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Trump, C. L. and W. C. Leggett (1986). Optimum swimming speeds in fish: the problem of currents. Canadian Journal of Fisheries and Aquatic Sciences. 37:1086-1092.

A model is presented describing the energetic consequences of various behavioral responses to currents. To minimize the energy cost of migration, when confronted with currents, fish must optimize both the mean swimming speed and the degree to which swimming speed is altered in response to changes in current velocity. The optimum swimming speed in a current is U_o + 1/b where U_o = mean current speed and b is a constant in the equation E(t) = a e^-bW(t) describing the relationship between specific energy expenditure per unit time (E(t) and swimming speed W(t). In a variable current, such as might occur in estuaries and coastal areas, energy expenditure is minimized when these variations are ignored and a constant speed through the water is maintained. This is true even in conditions where occasional retrograde motion over the botton may occur. The added energy costs of swimming at mean speeds or of varying swimming speeds in response to changes in current velocity are rigorously defined. Predictions of the model are in general agreement with empirical data on fish swimming behavior.