Locating the source of odor in a turbulent environment -a common behavior for living organisms -is non-trivial because of the random nature of mixing. Here we analyze the statistical physics aspects of the problem and propose an efficient strategy for olfactory search which can work in turbulent plumes. The algorithm combines the maximum likelihood inference of the source position with an active search. Our approach provides the theoretical basis for the design of olfactory robots and the quantitative tools for the analysis of the observed olfactory search behavior of living creatures (e.g. odor modulated optomotor anemotaxis of moth). Olfactory search strategies are interesting because of their relevance to animal behavior [1, 2, 3, 4, 5, 6] and because of their potential utility in practical applications (such as searching for chemical leaks, drugs and explosives [27] ). Both, the attempt to characterize and understand the olfactory behavior of living organisms [1, 2, 3, 4, 5, 6] and the more recent effort to design and build "sniffing machines" -robots that navigate using odors as a guide [27, 26, 28, 29] face the common problem of understanding how the information gained from sporadic detection of odor dispersed in a naturally turbulent flow can be efficiently utilized for locating the source. Here we shall discuss the statistical aspects of turbulent odor dispersal and propose a novel and well defined search algorithm, which we shall first define in the context of a simplified model of the turbulent plume and later restate in the form applicable to natural environment. The proposed search algorithm can be used in robotic applications and provides a plausible algorithmic interpretation for aspects of insect olfactory search behavior. The most familiar strategy for locating the source of a substance is chemotaxis [7, 30] which consists of motion in the direction of the local concentration gradient. Chemotaxis works on small scales, where the substance spreads by diffusion and the field of concentration is smooth which is appropriate to the environment of bacteria, amoebae or single eukaryotic cells [30, 31] . On the other hand, larger animals tracing odors in turbulent flows, e.g. in atmosphere, have to deal with the complex fluctuating structure of the odor plume caused by the randomness in the flow which disperses it. This makes the search a much more complex task. The odor is not always present and when it is detected, the local concentration gradient typically does not point toward the source [2, 8, 9, 10, 11] . A more complex strategy is required and additional information such as the current wind direction (and velocity) is very valuable. One of the best characterized olfactory search behaviors is the "odor-modulated optomotor anemotaxis", which is employed by males of certain species of moths (see [1, 2] ) in order to locate the source of a pheromone (i.e. potential mate), and which involves, in addition to the sense of smell, the ability to determine the wind direction * . The moth's olfactory pursuit flight exhibits a counterturning pattern: a succession of turns alternatively to left and right with respect to the wind direction † . Counterturning is further classified as i) casting and ii) zigzagging [15, 16, 17, 18] . The two differ in the extent of upwind progression: "zigzagging" is counterturning with a significant resultant move- * Moths determine instantaneous direction of wind visually by looking at the motion of objects on the ground: when the moth is heading upwind its body axis is aligned with the direction of motion of the objects (see C. T. David, Ref. [1], p. 49). † It has been found that counterturns are self-steered as opposed to gradient-steered [15, 16] , which is to say that the moth makes each turn not because it reaches the boundary of the plume and feels the lateral gradient of the concentration, but due to internal turn generator which alternates between right and left.
Work by Balkovsky and Shraiman REF on the subject of statistical analysis of the plume is also relevant.
Olfactory search at high Reynolds number
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