The unsteady hydrodynamic interaction of two bodies moving in a shallow fluid is examined by applying slender-body theory. The bodies are assumed to be in each other's far field and the free surface is assumed to be rigid. By matched asymptotics, the inner and outer problems are formulated and a pair of coupled integro-differential equations for determining the unknown cross-flows is derived. The degree of coupling is shown to be related to a bottom-clearance parameter. Expressions are given for the unsteady sinkage force, trimming moment, sway force, and yaw moment. Numerical calculations for two weakly coupled cases are presented. One corresponds to the interaction of a stationary body with a passing one, the other to the interaction of two bodies moving in a steady configuration. Theoretical results are compared with existing experimental data.
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