a) (b)(c) (d) Figure 1: (a) Conventional photograph of a scene, illuminated by a projector with all its pixels turned on. (b) After measuring the light transport between the projector and the camera using structured illumination, our technique is able to synthesize a photorealistic image from the point of view of the projector. This image has the resolution of the projector and is illuminated by a light source at the position of the camera. The technique can capture subtle illumination effects such as caustics and self-shadowing. Note, for example, how the glass bottle in the primal image (a) appears as the caustic in the dual image (b) and vice-versa. Because we have determined the complete light transport between the projector and camera, it is easy to relight the dual image using a synthetic light source (c) or a light modified by a matte captured later by the same camera (d). AbstractWe present a novel photographic technique called dual photography, which exploits Helmholtz reciprocity to interchange the lights and cameras in a scene. With a video projector providing structured illumination, reciprocity permits us to generate pictures from the viewpoint of the projector, even though no camera was present at that location. The technique is completely image-based, requiring no knowledge of scene geometry or surface properties, and by its nature automatically includes all transport paths, including shadows, inter-reflections and caustics. In its simplest form, the technique can be used to take photographs without a camera; we demonstrate this by capturing a photograph using a projector and a photo-resistor. If the photo-resistor is replaced by a camera, we can produce a 4D dataset that allows for relighting with 2D incident illumination. Using an array of cameras we can produce a 6D slice of the 8D reflectance field that allows for relighting with arbitrary light fields. Since an array of cameras can operate in parallel without interference, whereas an array of light sources cannot, dual photography is fundamentally a more efficient way to capture such a 6D dataset than a system based on multiple projectors and one camera. As an example, we show how dual photography can be used to capture and relight scenes.

In this work a study has been made of the Stuart (1960)–Watson (1960) formalism as applied to plane Poiseuille flow. In particular, the higher-order Landau coefficients have been calculated for the Reynolds & Potter (1967) method and for the Watson (1960) method. The results have been used to study the convergence of the Stuart–Landau series. A convergence curve in the (α, R)-plane has been obtained by using suitable Domb–Sykes plots. In the region of poor convergence of the series, and also in a part of the divergent region of the series, it has been found that the Shanks (1955) method, using the em1 transformation, serves as a very effective way of finding the proper sum of the series, or of finding the proper antilimit of the series. The results for the velocity calculations at R = 5000 are in very good agreement with Herbert's (1977) Fourier-truncation method using N = 4. The Watson method and the Reynolds & Potter method have also been compared inthe subcritical and supercritical regions. It is found in the supercritical region that there is not much difference in the results by the ‘true problem’ of Watson and the ‘false problem’ of Reynolds & Potter when the respective series in both methods are summed by the Shanks method. This fact could possibly be capitalized upon in the subcritical region, where the Watson method is difficult to apply.

In our earlier work we have shown the relevance of stability theory in understanding the sustenance of turbulence in turbulent boundary layers. Here we adopt the same model to study the evolution of organised disturbances in turbulent channel flow. Since the dominant modes are wall modes we find that the stability characteristics in the two flows are nearly identical although the boundary conditions (at the edge of the boundary layer and at the centre of the channel) are different. Comparisons with the experiments of Hussain and Reynolds are also presented.

The problem has been examined using a kinematic model for wall pliability, wherein a kinematic postulation of the wall boundary conditions is made. A form of the normalized wall-displacement and its phase are used as additional parameters in an extended eigenvalue problem. Using this technique the entire gamut of possibilities regarding stability of flow past (normally) pliable walls can be examined, yet without recourse to any specific material properties for the wall. Rather, the results based on the kinematic model can be used to back-calculate the material properties corresponding to any chosen model for the dynamics of the wall. A sample back calculation is discussed herein for the Benjamin–Landahl wall model, and based on this some predictions are made regarding both stabilization of the flow and physical realizability of modes. It is believed that the kinematic model will prove useful in further understanding of the problem, and in the design of stabilizing coatings.The results show that there are three important ‘mode classes’ (distinct from ‘modes’), namely the Tollmien–Schlichting (TS), resonant (R) and Kelvin–Helmholtz (KH). Whereas the TS and R mode classes broadly agree with modes bearing similar names as found by earlier workers, the present KH mode class is difficult to classify based on earlier work. Moreover, there are also important transitional mode classes in the regions of bifurcations of the regular mode classes.Two important concepts evolve in connection with the TS and R mode classes, namely the existence of ‘stable pockets’ for the former and ‘unstable pockets’ for the latter. It is also confirmed herein that there are conflicting requirements on the damping d to stabilize TS and R modes. Considering these points it has been suggested that TS and R modes be avoided by keeping soft surfaces as compliant coatings. However, this in turn leads to instabilities from one of the transitional mode classes. It is also seen that a soft surface that is also marginally active (i.e. having a small negative value of d) could render even better stabilization.

This paper is in continuation of our earlier work on the role of hydrodynamic stability theory in understanding wall-bounded turbulent flows. Work in this area was pioneered by Malkus, followed by Reynolds, Tiederman and Hussain. Numerical results showed that the linear instability modes are damped, a result also confirmed by our earlier work for the boundary layer flow case. This led to waning of interest in this approach. In the present work the problem is reformulated using an improved nonisotropic model for the stress tensor based on the model of Pope. This improved model does yield unstable wall modes. A wide range of unstable wavenumbers is observed and these unstable modes mimic some of the key features of wall-bounded turbulent flows. Comparisons with experimental data are also presented. The present work keeps alive the question of relevance of stability theory to wall-bounded turbulent flows.