves in an isothermal, motionless atmosphere. The intensity I and rotational temperature T oscillations, 61 and 6T, are conveniently related by the ratio •/= (6I/I-)/(6T/•, where the overbar refers to time-averaged quantities. The ratio •/ is a complex quantity that depends on the properties of the basic state atmosphere (temperature, thermodynamic parameters, major constituent 0 2, N 2 and minor constituent O, 0 3, OH, H, HO 2 concentrations, and scale heights), chemical reaction rate constants, wave period, horizontal wavelength, and direction of wave energy propagation (upward or downward). The intensity-temperature oscillation ratio r/is evaluated for a nominal case corresponding to an altitude of about 83 km in a nightside model atmosphere with an atomic oxygen scale height of -2.8 km; horizontal wavelength 2,, is 100 km, and wave energy propagation is upward. Over a broad range of acoustic periods [r/I varies between 7 and 8, and r/ is approximately in phase with the temperature fluctuations. At gravity wave periods, I•l decreases with increasing period from a maximum value of about 7.0; at a period of about 3 hours, I,/I is about 1.8. The phase of r/ and 6T are within 45 ø in the gravity wave regime. The main effect of order of magnitude changes in 2,, is the modification of the location and width (in period) of evanescent regions. At hour periods, I•l increases as the magnitude of atomic oxygen scale height decreases' at periods of several hours, I•/[ is about 1/3 greater for an atomic oxygen scale height of -2 km than for the nominal scale height. The amplitude Qf r/is essentially independent of the direction of wave energy propagation, but the phase of •1 relative to that of 6T depends on the upward or downward sense of energy propagation at periods in close proximity to the evanescent regime. The magnitude of r/ at gravity wave periods can depend sensitively on the altitude of the OH emission layer' higher OH emission heights give smaller values of I•l at 10-min periods, providing the 0 3 scale height is not too great. Neglect of minor constituent photochemistry in computing r/is a tolerable approximation at acoustic wave periods, but it is entirely inadequate at gravity wave periods. Inclusion of dynamical effects is absolutely essential for a valid assessment of r/at any period. Observations of the wave-induced oscillations in the intensity c5I and temperature cST of the OH nightglow can be combined with a theory relating c5I and cST to infer both the concentrations and scale heights of the major and minor species involved in OH mesopause photochemistry and the periods and horizontal wavelengths of the disturbing waves. o However, relatively little has been done along these lines despite the availability of relevant data, perhaps because of theore...

145that an increase in the medium permeability increases the mean velocity, the rate of increase being much faster in the case of larger values of K. ConclusionAn analytical study of thermal convection within a porous layer induced by a travelling thermal wave has been presented. Using the Brinkman model, expressions for the fluctuating flow and the mean flow were obtained with long wave approximation. The discussions were generally valid in respect of other values of P also. The magnitude of the mean flow velocity is comparitively smaller in the back-flow region than in the other region. The vertically averaged mean flow has been highlighted.References 1 LAPWOOD, E. R.: Convection ofa fluid in a porous medium. Proc. Camb. Phil. SOC. 44(1 948), 508 -521.2 PALM, E.; WEBER, J. E.; KVERNHOLD, 0.: On steady convection in a porous medium.

A pseudo-spectral numerical scheme is used to study two-dimensional, single-cell, time-dependent convection in a square cross-section of fluid saturated porous material heated from below. With increasing Rayleigh number R convection evolves from steady S to chaotic NP through the sequence of bifurcations S→P(1)→QP2→P(2)→NP, where P(1) and P(2) are simply periodic regimes and QP2 is a quasi-periodic state with two basic frequencies. The transitions (from onset of convection to chaos) occur at Rayleigh numbers of 4π2, 380–400, 500–520, 560–570, and 850–1000. In the first simply periodic regime the fundamental frequency f1 varies as $R^{\frac{7}{8}} $ and the average Nusselt number $\overline{Nu}$ is proportional to $R^{\frac{2}{3}}$; in P(2), f1 varies as $R^{\frac{3}{2}}$ and $\overline{Nu}\propto R^{\frac{11}{10}}$. Convection in QP2 exhibits hysteresis, i.e. if the QP2 state is reached from P(1) (P(2)) by increasing (decreasing) R then the frequency with the largest spectral power is the one consistent with the extrapolation of f1 according to $R^{\frac{7}{8}}(R^{\frac{3}{2}})$. The chaotic states are characterized by spectral peaks with at least 3 fundamental frequencies superimposed on a broadband background noise. The time dependence of these states arises from the random generation of tongue-like disturbances within the horizontal thermal boundary layers. Transition to the chaotic regime is accompanied by the growth of spectral components that destroy the centre-symmetry of convection in the other states. Over-truncation can lead to spurious transitions and bifurcation sequences; in general it produces overly complex flows.

The propagation characteristics of plane acoustic‐gravity waves in an atmosphere in diffusive equilibrium are studied by using a two‐fluid model which takes into account the collisional transfer of both momentum and energy between species. At wave periods of less than the shortest characteristic diffusion time for the minor gas, significant amplitude and phase differences between the wave‐induced density fluctuations of individual gases occur because of the different scale heights of the gases. At longer periods, diffusion induced by the wave acts to eliminate these amplitude and phase differences and restore the perturbed fluid to diffusive equilibrium. Vertical diffusion is most important at large scale sizes, but horizontal diffusion dominates for horizontal wavelengths of less than several hundred kilometers. As a result of wave‐induced diffusion, AE‐C satellite measurements of neutral density fluctuations of thermospheric constituents at 215‐km altitude are only compatible with internal gravity waves with periods of ∼15–30 min, horizontal wavelengths of ≃150–400 km, and downward phase propagation. Diffusion increases in importance with altitude, but is significant for periods of ≳30 min even at 150‐km altitude. Velocity and temperature differences for acoustic‐gravity waves are greatest at periods near the mean collision time and diffusion time. Vertical velocity differences between species can be as large as 40% in amplitude and 17° in phase at 215‐km altitude. Temperature perturbation differences are much smaller but can reach 17% in amplitude and 6.5° in phase at 300‐km altitude. Two other solutions to the governing equations, which may be called diffusion waves, have properties drastically different from the acoustic‐gravity wave solutions, including order‐of‐magnitude amplitude differences and close to 180° phase differences between the density, velocity, and temperature perturbations of the two species at most periods. Because of the velocity and temperature differences between species, dissipation of wave energy will occur. Damping of acoustic‐gravity waves is most significant at periods comparable to the mean collision and diffusion times and can be as large as 50–60% per wave cycle. This effectively filters out those waves with periods long enough to be affected by diffusion except when the observation is near the wave source. The predictions of the theory are consistent with a high‐latitude, lower‐altitude source like Joule heating or particle precipitation for the medium‐scale waves and a more localized random source for the smaller‐scale waves observed by AE‐C.

Natural convection of water in thick geothermal layers, across which there are temperature differences as large as 345 K and pressure differences as great as 1 kbar, is investigated. Complete account is taken of the variable thermodynamic and transport properties of water as well as of non‐Boussinesq effects. The increase of thermal expansivity with temperature by as much as a factor of 70 and the decrease of viscosity by more than 1 order of magnitude are primarily responsible for the enhanced instability to convection of a water‐saturated porous layer compared with a porous layer saturated with a Boussinesq fluid having the constant properties of surface water. The critical Rayleigh number, critical wave number, and streamline and isotherm patterns are determined at the onset of convection for temperature gradients of 25, 50, 75, 100, 150, and 200 K/km in layers as thick as 10 km. The critical surface Rayleigh number is reduced by as much as a factor of 31 below the value of 4π2 appropriate for a constant property Boussinesq fluid. Variable water properties thus allow convection to occur for smaller vertical temperature differences in rock of a given permeability or for smaller permeability at a given temperature difference. The horizontal scale of convection is somewhat reduced, and the flow is concentrated toward the bottom of the porous layer by effects of variable expansivity and viscosity.