Wind effects on the water in a narrow two-layered lake. Part I. Theoretical analysis. Part II. Analysis of observations from Windermere. Part III. Application of the theory to Windermere

Abstract

This paper presents a theoretical study of water movement in a long narrow lake subject to wind action during the summer season of thermal stratification. A model basin of uniform depth and width, consisting of two homogeneous layers of slightly different density, is considered. The motion of the water is assumed to be two dimensional in the vertical longitudinal section; geostrophic effects are ignored. The top and bottom layers in the model respectively represent the relatively warm surface water and the colder bottom water in the natural lake. Hydrodynamical equations are formulated in terms of the currents in the upper and lower layers, the elevation of the interface between the layers, and the elevation of the water surface. Solutions are sought to determine the dynamic response of the basin to an instantaneous rise in the wind stress applied tangentially over the surface. Three cases are considered corresponding to different frictional conditions at the bottom of the basin: (i) bottom friction zero, (ii) bottom friction proportional to the depth mean of the horizontal current in the lower layer, (iii) bottom current zero. It is assumed that internal friction is zero at the interface between the layers (this interface corresponds to the thermocline boundary in reality). Results obtained show that in the motion of the water there are ordinary and internal seiches characteristic of the two-layered model, together with a wind-driven circulation in the top layer. The theory is applied to determine vertical oscillations of the thermocline in an actual lake (Windermere) at one station, in response to a succession of wind pulses representing actual wind conditions over the lake. The oscillations thus obtained from theory compare satisfactorily with those derived from temperature observations taken in the lake. Depth-mean currents in the lake are deduced from theory, but there are no current measurements against which these values may be tested. The paper is divided into three parts. Part I deals with the development of the theory. Part II gives an account of actual physical conditions in Windermere, describing the analysis of temperature observations taken in the lake (yielding thermocline movements) and the analysis of wind records (yielding corresponding values of wind stress over the water surface). Part III is concerned with the numerical application of the theory to Windermere (under conditions described in part II), and gives general conclusions resulting from the entire work.