Remote sensing of mesospheric dust layers using active modulation of PMWE by high-power radio waves

This paper presents the first study of the modulation of polar mesospheric winter echoes (PMWE) by artificial radio wave heating using computational modeling and experimental observation in different radar frequency bands. The temporal behavior of PMWE response to HF pump heating can be employed to diagnose the charged dust layer associated with mesospheric smoke particles. Specifically, the rise and fall time of radar echo strength as well as relaxation and recovery time after heater turn-on and turnoff are distinct parameters that are a function of radar frequency. The variation of PMWE strength with PMWE source region parameters such as electron-neutral collision frequency, photodetachment current, electron temperature enhancement ratio, dust density, and radius is considered. The comparison of recent PMWE measurements at 56 MHz and 224 MHz with computational results is discussed, and dust parameters in the PMWE generation regime are estimated. Predictions for HF PMWE modification and its connection to the dust charging process by free electrons is investigated. The possibility for remote sensing of dust and plasma parameters in artificially modified PMWE regions using simultaneous measurements in multiple frequency bands are discussed. © 2016. American Geophysical Union. All Rights Reserved

On the Spectral Convergence of the Supercompact Finite-Difference Schemes for the f-Plane Shallow-Water Equations

For the f-plane shallow-water equations, the convergence properties of the supercompact finite-difference method (SCFDM) are examined during the evolution of complex, nonlinear flows spawned by an unstable jet. The second-, fourth-, sixth-, and eighth-order SCFDMs are compared with a standard pseudospectral (PS) method. To control the buildup of small-scale activity and thus the potential for numerical instability, the vorticity field is damped explicitly by the application of a triharmonic hyperdiffusion operator acting on the vorticity field. The global distribution of mass between isolevels of potential vorticity, called mass error, and the representation of the balance and imbalance are used to assess numerical accuracy. In each of the quantitative measures, a clear convergence of the SCFDM to the PS method is observed. There is no saturation in accuracy up to the eighth order examined. Taking the PS solution as the reference, for the fundamental quantity of potential vorticity the rate of convergence to PS turns out to be algebraic and near-quadratic.</p

Difference forms

Currently, there is much interest in the development of geometric integrators, which retain analogues of geometric properties of an approximated system. This paper provides a means of ensuring that finite difference schemes accurately mirror global properties of approximated systems. To this end, we introduce a cohomology theory for lattice varieties, on which finite difference schemes and other difference equations are defined. We do not assume that there is any continuous space, or that a scheme or difference equation has a continuum limit. This distinguishes our approach from theories of "discrete differential forms" built on simplicial approximations and Whitney forms, and from cohomology theories built on cubical complexes. Indeed, whereas cochains on cubical complexes can be mapped injectively to our difference forms, a bijection may not exist. Thus our approach generalizes what can be achieved with cubical cohomology. The fundamental property that we use to prove our results is the natural ordering on the integers. We show that our cohomology can be calculated from a good cover, just as de Rham cohomology can. We postulate that the dimension of solution space of a globally defined linear recurrence relation equals the analogue of the Euler characteristic for the lattice variety. Most of our exposition deals with forward differences, but little modification is needed to treat other finite difference schemes, including Gauss-Legendre and Preissmann schemes

The interior energy pathway: Inertia-gravity wave emission by oceanic flows

We review the possible role of spontaneous emission and subsequent capture of internal gravity waves (IGWs) for dissipation in oceanic flows under conditions characteristic for the ocean circulation. Dissipation is necessary for the transfer of energy from the essentially balanced large-scale ocean circulation and mesoscale eddy fields down to smaller scales where instabilities and subsequent small-scale turbulence complete the route to dissipation. Spontaneous wave emission by flows is a viable route to dissipation. For quasi-balanced flows, characterized by a small Rossby number, the amplitudes of emitted waves are expected to be small. However, once being emitted into a three-dimensional eddying flow field, waves can undergo refraction and may be ``captured.'' During wave capture, the wavenumber grows exponentially, ultimately leading to breakup and dissipation. For flows with not too small Rossby number, e.g., for flows in the vicinity of strong fronts, dissipation occurs in a more complex manner. It can occur via spontaneous wave emission and subsequent wave capture, with the amplitudes of waves emitted in frontal systems being expected to be larger than amplitudes of waves emitted by quasi-balanced flows. It can also occur through turbulence and filamentation emerging from frontogenesis. So far, quantitative importance of this energy pathway---crucial for determining correct eddy viscosities in general circulation models---is not known. Toward an answer to this question, we discuss IGWs diagnostics, review spontaneous emission of both quasi-balanced and less-balanced frontal flows, and discuss recent numerical results based on a high-resolution ocean general circulation model

Multi-scale Methods for Geophysical Flows

Geophysical flows comprise a broad range of spatial and temporal scales, from planetary- to meso-scale and microscopic turbulence regimes. The relation of scales and flow phenomena is essential in order to validate and improve current numerical weather and climate prediction models. While regime separation is often possible on a formal level via multi-scale analysis, the systematic exploration, structure preservation, and mathematical details remain challenging. This chapter provides an entry to the literature and reviews fundamental notions as background for the later chapters in this collection and as a departure point for original research in the field