<p>In this paper, we investigate kinetic energy and streamline properties for an irrotational periodic geophysical traveling surface water waves propagating in equatorial oceanic regions. Relying on the methods from complex analysis, we prove the logarithmic convexity and monotonicity of specific flow variables. We find that the fluid particle trajectory exhibits the same patterns, undergoing a horizontal shift after each elapsed time (the time taken for a particle to traverse one period in the moving plane), while maintaining zero net displacement in the vertical direction. There are no closed paths for all particles and the drift of any streamline is positive in equatorial Stokes flow. By means of conformal mappings, we derive some qualitative results for kinetic energy and streamline, such as the convexity and monotonicity of the integral means of kinetic energy, elapsed time being independent of the labelling initial domain, the concavity and monotonicity of total kinetic energy within the region between two streamlines and the convexity and monotonicity of total kinetic energy over over an elapsed time. Taking advantage of the Bernoulli’s law and the Schwarz reflection principle, we show that the extremum of the kinetic energy is attained on the free surface for irrotational equatorial wind waves.</p>