The mean circulation in a coastal zone of variable depth may under certain circumstances be modeled by linear equations, including a bottom friction linear in the depth-averaged velocity. The resulting steady-state problem is similar to the problem of topographic wave generation by wind. The equation governing the pressure field has the form of a one-dimensional heat conduction equation, with longshore distance in the direction of topographic wave propagation playing the role of time. The effects of wind stress or of freshwater influx are felt only over the forward portion of a long shelf (i.a., that portion to which topographic waves propagate from the source region). Various simple solutions can be written down for the arrested topographic wave problem in virtue of the heat conduction analogy. They generally show the presence of a pressure field trapped in a nearshore band. For periodic wind stress, for example, the scale width of the trapped pressure field is L=(2r/fks)1/2, where r is a bottom... Abstract The mean circulation in a coastal zone of variable depth may under certain circumstances be modeled by linear equations, including a bottom friction linear in the depth-averaged velocity. The resulting steady-state problem is similar to the problem of topographic wave generation by wind. The equation governing the pressure field has the form of a one-dimensional heat conduction equation, with longshore distance in the direction of topographic wave propagation playing the role of time. The effects of wind stress or of freshwater influx are felt only over the forward portion of a long shelf (i.a., that portion to which topographic waves propagate from the source region). Various simple solutions can be written down for the arrested topographic wave problem in virtue of the heat conduction analogy. They generally show the presence of a pressure field trapped in a nearshore band. For periodic wind stress, for example, the scale width of the trapped pressure field is L=(2r/fks)1/2, where r is a bottom...