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Most bacteria in the ocean can be motile. Chemotaxis allows bacteria to detect nutrient gradients, and hence motility is believed to serve as a method of approaching sources of food. This picture is well established in a stagnant environment. In the ocean a shear microenvironment is associated with turbulence. This shear flow prevents clustering of bacteria around local nutrient sources if they swim in the commonly assumed "run-and-tumble" strategy. Recent observations, however, indicate a "back-and-forth" swimming behavior for marine bacteria. In a theoretical study we compare the two bacterial swimming strategies in a realistic ocean environment. The "back-and-forth" strategy is found to enable the bacteria to stay close to a nutrient source even under high shear. Furthermore, rotational diffusion driven by thermal noise can significantly enhance the efficiency of this strategy. The superiority of the "back-and-forth" strategy suggests that bacterial motility has a control function rather than an approach function under turbulent conditions.