The effect of wall cooling on a compressible turbulent boundary layer

Experimental results are presented for two turbulent boundary-layer experiments conducted at a free-stream Mach number of 4 with wall cooling. The first experiment examines a constant-temperature cold-wall boundary layer subjected to adverse and favourable pressure gradients. It is shown that the boundary-layer data display good agreement with Coles’ general composite boundary-layer profile using Van Driest's transformation. Further, the pressure-gradient parameter β_K found in previous studies to correlate adiabatic high-speed data with low-speed data also correlates the present cooled-wall high-speed data. The second experiment treats the response of a constant-pressure high-speed boundary layer to a near step change in wall temperature. It is found that the growth rate of the thermal boundary layer within the existing turbulent boundary layer varies considerably depending upon the direction of the wall temperature change. For the case of an initially cooled boundary layer flowing onto a wall near the recovery temperature, it is found that δ_T ~ x whereas the case of an adiabatic boundary layer flowing onto a cooled wall gives δ_T ~ x^½. The apparent origin of the thermal boundary layer also changes considerably, which is accounted for by the variation in sublayer thicknesses and growth rates within the sublayer

An experiment on the adiabatic compressible turbulent boundary layer in adverse and favourable pressure gradients

A wind-tunnel model was developed to study the two-dimensional turbulent boundary layer in adverse and favourable pressure gradients with out the effects of streamwise surface curvature. Experiments were performed at Mach 4 with an adiabatic wall, and mean flow measurements within the boundary layer were obtained. The data, when viewed in the velocity transformation suggested by Van Driest, show good general agreement with the composite boundary-layer profile developed for the low-speed turbulent boundary layer. Moreover, the pressure gradient parameter suggested by Alber & Coats was found to correlate the data with low-speed results

All null supersymmetric backgrounds of N=2, D=4 gauged supergravity coupled to abelian vector multiplets

The lightlike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to an arbitrary number of abelian vector multiplets are classified using spinorial geometry techniques. The solutions fall into two classes, depending on whether the Killing spinor is constant or not. In both cases, we give explicit examples of supersymmetric backgrounds. Among these BPS solutions, which preserve one quarter of the supersymmetry, there are gravitational waves propagating on domain walls or on bubbles of nothing that asymptote to AdS_4. Furthermore, we obtain the additional constraints obeyed by half-supersymmetric vacua. These are divided into four categories, that include bubbles of nothing which are asymptotically AdS_4, pp-waves on domain walls, AdS_3 x R, and spacetimes conformal to AdS_3 times an interval.Comment: 55 pages, uses JHEP3.cls. v2: Minor errors corrected, small changes in introductio

M-Horizons

We solve the Killing spinor equations and determine the near horizon geometries of M-theory that preserve at least one supersymmetry. The M-horizon spatial sections are 9-dimensional manifolds with a Spin(7) structure restricted by geometric constraints which we give explicitly. We also provide an alternative characterization of the solutions of the Killing spinor equation, utilizing the compactness of the horizon section and the field equations, by proving a Lichnerowicz type of theorem which implies that the zero modes of a Dirac operator coupled to 4-form fluxes are Killing spinors. We use this, and the maximum principle, to solve the field equations of the theory for some special cases and present some examples.Comment: 36 pages, latex. Reference added, minor typos correcte

Classification of IIB backgrounds with 28 supersymmetries

We show that all IIB backgrounds with strictly 28 supersymmetries are locally isometric to the plane wave solution of arXiv:hep-th/0206195. Moreover, we demonstrate that all solutions with more than 26 supersymmetries and only 5-form flux are maximally supersymmetric. The N=28 plane wave solution is a superposition of the maximally supersymmetric IIB plane wave with a heterotic string solution. We investigate the propagation of strings in this background, find the spectrum and give the string light-cone Hamiltonian.Comment: 30 pages, typos correcte

Supersymmetric solutions of gauged five-dimensional supergravity with general matter couplings

We perform the characterization program for the supersymmetric configurations and solutions of the $\mathcal{N}=1$, $d=5$ Supergravity Theory coupled to an arbitrary number of vectors, tensors and hypermultiplets and with general non-Abelian gaugins. By using the conditions yielded by the characterization program, new exact supersymmetric solutions are found in the $SO(4,1)/SO(4)$ model for the hyperscalars and with $SU(2)\times U(1)$ as the gauge group. The solutions also content non-trivial vector and massive tensor fields, the latter being charged under the U(1) sector of the gauge group and with selfdual spatial components. These solutions are black holes with $AdS_2 \times S^3$ near horizon geometry in the gauged version of the theory and for the ungauged case we found naked singularities. We also analyze supersymmetric solutions with only the scalars $\phi^x$ of the vector/tensor multiplets and the metric as the non-trivial fields. We find that only in the null class the scalars $\phi^x$ can be non-constant and for the case of constant $\phi^x$ we refine the classification in terms of the contributions to the scalar potential.Comment: Minor changes in wording and some typos corrected. Version to appear in Class. Quantum Grav. 38 page

All the timelike supersymmetric solutions of all ungauged d=4 supergravities

We determine the form of all timelike supersymmetric solutions of all N greater or equal than 2, d=4 ungauged supergravities, for N less or equal than 4 coupled to vector supermultiplets, using the $Usp(n+1,n+1)-symmetric formulation of Andrianopoli, D'Auria and Ferrara and the spinor-bilinears method, while preserving the global symmetries of the theories all the way. As previously conjectured in the literature, the supersymmetric solutions are always associated to a truncation to an N=2 theory that may include hypermultiplets, although fields which are eliminated in the truncations can have non-trivial values, as is required by the preservation of the global symmetry of the theories. The solutions are determined by a number of independent functions, harmonic in transverse space, which is twice the number of vector fields of the theory (n+1). The transverse space is flat if an only if the would-be hyperscalars of the associated N=2 truncation are trivial.Comment: v3: Some changes in the introduction. Version to be published in JHE

The Potential For UK Portfolio Investors To Finance Sustainable Tropical Forestry

Environmental Economics and Policy, Resource /Energy Economics and Policy,

The spinorial geometry of supersymmetric heterotic string backgrounds

We determine the geometry of supersymmetric heterotic string backgrounds for which all parallel spinors with respect to the connection $\hat\nabla$ with torsion $H$, the NS$\otimes$NS three-form field strength, are Killing. We find that there are two classes of such backgrounds, the null and the timelike. The Killing spinors of the null backgrounds have stability subgroups K\ltimes\bR^8 in $Spin(9,1)$, for $K=Spin(7)$, SU(4), $Sp(2)$, $SU(2)\times SU(2)$ and $\{1\}$, and the Killing spinors of the timelike backgrounds have stability subgroups $G_2$, SU(3), SU(2) and $\{1\}$. The former admit a single null $\hat\nabla$-parallel vector field while the latter admit a timelike and two, three, five and nine spacelike $\hat\nabla$-parallel vector fields, respectively. The spacetime of the null backgrounds is a Lorentzian two-parameter family of Riemannian manifolds $B$ with skew-symmetric torsion. If the rotation of the null vector field vanishes, the holonomy of the connection with torsion of $B$ is contained in $K$. The spacetime of time-like backgrounds is a principal bundle $P$ with fibre a Lorentzian Lie group and base space a suitable Riemannian manifold with skew-symmetric torsion. The principal bundle is equipped with a connection $\lambda$ which determines the non-horizontal part of the spacetime metric and of $H$. The curvature of $\lambda$ takes values in an appropriate Lie algebra constructed from that of $K$. In addition $dH$ has only horizontal components and contains the Pontrjagin class of $P$. We have computed in all cases the Killing spinor bilinears, expressed the fluxes in terms of the geometry and determine the field equations that are implied by the Killing spinor equations.Comment: 73pp. v2: minor change

Solutions of Minimal Four Dimensional de Sitter Supergravity

Pseudo-supersymmetric solutions of minimal $N=2$, $D=4$ de Sitter supergravity are classified using spinorial geometry techniques. We find three classes of solutions. The first class of solution consists of geometries which are fibrations over a 3-dimensional manifold equipped with a Gauduchon-Tod structure. The second class of solution is the cosmological Majumdar-Papapetrou solution of Kastor and Traschen, and the third corresponds to gravitational waves propagating in the Nariai cosmology.Comment: 17 Pages. Minor correction to section 4; equation (4.21) corrected and (old) equation (4.26) deleted; the final result is unchange