PRISM (Polarized Radiation Imaging and Spectroscopy Mission): an extended white paper

PRISM (Polarized Radiation Imaging and Spectroscopy Mission) was proposed to ESA in May 2013 as a large-class mission for investigating within the framework of the ESA Cosmic Vision program a set of important scientific questions that require high res- olution, high sensitivity, full-sky observations of the sky emission at wavelengths ranging from millimeter-wave to the far-infrared. PRISM’s main objective is to explore the distant universe, probing cosmic history from very early times until now as well as the structures, distribution of matter, and velocity flows throughout our Hubble volume. PRISM will survey the full sky in a large number of frequency bands in both intensity and polarization and will measure the absolute spectrum of sky emission more than three orders of magnitude bet- ter than COBE FIRAS. The data obtained will allow us to precisely measure the absolute sky brightness and polarization of all the components of the sky emission in the observed frequency range, separating the primordial and extragalactic components cleanly from the galactic and zodiacal light emissions. The aim of this Extended White Paper is to provide a more detailed overview of the highlights of the new science that will be made possible by PRISM, which include: (1) the ultimate galaxy cluster survey using the Sunyaev-Zeldovich (SZ) e↵ect, detecting approximately 106 clusters extending to large redshift, including a char- acterization of the gas temperature of the brightest ones (through the relativistic corrections to the classic SZ template) as well as a peculiar velocity survey using the kinetic SZ e↵ect that comprises our entire Hubble volume; (2) a detailed characterization of the properties and evolution of dusty galaxies, where the most of the star formation in the universe took place, the faintest population of which constitute the di↵use CIB (Cosmic Infrared Background); (3) a characterization of the B modes from primordial gravity waves generated during inflation and from gravitational lensing, as well as the ultimate search for primordial non-Gaussianity using CMB polarization, which is less contaminated by foregrounds on small scales than thetemperature anisotropies; (4) a search for distortions from a perfect blackbody spectrum, which include some nearly certain signals and others that are more speculative but more informative; and (5) a study of the role of the magnetic field in star formation and its inter- action with other components of the interstellar medium of our Galaxy. These are but a few of the highlights presented here along with a description of the proposed instrument.

Accurate series solutions for gravity-driven Stokes waves

In the past, high order series expansion techniques have been used to study the nonlinear equations that govern the form of periodic Stokes waves moving steadily on the surface of an inviscid fluid. In the present study, two such series solutions are recomputed using exact arithmetic, eliminating any loss of accuracy due to accumulation of round-off error, allowing a much greater number of terms to be found with confidence. It is shown that higher order behaviour of series generated by the solution casts doubt over arguments that rely on estimating the series’ radius of convergence. Further, the exact nature of the series is used to shed light on the unusual nature of convergence of higher order Pade approximants near the highest wave. Finally, it is concluded that, provided exact values are used in the series, these Pade approximants prove very effective in successfully predicting three turning points in both the dispersion relation and the total energy.

Impact of mass lumping on gravity and Rossby waves in 2D finite-element shallow-water models

The goal of this study is to evaluate the effect of mass lumping on the dispersion properties of four finite-element velocity/surface-elevation pairs that are used to approximate the linear shallow-water equations. For each pair, the dispersion relation, obtained using the mass lumping technique, is computed and analysed for both gravity and Rossby waves. The dispersion relations are compared with those obtained for the consistent schemes (without lumping) and the continuous case. The P0-P1, RT0 and P-P1 pairs are shown to preserve good dispersive properties when the mass matrix is lumped. Test problems to simulate fast gravity and slow Rossby waves are in good agreement with the analytical results.

The effect of the surface tension on non-propagating solitary waves

In this paper, the effect of the surface tension is considered carefully in the study of non-propagating solitary waves. The parameter plane of the surface tension and the fluid depth is divided into three regions; in two of them a breather soliton can be produced. In literature the parameters of breather solitons are all in one of the parameter regions. The new region reported here has been confirmed by our experiments. In the third region, the theoretical solution is a kink soliton, but a kind of the non-propagating solitary wave similar to the breather soliton was found in our experiments besides the kink soliton.

Experimental, Numerical and Analytical Studies of the MHD-driven plasma jet, instabilities and waves

This thesis describes a series of experimental, numerical, and analytical studies involving the Caltech magnetohydrodynamically (MHD)-driven plasma jet experiment. The plasma jet is created via a capacitor discharge that powers a magnetized coaxial planar electrodes system. The jet is collimated and accelerated by the MHD forces.

We present three-dimensional ideal MHD finite-volume simulations of the plasma jet experiment using an astrophysical magnetic tower as the baseline model. A compact magnetic energy/helicity injection is exploited in the simulation analogous to both the experiment and to astrophysical situations. Detailed analysis provides a comprehensive description of the interplay of magnetic force, pressure, and flow effects. We delineate both the jet structure and the transition process that converts the injected magnetic energy to other forms.

When the experimental jet is sufficiently long, it undergoes a global kink instability and then a secondary local Rayleigh-Taylor instability caused by lateral acceleration of the kink instability. We present an MHD theory of the Rayleigh-Taylor instability on the cylindrical surface of a plasma flux rope in the presence of a lateral external gravity. The Rayleigh-Taylor instability is found to couple to the classic current-driven instability, resulting in a new type of hybrid instability. The coupled instability, produced by combination of helical magnetic field, curvature of the cylindrical geometry, and lateral gravity, is fundamentally different from the classic magnetic Rayleigh-Taylor instability occurring at a two-dimensional planar interface.

In the experiment, this instability cascade from macro-scale to micro-scale eventually leads to the failure of MHD. When the Rayleigh-Taylor instability becomes nonlinear, it compresses and pinches the plasma jet to a scale smaller than the ion skin depth and triggers a fast magnetic reconnection. We built a specially designed high-speed 3D magnetic probe and successfully detected the high frequency magnetic fluctuations of broadband whistler waves associated with the fast reconnection. The magnetic fluctuations exhibit power-law spectra. The magnetic components of single-frequency whistler waves are found to be circularly polarized regardless of the angle between the wave propagation direction and the background magnetic field.

Development of roll waves in open channels

This study is concerned with some of the properties of roll waves that develop naturally from a turbulent uniform flow in a wide rectangular channel on a constant steep slope . The wave properties considered were depth at the wave crest, depth at the wave trough, wave period, and wave velocity . The primary focus was on the mean values and standard deviations of the crest depths and wave periods at a given station and how these quantities varied with distance along the channel.

The wave properties were measured in a laboratory channel in which roll waves developed naturally from a uniform flow . The Froude number F (F = u_n/√gh_n, u_n = normal velocity , h_n = normal depth, g =acceleration of gravity) ranged from 3. 4 to 6. 0 for channel slopes S_o of . 05 and . 12 respectively . In the initial phase of their development the roll waves appeared as small amplitude waves with a continuous water surface profile . These small amplitude waves subsequently developed into large amplitude shock waves. Shock waves were found to overtake and combine with other shock waves with the result that the crest depth of the combined wave was larger than the crest depths before the overtake. Once roll waves began to develop, the mean value of the crest depths h_nmax increased with distance . Once the shock waves began to overtake, the mean wave period T_av increased approximately linearly with distance.

For a given Froude number and channel slope the observed quantities h^-_max/h_n , T' (T' = S_o T_av √g/h_n), and the standard deviations of h^-_max/h_n and T', could be expressed as unique functions of l/h_n (l = distance from beginning of channel) for the two-fold change in h_n occurring in the observed flows . A given value of h^-_max/h_n occurred at smaller values of l/h_n as the Froude number was increased. For a given value of h /hh^-_max/h_n the growth rate of δh^-_max/h^-_maxδl of the shock waves increased as the Froude number was increased.

A laboratory channel was also used to measure the wave properties of periodic permanent roll waves. For a given Froude number and channel slope the h^-_max/h_n vs. T' relation did not agree with a theory in which the weight of the shock front was neglected. After the theory was modified to include this weight, the observed values of h^-_max/h_n were within an average of 6.5 percent of the predicted values, and the maximum discrepancy was 13.5 percent.

For h^-_max/h_n sufficiently large (h^-_max/h_n > approximately 1.5) it was found that the h^-_max/h_n vs. T' relation for natural roll waves was practically identical to the h^-_max/h_n vs. T' relation for periodic permanent roll waves at the same Froude number and slope. As a result of this correspondence between periodic and natural roll waves, the growth rate δh^-_max/h^-_maxδl of shock waves was predicted to depend on the channel slope, and this slope dependence was observed in the experiments.

On some properties of traveling water waves with vorticity

We prove that for a large class of vorticity functions the crests of any corresponding traveling gravity water wave of finite depth are necessarily points of maximal horizontal velocity. We also show that for waves with nonpositive vorticity the pressure everywhere in the fluid is larger than the atmospheric pressure. A related a priori estimate for waves with nonnegative vorticity is also given.

On the existence of extreme waves and the Stokes conjecture with vorticity

This is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with stagnation points at its crests. We also show that, for any vorticity function, the profile of an extreme wave must have either a corner of 120° or a horizontal tangent at any stagnation point about which it is supposed symmetric. Moreover, the profile necessarily has a corner of 120° if the vorticity is nonnegative near the free surface.

The Stokes conjecture for waves with vorticity

We study stagnation points of two-dimensional steady gravity free-surface water waves with vorticity. We obtain for example that, in the case where the free surface is an injective curve, the asymptotics at any stagnation point is given either by the “Stokes corner flow” where the free surface has a corner of 120°, or the free surface ends in a horizontal cusp, or the free surface is horizontally flat at the stagnation point. The cusp case is a new feature in the case with vorticity, and it is not possible in the absence of vorticity. In a second main result we exclude horizontally flat singularities in the case that the vorticity is 0 on the free surface. Here the vorticity may have infinitely many sign changes accumulating at the free surface, which makes this case particularly difficult and explains why it has been almost untouched by research so far. Our results are based on calculations in the original variables and do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity.

On the momentum fluxes associated with mountain waves in directionally sheared flows

The direct impact of mountain waves on the atmospheric circulation is due to the deposition of wave momentum at critical levels, or levels where the waves break. The first process is treated analytically in this study within the framework of linear theory. The variation of the momentum flux with height is investigated for relatively large shears, extending the authors’ previous calculations of the surface gravity wave drag to the whole atmosphere. A Wentzel–Kramers–Brillouin (WKB) approximation is used to treat inviscid, steady, nonrotating, hydrostatic flow with directional shear over a circular mesoscale mountain, for generic wind profiles. This approximation must be extended to third order to obtain momentum flux expressions that are accurate to second order. Since the momentum flux only varies because of wave filtering by critical levels, the application of contour integration techniques enables it to be expressed in terms of simple 1D integrals. On the other hand, the momentum flux divergence (which corresponds to the force on the atmosphere that must be represented in gravity wave drag parameterizations) is given in closed analytical form. The momentum flux expressions are tested for idealized wind profiles, where they become a function of the Richardson number (Ri). These expressions tend, for high Ri, to results by previous authors, where wind profile effects on the surface drag were neglected and critical levels acted as perfect absorbers. The linear results are compared with linear and nonlinear numerical simulations, showing a considerable improvement upon corresponding results derived for higher Ri.

Sensitivity of simulated climate to conservation of momentum in gravity wave drag parameterization

The Canadian Middle Atmosphere Model is used to examine the sensitivity of simulated climate to conservation of momentum in gravity wave drag parameterization. Momentum conservation requires that the parameterized gravity wave momentum flux at the top of the model be zero and corresponds to the physical boundary condition of no momentum flux at the top of the atmosphere. Allowing momentum flux to escape the model domain violates momentum conservation. Here the impact of momentum conservation in two sets of model simulations is investigated. In the first set, the simulation of present-day climate for two model-lid height configurations, 0.001 and 10 hPa, which are identical below 10 hPa, is considered. The impact of momentum conservation on the climate with the model lid at 0.001 hPa is minimal, which is expected because of the small amount of gravity wave momentum flux reaching 0.001 hPa. When the lid is lowered to 10 hPa and momentum is conserved, there is only a modest impact on the climate in the Northern Hemisphere; however, the Southern Hemisphere climate is more adversely affected by the deflection of resolved waves near the model lid. When momentum is not conserved in the 10-hPa model the climate is further degraded in both hemispheres, particularly in winter at high latitudes, and the impact of momentum conservation extends all the way to the surface. In the second set of simulations, the impact of momentum conservation and model-lid height on the modeled response to ozone depletion in the Southern Hemisphere is considered, and it is found that the response can display significant sensitivity to both factors. In particular, both the lower-stratospheric polar temperature and surface responses are significantly altered when the lid is lowered, with the effect being most severe when momentum is not conserved. The implications with regard to the current round of Intergovernmental Panel on Climate Change model projections are discussed.

Impact of non-hydrostatic effects and trapped lee waves on mountain wave drag in directionally sheared flow

The orographic gravity wave drag produced in flow over an axisymmetric mountain when both vertical wind shear and non-hydrostatic effects are important was calculated using a semi-analytical two-layer linear model, including unidirectional or directional constant wind shear in a layer near the surface, above which the wind is constant. The drag behaviour is determined by partial wave reflection at the shear discontinuity, wave absorption at critical levels (both of which exist in hydrostatic flow), and total wave reflection at levels where the waves become evanescent (an intrinsically non-hydrostatic effect), which produces resonant trapped lee wave modes. As a result of constructive or destructive wave interference, the drag oscillates with the thickness of the constant-shear layer and the Richardson number within it (Ri), generally decreasing at low Ri and when the flow is strongly non-hydrostatic. Critical level absorption, which increases with the angle spanned by the wind velocity in the constant-shear layer, shields the surface from reflected waves, keeping the drag closer to its hydrostatic limit. While, for the parameter range considered here, the drag seldom exceeds this limit, a substantial drag fraction may be produced by trapped lee waves, particularly when the flow is strongly non-hydrostatic, the lower layer is thick and Ri is relatively high. In directionally sheared flows with Ri = O(1), the drag may be misaligned with the surface wind in a direction opposite to the shear, a behaviour which is totally due to non-trapped waves. The trapped lee wave drag, whose reaction force on the atmosphere is felt at low levels, may therefore have a distinctly different direction from the drag associated with vertically propagating waves, which acts on the atmosphere at higher levels.

The longitudinal variation of equatorial waves due to propagation on a varying zonal flow

The general 1-D theory of waves propagating on a zonally varying flow is developed from basic wave theory, and equations are derived for the variation of wavenumber and energy along ray paths. Different categories of behaviour are found, depending on the sign of the group velocity (cg) and a wave property, B. For B positive the wave energy and the wave number vary in the same sense, with maxima in relative easterlies or westerlies, depending on the sign of cg. Also the wave accumulation of Webster and Chang (1988) occurs where cg goes to zero. However for B negative they behave in opposite senses and wave accumulation does not occur. The zonal propagation of the gravest equatorial waves is analysed in detail using the theory. For non-dispersive Kelvin waves, B reduces to 2, and analytic solution is possible. B is positive for all the waves considered, except for the westward moving mixed Rossby-gravity (WMRG) wave which can have negative as well as positive B. Comparison is made between the observed climatologies of the individual equatorial waves and the result of pure propagation on the climatological upper tropospheric flow. The Kelvin wave distribution is in remarkable agreement, considering the approximations made. Some aspects of the WMRG and Rossby wave distributions are also in qualitative agreement. However the observed maxima in these waves in the winter westerlies in the eastern Pacific and Atlantic are not consistent with the theory. This is consistent with the importance of the sources of equatorial waves in these westerly duct regions due to higher latitude wave activity.

ENSO related variation of equatorial MRG and Rossby waves and forcing from higher latitudes

The contrasting behaviour of westward-moving mixed Rossby-gravity (WMRG) and the first Rossby (R1) waves in El Niño (EN) and La Niña (LN) seasons is documented with a focus on the Northern Hemisphere winter. The eastward-moving variance in the upper troposphere is dominated by WMRG and R1 structures that appear to be Doppler-shifted by the flow and are referred to as WMRG-E and R1-E. In the East Pacific and Atlantic the years with stronger equatorial westerly winds have the stronger WMRG and WMRG- E. In the East Pacific, R1 is also a maximum in LN. However, R1-E exhibits an eastward-shift between LN and EN. The changes with ENSO phase provide a test-bed for the understanding of these waves. In the East Pacific and Atlantic, the stronger WMRG-E and WMRG with stronger westerlies are in accord with the dispersion relation with simple Doppler-shifting by the zonal flow. The possible existence of free waves can also explain stronger R1 in EN in the Eastern Hemisphere. 1-D free wave propagation theory based on wave activity conservation is also important for R1. However, this theory is unable to explain the amplitude maxima for other waves observed in the strong equatorial westerly regions in the Western Hemisphere, and certainly not their ENSO-related variation. The forcing of equatorial waves by higher latitude wave activity and its variation with ENSO phase is therefore examined. Propagation of extratropical eastward-moving Rossby wave activity through the westerly ducts into the equatorial region where it triggers WMRG-E is favoured in the stronger westerlies, in LN in the East Pacific and EN in the Atlantic. It is also found that WMRG is forced by Southern Hemisphere westward-moving wavetrains arching into the equatorial region where they are reflected. The most significant mechanism for both R1 and R1-E appear to be lateral forcing by subtropical wavetrains.