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Initial transients in long wave computations are identified as free mode responses, forced by the incompatibility between the initial conditions and the forced response. Their character is described in the context of two typical onedimensional channel problems and an analytical solution to the linearized equations. Strategies to avoid initial transients are investigated in detail, in particular, initiallyenhanced friction, the gradual introduction of forcing and various radiation boundary conditions. A modified Reid radiation boundary condition is recommended for general application, supplemented where necessary by gradual introduction of the forcing to minimize initial spike responses.

An improved understanding of the dispersal patterns of marine organisms is a prerequisite for successful marine resource management. For species with dispersing larvae, regional–scale hydrodynamic models provide a means of obtaining results over relevant spatial and temporal scales. In an effort to better understand the role of the physical environment in dispersal, we simulated the transport of reef fish larvae among 321 reefs in and around the Cairns Section of the Great Barrier Reef Marine Park over a period of 20 years. Based on regional–scale hydrodynamics, our models predict the spatial and temporal frequency of significant self–recruitment of the larvae of certain species. Furthermore, the results suggest the importance of a select few local populations in ensuring the persistence of reef fish metapopulations over regional scales.

A. R. Robinson has proposed a method for studying population growth and advection in the sea. The assumption made by Robinson of a non–divergent velocity field for the biological tracer may not be valid for many situations. When the assumption is valid the biological dynamics of an advected patch are no different from those of a stationary patch, unless a greater degree of spatial structure is incorporated than he considers. The generality and applicability of the model are increased if the assumption of non–divergence can be relaxed. If the velocity field associated with a patch is convergent, as can occur for many biological tracers, then new dynamics arise, both in a Lagrangian sense and when working at the whole–patch level. These new dynamics are explored for four fundamental examples, which could provide new paradigms for spatially explicit models in mathematical ecology.

Initial transients in long wave computations are identified as free mode responses, forced by the incompatibility between the initial conditions and the forced response. Their character is described in the context of two typical one‐dimensional channel problems and an analytical solution to the linearized equations. Strategies to avoid initial transients are investigated in detail, in particular, initially‐enhanced friction, the gradual introduction of forcing and various radiation boundary conditions. A modified Reid radiation boundary condition is recommended for general application, supplemented where necessary by gradual introduction of the forcing to minimize initial spike responses.