Comparing time surfaces at different integration time points, or from different seeding areas, can provide valuable insight into transport phenomena of fluid flows. Such a comparative study is challenging due to the often convoluted shapes of these surfaces. We propose a new approach for comparative flow visualization based on time surfaces, which exploits the idea of embedding the surfaces in a carefully designed, reformed 2D visualization space. Such an embedding enables new opportunities for comparative flow visualization. We present three different strategies for comparative flow visualization that take advantage of the reformation. By reforming the time surfaces, we not only mitigate occlusion issues, but we can devote also the third dimension of the visualization space to the comparative aspects of the visualization. Our approach is effective in a variety of flow study cases. The direct comparison of individual time surfaces reveals small scale differences and fine details about the fluid's motion. The concurrent study of multiple surface families enables the identification and the comparison of the most prominent motion patterns. This work was developed in close collaboration with an expert in fluid dynamics, who assessed the potential usefulness of this approach in his field.

Abstract In the visualization of flow simulation data, feature detectors often tend to result in overly rich response, making some sort of filtering or simplification necessary to convey meaningful images. In this paper we present an approach that builds upon a decomposition of the flow field according to dynamical importance of different scales of motion energy. Focusing on the high‐energy scales leads to a reduction of the flow field while retaining the underlying physical process. The presented method acknowledges the intrinsic structures of the flow according to its energy and therefore allows to focus on the energetically most interesting aspects of the flow. Our analysis shows that this approach can be used for methods based on both local feature extraction and particle integration and we provide a discussion of the error caused by the approximation. Finally, we illustrate the use of the proposed approach for both a local and a global feature detector and in the context of numerical flow simulations.

This study was initiated by the scientifically interesting prospect of applying advanced visualization techniques to gain further insight into various spatio-temporal characteristics of turbulent flows. The ability to study complex kinematical and dynamical features of turbulence provides means of extracting the underlying physics of turbulent fluid motion. The objective is to analyze the use of a vorticity field line approach to study numerically generated incompressible turbulent flows. In order to study the vorticity field, we present a field line animation technique which uses a specialized particle advection and seeding strategy. Efficient analysis is achieved by decoupling the rendering stage from the preceding stages of the visualization method. This allows interactive exploration of multiple fields simultaneously, which sets the stage for a more complete analysis of the flow field. Multifield visualizations are obtained using a flexible volume rendering framework which is presented in this paper. Vorticity field lines have been employed as indicators to provide a means to identify "ejection" and "sweep" regions; two particularly important spatio-temporal events in wall-bounded turbulent flows. Their relation to the rate of turbulent kinetic energy production and viscous dissipation, respectively, have been identified.

Line Integral Convolution (LIC) is a powerful texture-based technique for visualizing vector fields. Due to the high computational expense of generating the 3D textures and the difficulties of effectively displaying the result, LIC has most commonly been used to depict vector fields in 2D or over a surface in 3D. Here, we propose new methods for more effective volume visualization of three-dimensional vector fields using LIC: 1) We present a fast method for computing volume LIC textures that exploits the sparsity of the input texture. 2) We propose the use of a shading technique, called limb darkening, to reveal the depth relations among the field lines. The shading effect is obtained simply by using appropriate transfer functions and, therefore, avoids using expensive shading techniques. 3) We demonstrate how two-field visualization techniques can be used to enhance the visual information describing a vector field. The volume LIC textures are rendered using texture-based rendering techniques, which allows interactive exploration of a vector field.