Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part II: combined effects of gravity waves and equatorial planetary waves

This study examines the effect of combining equatorial planetary wave drag and gravity wave drag in a one-dimensional zonal mean model of the quasi-biennial oscillation (QBO). Several different combinations of planetary wave and gravity wave drag schemes are considered in the investigations, with the aim being to assess which aspects of the different schemes affect the nature of the modeled QBO. Results show that it is possible to generate a realistic-looking QBO with various combinations of drag from the two types of waves, but there are some constraints on the wave input spectra and amplitudes. For example, if the phase speeds of the gravity waves in the input spectrum are large relative to those of the equatorial planetary waves, critical level absorption of the equatorial planetary waves may occur. The resulting mean-wind oscillation, in that case, is driven almost exclusively by the gravity wave drag, with only a small contribution from the planetary waves at low levels. With an appropriate choice of wave input parameters, it is possible to obtain a QBO with a realistic period and to which both types of waves contribute. This is the regime in which the terrestrial QBO appears to reside. There may also be constraints on the initial strength of the wind shear, and these are similar to the constraints that apply when gravity wave drag is used without any planetary wave drag. In recent years, it has been observed that, in order to simulate the QBO accurately, general circulation models require parameterized gravity wave drag, in addition to the drag from resolved planetary-scale waves, and that even if the planetary wave amplitudes are incorrect, the gravity wave drag can be adjusted to compensate. This study provides a basis for knowing that such a compensation is possible.

Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.

Nonlinear stability of Euler flows in two-dimensional periodic domains

The non-quadratic conservation laws of the two-dimensional Euler equations are used to show that the gravest modes in a doubly-periodic domain with aspect ratio L = 1 are stable up to translations (or structurally stable) for finite-amplitude disturbances. This extends a previous result based on conservation of energy and enstrophy alone. When L 1, a saturation bound is established for the mode with wavenumber |k| = L −1 (the next-gravest mode), which is linearly unstable. The method is applied to prove nonlinear structural stability of planetary wave two on a rotating sphere.

Nonlinear stability of continuously stratified quasi-geostrophic flow

Nonlinear stability theorems analogous to Arnol'd's second stability theorem are established for continuously stratified quasi-geostrophic flow with general nonlinear boundary conditions in a vertically and horizontally confined domain. Both the standard quasi-geostrophic model and the modified quasi-geostrophic model (incorporating effects of hydrostatic compressibility) are treated. The results establish explicit upper bounds on the disturbance energy, the disturbance potential enstrophy, and the disturbance available potential energy on the horizontal boundaries, in terms of the initial disturbance fields. Nonlinear stability in the sense of Liapunov is also established.

Nonlinear stability of multilayer quasi-geostrophic flow

New nonlinear stability theorems are derived for disturbances to steady basic flows in the context of the multilayer quasi-geostrophic equations. These theorems are analogues of Arnol’d's second stability theorem, the latter applying to the two-dimensional Euler equations. Explicit upper bounds are obtained on both the disturbance energy and disturbance potential enstrophy in terms of the initial disturbance fields. An important feature of the present analysis is that the disturbances are allowed to have non-zero circulation. While Arnol’d's stability method relies on the energy–Casimir invariant being sign-definite, the new criteria can be applied to cases where it is sign-indefinite because of the disturbance circulations. A version of Andrews’ theorem is established for this problem, and uniform potential vorticity flow is shown to be nonlinearly stable. The special case of two-layer flow is treated in detail, with particular attention paid to the Phillips model of baroclinic instability. It is found that the short-wave portion of the marginal stability curve found in linear theory is precisely captured by the new nonlinear stability criteria.

On Arnol'd's second nonlinear stability theorem for two-dimensional quasi-geostrophic flow

Arnol'd's second hydrodynamical stability theorem, proven originally for the two-dimensional Euler equations, can establish nonlinear stability of steady flows that are maxima of a suitably chosen energy-Casimir invariant. The usual derivations of this theorem require an assumption of zero disturbance circulation. In the present work an analogue of Arnol'd's second theorem is developed in the more general case of two-dimensional quasi-geostrophic flow, with the important feature that the disturbances are allowed to have non-zero circulation. New nonlinear stability criteria are derived, and explicit bounds are obtained on both the disturbance energy and potential enstrophy which are expressed in terms of the initial disturbance fields. While Arnol'd's stability method relies on the second variation of the energy-Casimir invariant being sign-definite, the new criteria can be applied to cases where the second variation is sign-indefinite because of the disturbance circulations. A version of Andrews' theorem is also established for this problem.

Complex dynamics in simple systems with periodic parameter oscillations

We study systems with periodically oscillating parameters that can give way to complex periodic or nonperiodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal Lyapunov exponent corresponds to a stable periodic orbit. By this, extremely complicated periodic orbits composed of contracting and expanding phases appear in a natural way. Employing the technique of ϵ-uncertain points, we find that values of the control parameters supporting such periodic motion are densely embedded in a set of values for which the motion is chaotic. When a tiny amount of noise is coupled to the system, dynamics with positive and with negative nontrivial Lyapunov exponents are indistinguishable. We discuss two physical systems, an oscillatory flow inside a duct and a dripping faucet with variable water supply, where such a mechanism seems to be responsible for a complicated alternation of laminar and turbulent phases.

High-latitude influence of the quasi-biennial oscillation

The interannual variability of the stratospheric winter polar vortex is correlated with the phase of the quasi-biennial oscillation (QBO) of tropical stratospheric winds. This dynamical coupling between high and low latitudes, often referred to as the Holton–Tan effect, has been the subject of numerous observational and modelling studies, yet important questions regarding its mechanism remain unanswered. In particular it remains unclear which vertical levels of the QBO exert the strongest influence on the winter polar vortex, and how QBO–vortex coupling interacts with the effects of other sources of atmospheric interannual variability such as the 11-year solar cycle or the El Nino Southern Oscillation. As stratosphere-resolving general circulation models begin to resolve the QBO and represent its teleconnections with other parts of the climate system, it seems timely to summarize what is currently known about the QBO’s high-latitude influence. In this review article, we offer a synthesis of the modelling and observational analyses of QBO–vortex coupling that have appeared in the literature, and update the observational record.

A numerical model of the ionospheric signatures of time-varying magnetic reconnection: III. Quasi-instantaneous convection responses in the Cowley-Lockwood paradigm

Using a numerical implementation of the Cowley and Lockwood (1992) model of flow excitation in the magnetosphere–ionosphere (MI) system, we show that both an expanding (on a _12-min timescale) and a quasiinstantaneous response in ionospheric convection to the onset of magnetopause reconnection can be accommodated by the Cowley–Lockwood conceptual framework. This model has a key feature of time dependence, necessarily considering the history of the coupled MI system. We show that a residual flow, driven by prior magnetopause reconnection, can produce a quasi-instantaneous global ionospheric convection response; perturbations from an equilibrium state may also be present from tail reconnection, which will superpose constructively to give a similar effect. On the other hand, when the MI system is relatively free of pre-existing flow, we can most clearly see the expanding nature of the response. As the open-closed field line boundary will frequently be in motion from such prior reconnection (both at the dayside magnetopause and in the cross-tail current sheet), it is expected that there will usually be some level of combined response to dayside reconnection.

Periodic auroral events at the high-latitude convection reversal in the 16 MLT region

Combined optical and radar observations of two breakup-like auroral events near the polar cap boundary, within 74–76° MLAT and 1210 – 1240 UT (roughly 1540 – 1610 MLT) on 9 Jan. 1989 are reported. A two-component structure of the auroral phenomenon is indicated, with a local intensification of the pre-existing arc as well as a separate, tailward moving discrete auroral event on the poleward side of the background aurora, close to the reversal between well-defined zones of sunward and tailward ion flows. The all-sky TV observations do not indicate a connection between the two components, which also show different optical spectral composition. The 16 MLT background arc is located on sunward convecting field lines, as opposed to the 12–14 MLT auroral emission observed on this day. Although the magnetospheric plasma source (s) of the 16 MLT events are not easily identified from these ground-based data alone, it is suggested that the lower and higher latitude components, may map to the plasma sheet boundary layer and along open field lines to the magnetopause boundary, respectively. The events occur at the time of enhancements of westward ionospheric ion flow and corresponding eastward electrojet current south of 74° MLAT. Thus, they seem to be very significant events, involving periodic (10 min period), tailward moving filaments of field-aligned current/discrete auroral emission at the 16 MLT polar cap boundary.

Determination of the embedded thermo-optical expansion coefficients of PbTe and ZnSe thin film infrared multilayers

This paper reports the first derived thermo-optical properties for vacuum deposited infrared thin films embedded in multilayers. These properties were extracted from the temperature-dependence of manufactured narrow bandpass filters across the 4-17 µm mid-infrared wavelength region. Using a repository of spaceflight multi-cavity bandpass filters, the thermo-optical expansion coefficients of PbTe and ZnSe were determined across an elevated temperature range 20-160 ºC. Embedded ZnSe films showed thermo-optical properties similar to reported bulk values, whilst the embedded PbTe films of lower optical density, deviate from reference literature sources. Detailed knowledge of derived coefficients is essential to the multilayer design of temperature-invariant narrow bandpass filters for use in non-cooled infrared detection systems. We further present manufacture of the first reported temperature-invariant multi-cavity narrow bandpass filter utilizing PbS chalcogenide layer material.

Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model

We design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of Allen–Cahn/Cahn–Hilliard/Navier–Stokes–Korteweg type which allows for phase transitions. We show that the scheme is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to discrete equivalents of those effects already causing dissipation on the continuous level, that is, there is no artificial numerical dissipation added into the scheme. In this sense the methods are consistent with the energy dissipation of the continuous PDE system.

Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities

We construct a quasi-sure version (in the sense of Malliavin) of geometric rough paths associated with a Gaussian process with long-time memory. As an application we establish a large deviation principle (LDP) for capacities for such Gaussian rough paths. Together with Lyons' universal limit theorem, our results yield immediately the corresponding results for pathwise solutions to stochastic differential equations driven by such Gaussian process in the sense of rough paths. Moreover, our LDP result implies the result of Yoshida on the LDP for capacities over the abstract Wiener space associated with such Gaussian process.