Four different two‐dimensional (perpendicular to the ambient magnetic field) plasma fluid‐type numerical simulations following the nonlinear evolution of the collisional Rayleigh‐Taylor instability in the nighttime equatorial F region ionosphere have been performed. Realistic altitude dependent ion‐neutral collision frequencies, recombination rates, and ambient electron density profiles were used. In three cases (ESF 0, 1, 3) the electron density profile was kept constant, with a minimum bottomside background electron density gradient scale length L ∼ 10 km, but the altitude of the F peak was changed, with F peak altitudes at 340, 350, and 430 km. All cases resulted in bottomside growth of the instability (spread F) with dramatically different time scales for development. Plasma density depletions were produced on the bottomside with rise velocities, produced by nonlinear polarization E × B forces, of 2.5, 12, and 160 m/s and percentage depletions of 16, 40, and 85, respectively. In one case, ESF 0, the bubble did not rise to the topside, but in ESF 1 and 3, topside irregularities were produced by the bubbles (where linear theory predicts no irregularities). In these three cases, spread F could be described from weak to strong. In the fourth case (ESF 2) the altitude of the F peak was 350 km, but the minimum L on the bottomside was changed to 5 km. This resulted in a bubble rise velocity of ∼23 m/s and a 60% depletion with strong bottomside and moderate topside spread F and a time scale for development between ESF 1 and 3. Two other cases, ESF 0′ and 0″ with peaks at 330 and 300 km, respectively, and bottomside L ∼ 10 km, were investigated via linear theory. These cases resulted in extremely weak bottomside spread F and no spread F (entire bottomside linearly stable), respectively. These simulations show that under appropriate conditions, the collisional Rayleigh‐Taylor instability causes linear growth on the bottomside of the F region. This causes the formation of plasma density depletions (bubbles) which rise to the topside (under appropriate conditions) F region by polarization E × B motion. High altitude of the F peak, small bottomside electron density gradient scale lengths, and large percentage depletions yield large vertical bubble rise velocities, with the first two conditions favoring bottomside linear growth of the instability. The numerical simulation results are in good agreement with rocket and satellite in situ measurements and radar backscatter measurements, including some of the recent results from the August 1977 coordinated ground‐based measurement campaign conducted by Defense Nuclear Agency at Kwajalein.

This paper derives a simple three-dimensional time domain formulation for small angle propagation of finite amplitude acoustic pulses and weak shocks in a medium that can be range dependent. The formulation is closely related to a full wave model, and does not contain the artificial singularities of ray-based models at caustics. The simplicity of the formulation suggests that it may be of value for broadband linear as well as nonlinear propagation. Two derivations are given: one heuristic and the other a formal series expansion from the fluid equations. The result is a first-order nonlinear progressive wave equation (NPE) cast in a wave-following frame of reference.The NPE is shown to be the nonlinear time domain counterpart of the frequency domain parabolic wave equation (PE). The NPE gives a natural separation of terms governing refraction, spreading, and nonlinear steepening. Numerical calculations (not involving Fourier synthesis) are presented using the NPE to simulate the following cases: (a) broadband linear pulse propagation in a waveguide; (b) the development of an initially smooth nonlinear pulse into an N wave; and (c) the behavior of a weak shock at a caustic. Cases (a) and (b) are compared with analytic solutions.

Excitation of acoustic radiation into the air from a low-frequency point source under water is investigated using plane wave expansion of the source spectrum and Rayleigh reflection/transmission coefficients. Expressions are derived for the acoustic power radiated into air and water as a function of source depth and given to lowest order in the air/water density ratio. Near zero source depth, the radiation into the water is quenched by the source's acoustic image, while the power radiated into air reaches about 1% of the power that would be radiated into unbounded water.

A 1960 experiment is examined in which sound from three underwater explosions near Perth, Australia, was detected near Bermuda. A recent attempt [Munk et al., J. Phys. Ocean. 18, 1876 (1988) ] to calculate propagation paths for this event included rotational flattening of the Earth and horizontal refraction determined from the vertical sound speed minimum. That calculation left Bermuda in a shadow zone. The current work invokes adiabatic mode theory to include refraction due to horizontal variations in the vertical mode structure. These results include separate horizontal rays for each of the first few vertical modes, using an archival data set of 230 ocean sound profiles to generate the modes numerically. Where appropriate, interaction with bathymetry is included. This solution possesses two eigenray groups' Group A passes just south of the Cape of Good Hope, at which point group B is almost 1000 km to the south. Intermediate rays are blocked by islands. Group A proceeds unimpeded to Bermuda for a total time of flight of 13 354 q-5 s, while group B interacts slightly with bathymetry off Brazil, arriving at 13 403 q-9 s, and suffering roughly 7-12 dB more bottom attenuation. The spread in these arrivals overlaps satisfactorily with experimental data (main arrival at 13 364 q-5 s; pulse train half-width 15 s; second arrival 30 q-5 s later roughly 10 dB below the first arrival).

The two‐dimensional integrated Pedersen conductivity model for F region plasma cloud striation development may be cast in dimensionless form. The result implies that a structure's stability against bifurcation depends upon whether a diffusion parameter R exceeds a critical value. The critical R for striations is determined by high resolution computer simulation for conductivity ratios M from 2 to 30. Our results combined with electron diffusivity of order 1 m²/s agree with observed minimum scale sizes of 15 m. For turbulent diffusivity of order 100 m²/s, our results agree with frequent observations of kilometer scale structures which ‘freeze up’ and last for times of order 104 s. This lifetime is also predicted by our results.