Tensor spherical harmonics on S^2 and S^3 as eigenvalue problems

Tensor spherical harmonics for the 2‐sphere and 3‐sphere are discussed as eigenfunction problems of the Laplace operators on these manifolds. The scalar, vector, and second‐rank tensor harmonics are given explicitly in terms of known functions and their properties summarized

Generalized cylindrical coordinates for characteristic boundary conditions and characteristic interface conditions

The aim of this report is to derive generalized coordinates for the specific case of mapping only the streamwise and radial coordinate of a cylindrical coordinate system, while leaving the azimuthal coordinate unchanged. The characteristic equations and the required matrices for the transformation from conservative to characteristic form are presented for this specific case. All equations and procedures are based on previous work on generalized characteristic boundary conditions (Kim &amp; Lee, 2000) and characteristic interface conditions (Kim &amp; Lee, 2003).<br/

On wavenumber spectra for sound within subsonic jets

This paper clarifies the nature of sound spectra within subsonic jets. Three problems, of increasing complexity, are presented. Firstly, a point source is placed in a two-dimensional plug flow and the sound field is obtained analytically. Secondly, a point source is embedded in a diverging axisymmetric jet and the sound field is obtained by solving the linearised Euler equations. Finally, an analysis of the acoustic waves propagating through a turbulent jet obtained by direct numerical simulation is presented. In each problem, the pressure or density field are analysed in the frequency-wavenumber domain. It is found that acoustic waves can be classified into three main frequency-dependent groups. A physical justification is provided for this classification. The main conclusion is that, at low Strouhal numbers, acoustic waves satisfy the d'Alembertian dispersion relation.Comment: 20 pages, 9 figure

A modification of Amiet's classical trailing edge noise theory for strictly two dimensional flows

The aim of this report is to derive theoretical expressions for the far-field pressure generated by disturbances convecting over a trailing edge. First, a general calculation of thefar-field pressure is discussed. Then the classical theory of Amiet (1976b) is reviewed,listing the most relevant assumptions. Amiet's theory is then revised for two-dimensional flows

RANS Turbulence Model Development using CFD-Driven Machine Learning

This paper presents a novel CFD-driven machine learning framework to develop Reynolds-averaged Navier-Stokes (RANS) models. The CFD-driven training is an extension of the gene expression programming method (Weatheritt and Sandberg, 2016), but crucially the fitness of candidate models is now evaluated by running RANS calculations in an integrated way, rather than using an algebraic function. Unlike other data-driven methods that fit the Reynolds stresses of trained models to high-fidelity data, the cost function for the CFD-driven training can be defined based on any flow feature from the CFD results. This extends the applicability of the method especially when the training data is limited. Furthermore, the resulting model, which is the one providing the most accurate CFD results at the end of the training, inherently shows good performance in RANS calculations. To demonstrate the potential of this new method, the CFD-driven machine learning approach is applied to model development for wake mixing in turbomachines. A new model is trained based on a high-pressure turbine case and then tested for three additional cases, all representative of modern turbine nozzles. Despite the geometric configurations and operating conditions being different among the cases, the predicted wake mixing profiles are significantly improved in all of these a posteriori tests. Moreover, the model equation is explicitly given and available for analysis, thus it could be deduced that the enhanced wake prediction is predominantly due to the extra diffusion introduced by the CFD-driven model.Comment: Accepted by Journal of Computational Physic

Should we campaign against sex robots?

In September 2015 a well-publicised Campaign Against Sex Robots (CASR) was launched. Modelled on the longer-standing Campaign to Stop Killer Robots, the CASR opposes the development of sex robots on the grounds that the technology is being developed with a particular model of female-male relations (the prostitute-john model) in mind, and that this will prove harmful in various ways. In this chapter, we consider carefully the merits of campaigning against such a technology. We make three main arguments. First, we argue that the particular claims advanced by the CASR are unpersuasive, partly due to a lack of clarity about the campaign’s aims and partly due to substantive defects in the main ethical objections put forward by campaign’s founder(s). Second, broadening our inquiry beyond the arguments proferred by the campaign itself, we argue that it would be very difficult to endorse a general campaign against sex robots unless one embraced a highly conservative attitude towards the ethics of sex, which is likely to be unpalatable to those who are active in the campaign. In making this argument we draw upon lessons from the campaign against killer robots. Finally, we conclude by suggesting that although a generalised campaign against sex robots is unwarranted, there are legitimate concerns that one can raise about the development of sex robots