Cinematographic stereoscopic PIV, combined with Taylor's frozen flow hypothesis, is used to generate three-dimensional (3D) quasi-instantaneous pseudo volumes of the three-component (3C) velocity field in the far field of turbulent nonpremixed jet flames at jet exit Reynolds number Reδ in the range 8,000-15,300. The effect of heat release, however, lowers the local (i.e., based on local properties) Reynolds number to the range 1,500-2,500. The 3D data enable computation of all nine components of the velocity gradient tensor ∇u from which the major 3D kinematic quantities, such as strain rate, vorticity, dissipation and dilatation, are computed. The volumetric PIV is combined with simultaneously acquired 10 Hz OH planar laser-induced fluorescence (PLIF). A single plane of the OH distribution is imaged on the center-plane of the volume and provides an approximate planar representation of the instantaneous reaction zone. The pseudo-volumes are reconstructed from temporally and spatially resolved kilohertz-rate 3C velocity field measurements on an end-view plane (perpendicular to the jet flame axis) invoking Taylor's hypothesis. The interpretation of the measurements is therefore twofold: the measurements provide a time-series representation of all nine velocity gradients on a single end-view plane or, after volumetric reconstruction, they offer a volumetric representation, albeit approximate, of the spatial structure of the flow. The combined datasets enable investigation of the fine-scale spatial structure of turbulence, the effect of the reaction zone on these structures and the relationship between the jet kinematics and the reaction zone. Emphasis is placed on the energy dissipation field and on the presence and role of dilatation. Statistics of the components of the velocity gradient tensor and its derived quantities show that these jet flames exhibit strong similarities to incompressible turbulent flows, such as in the distribution of the principal strain rates and strain-vorticity alignment. However, the velocity-gradient statistics show that these jet flames do not exhibit small-scale isotropy but exhibit a strong preference for high-magnitude radial gradients, which are attributed to regions of strong shear induced by the reaction zone. The pseudo volumes reveal that the intense-vorticity field is organized in two major classes of structures: tube-like away from the reaction zone (the classical worms observed in incompressible turbulence) and sheet-like in the vicinity of the local reaction zone. Sheet-like structures are, however, the dominant ones. Moreover, unlike incompressible turbulence where sheet-like dissipative structures enfold, but don't coincide with, clusters of tube-like vortical structures, it is observed that the sheet-like intense-vorticity structures tend to closely correspond to sheet-like structures of high dissipation. The primary reason for these features is believed to be due to the stabilizing effect of heat release on these relatively low local Reynolds number jet flames. It is further observed that regions of both positive and negative dilatation are present and tend to be associated with the oxidizer and fuel sides of the OH zones, respectively. These dilatation features are mostly organized in small-scale, short-lived blobby structures that are believed to be mainly due to convection of regions of varying density rather than to instantaneous heat release rate. A model of the dilatation field developed by previous researchers using a flamelet approximation of the reaction zone was used to provide insights into the observed features of the dilatation field. Measurements in an unsteady laminar nonpremixed jet flame where dilatation is expected to be absent support the simplified model and indicate that the observed structure of dilatation is not just a result of residual noise in the measurements, although resolution effects might mask some of the features of the dilatation field. The field of kinetic energy dissipation is further investigated by decomposing the instantaneous dissipation field into the solenoidal, dilatational and inhomogeneous components. Analysis of the current measurements reveals that the effect of dilatation on dissipation is minimal at all times (it contributes to the mean kinetic energy dissipation only by about 5-10%). Most of the mean dissipation arises from the solenoidal component. On average, the inhomogeneous component is nearly zero, although instantaneously it can be the dominant component. Two mechanisms are believed to be important for energy dissipation. Near the reaction zone, where the stabilizing effect of heat release generates layers of laminar-like shear and hence high vorticity, solenoidal dissipation (which is proportional to the enstrophy) dominates. In the rest of the ow the inhomogeneous component dominates in regions subjected to complex systems of nested vortical structures where the mutual interaction of interwoven vortical structures in intervening regions generates intense dissipation. / text