By Robert A. Ragotzkie (auth.), Abraham Lerman (eds.)
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Extra resources for Lakes: Chemistry, Geology, Physics
They derive their high magnitude from wind stress and bottom stress and from the relatively rapid variation of these stresses in the vertical. The hydrostatic approximation reduces the number of momentum equations to be considered to two, and the Boussinesq approximation allows the effects of internal density differences to be described by a dynamic height term: D = fO P z Po Po dz (1) where Po is reference density and z = 0 is the undisturbed free surface. The Reynolds stresses in horizontal planes along the two horizontal coordinates, 7 x and 7 y, are conveniently converted to the kinematic quantities.
A corresponding alternative simplification of the heat conduction equation, valid mainly for short term phenomena, is then: dT =0 dt (6) where dldt indicates the total derivative. The temperature of fluid particles thus remains conserved in the course of their motion. An equilibrium density distribution may then be prescribed and various dynamical problems solved on the assumption that fluid particles retain their density. A class of conceptual models based on this approximation makes use of a two-layer approach, the lake being idealized as consisting of a light epilimnion and a heavy hypolimnion, an abrupt change of density taking place at the thermocline.
Depth-average long hore velocity in Lake Ontario trunk section due to a wind impulse of FI = 20,000 cm' seC'. 10 - 30 to 20 km FROM NORTH SHORE 40 50 60 30 G. T. Csanady L 20M lIZl :::i FIGURE 7. 5km The above discussion is based mainly on two of my own papers, Csanady (l973a, 1975a). However, credit for the first clear explanation of directly wind-driven coastal currents in homogeneous water belongs to Bennett (1972, see also 1974). His conclusions are best exhibited by some diagrams incorporating the results of numerical calculations for an idealized long and narrow basin, also including a reasonably realistic representation of internal friction.
Lakes: Chemistry, Geology, Physics by Robert A. Ragotzkie (auth.), Abraham Lerman (eds.)