We develop a plume tracking algorithm for a swarm of mobile sensing agents in turbulent flow. Inspired by blue crabs, we propose a stochastic model for plume spikes based on the Poisson counting process, which captures the turbulent characteristic of plumes. We then propose an approach to estimate the parameters of the spike model, and transform the turbulent plume field detected by sensing agents into a smoother scalar field that shares the same source with the plume field. This transformation allows us to design path planning algorithms for mobile sensing agents in the smoother field instead of in the turbulent plume field. Inspired by the source seeking behaviors of fish schools, we design a velocity controller for each mobile agent by decomposing the velocities into two perpendicular parts: the forward velocity incorporates feedback from the estimated spike parameters, and the side velocity keeps the swarm together. The combined velocity is then used to plan the path for each agent in the swarm. Theoretical justifications are provided for convergence of the agent group to the plume source. The algorithms are also demonstrated through simulations.