The simultaneous measurement of the velocities at two points with X-type hot wire probes has been performed in three regions of a plane jet (i.e., the potential core region, the interaction region and the self-preserving region). The Karhunen Loève (KL) expansion was applied to the velocity data, and the development of coherent structure was investigated by the eigenvalues and eigenfunctions as well as the spatial velocity correlations. It is found that in the potential core region the first and second modes are dominant in the kinetic energy with almost the same magnitude. The profiles of the eigenfunctions downstream of the interaction region show that the first mode of streamwise velocity u is asymmetrical about the jet centerline whereas that of cross-streamwise velocity v is symmetrical. These results are consistent with the feature of the two-point velocity correlation.

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The simultaneous measurement of the velocities at two points with X-type hot wire probes has been performed in three different downstream regions of a plane jet (the potential core region, the interaction region and the self-preserving region). By applying Karhunen-Lò eve (KL) expansion in space and time, the structure development of the plane jet is investigated from a viewpoint of both space and frequency. From the downstream variation of the eigenfunctions, it is found that in the early stage of the interaction region the profiles of the first u (streamwise component of velocity fluctuation) and v (cross-streamwise component of velocity fluctuation) mode in the low frequency range become self-similar, but in high frequency range these continue to change until the self-preserving region. The characteristics of coherent structure can be extracted efficiently by the two-point spatial velocity correlation reconstructed from the first mode of KL expansion.

In order to clarify the dynamics of the coherent structure in a turbulent plane jet, the simultaneous measurement of the main streamwise velocity at 21 points in the self-preserving region of a turbulent plane jet has been performed by an array of I-type hot-wire probes. Then the KL (Karhunen-Loève) expansion was applied to extract the coherent structure in the jet. The total number of eigenfunctions (modes) is N = 21, which corresponds to the number of probes. The eigenfunctions (modes) are numbered in order of magnitude of their corresponding eigenvalues. From the investigation of the random coefficients and the eigenfunctions (modes), it is found that the low-numbered (energetic) modes represent the large scale (coherent) structure, the middle-numbered modes represent the finer (small-scale) random structure, and the higher-numbered modes contribute mainly to the intermittent structure in the outer edge region. From the spatio-temporal velocity field reconstructed by the first KL mode, it is found that there exist a pair of fluid lumps with the positive and negative streamwise velocity fluctuation on the opposite sides of the jet centerline, and the signs of velocity fluctuation for those fluid lumps change alternately as time proceeds. These characteristics are consistent with the so called "jet flapping" phenomenon.