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The paper develops and demonstrates a method of classifying oceanographic processes using an autonomous-underwater vehicle (AUV). First, we establish the "mingled-spectrum principle" which concisely relates observations from a moving platform to the frequency-wavenumber spectrum of the surveyed process. This principle clearly reveals the role of the AUV speed in mingling time and space. An AUV can distinguish between oceanographic processes by jointly utilizing temporal and spatial information. A parametric tool for designing an AUV spectral classifier is then developed based on the mingled-spectrum principle. An AUV's controllable speed tunes the separability between the mingled spectra of different processes. This property is the key to optimizing the classifier's performance. As a case study, AUV-based classification is applied to distinguish ocean convection from internal waves. It is demonstrated that at a higher AUV speed, convection's distinct spatial feature is highlighted to the advantage of classification. Finally, the AUV classifier is tested by the Labrador Sea Convection Experiment of February 1998. We installed an Acoustic Doppler Velocimeter in an AUV and it measured flow velocity in the Labrador Sea. Based on the vertical flow velocity, the AUV-based classifier captures convection's occurrence. This finding is supported by other oceanographic observations in the same experiment.