10 Forced Motion Response in Enclosed Lakes K. Hutter, G. Bauer, Y. Wang and P. Gtiting Abstract We report experiences gained with two differentmodels that allow computation of the wind induced barotropic and baroclinic motion in lakes. Theseare: Nonlinear dispersive two-layeredwave model for finite depth fluids on the rotating Earth; Semi-spectral primitive equation model(SPEM)with implicit integration in time. The first is used to demonstrate that nonlinearities affect the fine structure of the thermocline responsewhen the wind input is strong. This is shownby means of computations with a rectangular basin of constant depth andwith Lake Constance. The implicitversion of SPEM is usedto study the Ekman problem and the baroclinic response in a rectangle and in Lake Constance. Both models concentrate upon the role playedby diffusionin predictingthe current andtemperature distribution thatis established in lakes under direct wind forcing. Introduction The most popular and probably also most successful tool for the interpretationof observations collected with moored instruments in enclosed lakes has so far been the theoretical-numerical analysis of barotropic and baroclinic linear wavesby use of the one- andtwo-layerfree shallow water equations; this has led to the identification (i) of the periods of Kelvin andPoincar6 typeeigenmodes of the gravity waves and(ii) very nearly alsoof topographic Rossby waves or higher order baroclinic gravitymodes, which require a three- or many-layerapproximation of the stratification;for a review, seee.g. Hutter (1993). Comparisons of measured time seriesof velocities and/or isotherm depths at selected positions in a (stratified) lake with corresponding time seriesdeduced from the linear shallow water equations subject to directwind forcing are muchless frequent despite the existenceof a formal analytical theory of forced oceanic waves (Fennel and Lass, 1989) and wind induced currents (Heaps, 1984; Kielmann and Simons, 1984; Simons, 1980; Csanady,1984). The reasons are that (i) thermocline excursions are often large, i.e., a considerablefraction of the epilimnion depth and (ii) vertical diffusion of momentum (and energy)is not negligible when the current distributionis to be predicted. Thus, the linear formulations offer no advantage and are insufficient. Nonlinearmodels have been developed on two levels: 1) two-layered large amplitude wave modelsfor finite depth fluids and 2) full scale numericalimplementations of the Physical Processes in Lakesand Oceans Coastaland EstuarineStudies Volume 54, Pages 137-166 Copyright1998 by the American Geophysical Union