Objective Observer-Relative Flow Visualization in Curved Spaces for Unsteady 2D Geophysical Flows

Abstract

Fig. 1. Observer motion relative to the time evolution of features: Hurricane Isabel in a time-dependent global wind data set. (Bottom left) The actual path of Isabel (from NHC/Wikipedia). (Top left) Our observer field u automatically follows the motion of Isabel without explicit tracking of its path. The shown path is simply a path line of u. (Right) Feature-relative visualization, focused on Isabel in the center, enabling analysis of its time evolution "in place." The hurricane appears steady, with the Earth moving inversely underneath.

Interactive Exploration of Physically-Observable Objective Vortices in Unsteady 2D Flow

“…To facilitate this, the second input to our system is another unsteady flow field u, which is used with the semantics of an observer field [18]. We can initialize the field u by computing (or loading) the solution of an objective optimization [14,18,39], but we can also simply use the field u := v. The latter can be used to "extract" observers from the input field v itself. Independent of how the observer field u is initialized, our framework represents all observers w by functions t → (a(t), b(t), c(t)) (Eq.…”

“…However, this only holds when all possible observers do, in fact, agree on the motion described by the field u. This is trivially the case when we choose u := v. Crucially, however, the same is true when u is computed via objective optimization, as those of Günther et al [14], Hadwiger et al [18], or Rautek et al [39]. Furthermore, we allow determining new observers by averaging or interpolation of a set of observers.…”

“…We propose the first framework for the interactive, objective exploration of unsteady 2D flow from the perspective of a set of physicallyrealizable observers. In contrast to prior work that uses a large number of observers jointly, such as one observer per space-time grid point [14], or a continuous field of observers [18,39], we focus on facilitating visualization and feature detection with respect to individual observers.…”

“…A significant amount of recent research in flow visualization and continuum mechanics has built on the concept of objectivity [14,17,19,39]. For vortex detection, for instance, it is crucial that the employed criteria are objective, because otherwise different observers can come to different conclusions on where vortices are located.…”

“…In particular, it is known that for many real-world flow phenomena a single reference frame is not sufficient in order to detect or depict all features of interest [14,29]. For this reason, generic objective approaches have been proposed that use a large number of observers and detect features jointly [4,14,18,39]. These approaches, however, focus on overall objectivity, and not on confirming that each detected feature would in fact be able to be perceived by a physically-realizable observer.…”