Vertical Circulation

The wind stress applied to the lake surface is directly transmitted through internal friction to a surface shear layer which, in general, is much thinner than the water column. In stratified water bodies, the thickness of that shear layer is determined by stratification: the vertical flux of momentum beyond the bottom of the SML, by viscous or turbulent processes, is considerably reduced by the existence of large density gradients. In homogeneous water bodies, those shear layers are referred to as Ekman layers and their thickness D is calculated as (2K//)y\ For turbulent flows, D is empirically found to scale as

where u* is the friction velocity at the free surface (defined as the square root of the result of dividing wind stress by water density), and the proportionality factor ranges from 0.1 to 0.4. For typical values of

-1 -0.6 -0.2 0.2 0.6 1 E-W velocity (cm s-1)

Figure 7 ADCP velocity measurements taken in the Oaks Arm of Clear Lake, California in the course of a field experiment (Data taken and provided by S.G. Monismith, Stanford University). The ADCP was mounted upside-down on a boat and operated on bottom-tracking mode. The depth of the water column was 10 m. The transect starts on the N-end of the basin and ends in Wheelan Cove at its southern shore. The East-West (EW) velocity component of the velocity field is shown as a cross-section in the lower part of the figure. Color marks the magnitude of the EW velocity: blue color represents velocities towards the West; red color represents velocities directed towards the East. Black arrows represent superficial velocity. Note that at the southern end, within Wheelan cove the measurements reveal the existence of a vortex structure, which forms as a result of the shoreline irregularity. The photograph was provided by S.G. Schladow, University of California - Davis.

"C1 y

(b)

Figure 8 (a) Interior velocities caused by wind acting in the negative x-direction in a deep basin of limited horizontal extent. Symbols defined in the text. (b) Vertical circulation in a small narrow lake.

Position

Position

Wind

Wind

Wind

Figure 9 Simulated steady state velocity profiles at two points in a 100 m deep rectangular flat bottom basin, with sides of length 65 km (in thex-direction) and 17 km (in they-direction). The arrows correspond to velocity vectors and are shown at 5-m depth intervals from the free surface to the bottom. These are results of simulations conducted with three-dimensional hydrodynamic model, where K(z) is set constant and equal to 0.02 m2 s~\ The top frame corresponds to a point located near the center of the basin while the lower frame is for a point located nearthe southern end. Adapted from Hutter K, Bauer G, Wang Y, and Guting P (1998) Forced motion response in enclosed lakes. In Imberger J (ed.) Physical Processes in Lakes and Oceans. American Geophysical Union, Washington D.C. pp 137-166. Copyright (1998) American Geophysical Union. Reproduced with permission of American Geophysical Union.

Wind

Figure 9 Simulated steady state velocity profiles at two points in a 100 m deep rectangular flat bottom basin, with sides of length 65 km (in thex-direction) and 17 km (in they-direction). The arrows correspond to velocity vectors and are shown at 5-m depth intervals from the free surface to the bottom. These are results of simulations conducted with three-dimensional hydrodynamic model, where K(z) is set constant and equal to 0.02 m2 s~\ The top frame corresponds to a point located near the center of the basin while the lower frame is for a point located nearthe southern end. Adapted from Hutter K, Bauer G, Wang Y, and Guting P (1998) Forced motion response in enclosed lakes. In Imberger J (ed.) Physical Processes in Lakes and Oceans. American Geophysical Union, Washington D.C. pp 137-166. Copyright (1998) American Geophysical Union. Reproduced with permission of American Geophysical Union.

u* = 10~2 ms_1 in mid-latitude lakes (f = 10~4 s-1) the Ekman boundary layer depth is of the order 10 m. Within the Ekman layer, the stresses reduce to zero, and both velocity magnitude and direction undergo significant changes.

The simplest possible model of velocity change with depth for lakes, is that of the steady-state local solution of eqns [1]—[3] (with K constant), for a flat bottom deep basin of limited horizontal dimensions

Position

Figure 10 Hodographs, i.e., time series of the horizontal velocities in the middle of the Obersee in Lake Constance, at 0, 5, and 10 m depths. The motion is set up from rest. The small circles mark time intervals of approximately four hours. Adapted from Wang Y, Hutter K, and Bauerle E (2001) Barotropic response in a lake to wind-forcing. Annales Geophysicae 19: 367-388. Reproduced with permission from European Geophysical Society.

Figure 10 Hodographs, i.e., time series of the horizontal velocities in the middle of the Obersee in Lake Constance, at 0, 5, and 10 m depths. The motion is set up from rest. The small circles mark time intervals of approximately four hours. Adapted from Wang Y, Hutter K, and Bauerle E (2001) Barotropic response in a lake to wind-forcing. Annales Geophysicae 19: 367-388. Reproduced with permission from European Geophysical Society.

acted upon by a constant and uniform wind stress in the y-direction, is (see Figure 8(a))

». , ». z/d\ z ■ z! =---h —— e ' cos--sin —

For z >> D, i.e., outside the Ekman layer, the velocity is in geostrophic balance with the pressure gradient that develops in response to wind forcing (or wind setup, eqn [11]). Closer to the surface, the velocity is a sum of the geostrophic velocity and the Ekman layer velocity (the exponentially decaying terms in eqns [19] and [20]). In the derivation of eqns [19] and [20], bottom stresses have been ignored. For deep basins, this is a reasonable assumption since the velocity near the bottom from eqn [19] and [20] is, in this case, negligible u*/fh.

In basins of intermediate depth, the velocity profiles will have both a surface (driven by wind stress) and bottom (driven by bottom stress or currents) Ekman layers. In both layers, the horizontal velocity vectors would tend to rotate clockwise (in the northern hemisphere) as one moves out of the boundary. The rate at which velocity vectors rotate with vertical v

Table 1 Circulation patterns of HB in natural systems (lakes and reservoirs): observations and models

Table 1 Circulation patterns of HB in natural systems (lakes and reservoirs): observations and models

Horizontal Lake Zonation

(6) Lake Tanganyika a)

(6) Lake Tanganyika a)

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