Correction: A 40‑year numerical experiment of circulations in Lake Biwa (2): winter overturn circulation

Some numerical experiments by the barotropic nonlinear two dimensional models are performed to study the water circulations in Lake Biwa, especially to study the large anticlockwise gyre in the north basin. The wind fields used in the experiments have no rotational component. This gyre is induced by the southerly wind and is approximately on the geostrophic balance. The vorticity of this gyre is contributed from the vertical stretching of the vortex tube by the variable bottom topography and the inertia term. But the latter term does not become effective if the bottom profile of the basin is flat. Therefore the horizontal circulation in the barotropic closed basin is the “topographic gyres”. The bottom stress has a little contribution to the vorticity balance of the gyre.

Some numerical experiments were made to examine the possibility of large anticlockwise circulation at Lake Biwa in summer caused by horizontally uniform heat flux across the lake surface. Flow is induced by the “topographic heat accumulation effect” due to the non-uniform water depth. To evaluate this flow, an axisymmetric model basin is used. Dependence of the magnitude of velocity on the horizontal and vertical Ekman numbers is also investigated. If the heating continues as long as the vertical diffusion time, fairly large velocity is created indicating a possibility that this is the origin of the lake current.

Seasonal change of the internal seiches' period will be treated by the spectrum analysis of the continuous temperature records which were obtained from the thermistor-buoy stations in Lake Biwa.The dominant period almost coincides with theoretical one which can be derived from a longitudinal internal seiche in a two-layered rectangular lake, but the observed spatial phase difference and amplitude cannot be explained reasonably by the concept of a simple longitudinal internal seiche. They rather correspond to the rotating internal KELVIN wave, which was found out from the numerical experiments in the preceding paper (6). The results of the “Round Cruise Survey” of the thermocline of Lake Biwa, which was carried out during the period from Aug. 9 to Aug. 13, 1973 shows that the dominant internal oscillation has a rotatory nature, that is, the high water region rotates along the lake shore in the anticlockwise direction with an apparent phase velocity of 2.2km/hr (in August). Such a rotatory behavior of the internal oscillation enables us to interpret reasonably the results of the spectrum analysis of the temperature records.

Various surveys and investigations on physical limnology have been carried out in Lake Biwa from the viewpoints of both pure and applied science. A general outline of these studies is reported here, placing emphasis on the relation to the lake's environmental problems.Many observations have made clear the general pattern of circulating current systems in the northern basin, and theoretical analyses with numerical experiments are conducted to discuss the generation mechanism of the circulating current.Field studies on dispersion and convergence at various coastal regions and river mouths are carried out to investigate the distribution of specific substances which flow into the lake from land.In the southern basin, it is shown from quantitative observations and numerical simulations that the lake current in the region is controlled by the prevailing wind system, and special care was taken to investigate an environmental change around a new man-made island off Yabase. As a part of the calculations on nutrient balance, the release rate of a nutrient (NH4-N) from lake bottom and its seasonal variation are investigated by sampling bottom muds in order to examine the effects of the released nutrient on the water quality of the lake

A 40-year numerical experiment of circulations in Lake Biwa (2): winter overturn circulation

A 40-year numerical experiment of circulations in Lake Biwa (1): summer gyre systems

Oscillations of surface and interface elevations and velocity have been calculated numerically in using a two layer model of constant depth with 25×62 square meshes of 1 km intervals. In that model, the mean depth of the interface is 17.5m and the density difference between the upper and lower layers is 2.5×10-3g/cm3 corresponding to the temperature difference of 13°C.Linear hydrodynamic equations for the equivalent volume transport and the equivalent elevations were integrated by means of an implicit method, taking into account of wind stress, bottom stress and CORIOLIS force.In the present numerical experiments, the four cases of duration time were treated, 450 minutes (NW-(1)) and 1200 minutes (NW-(2)) for NW-wind and 450 minutes for SW-wind and ESS-wind, to which the constant wind speed of 5m/sec was applied.From the results of FOURIER spectrum analysis for the calculated time series of elevation and velocity at various sampling positions in the model lake, it was found that the long period internal KELVIN waves progressing along the lake shore in the anticlockwise direction exist with the same period as that in the case of no rotation of the earth, and that the mean lake currents consisted of two or three gyres, are essentially affected by geostrophic condition, as usually observed in real Lake Biwa.

Water temperature near the surface of a lake increases with increasing air temperature, whichresults in stratification. The strength of stratification substantially influences the transport of dissolved oxygenfrom the surface to the bottom water of a lake. In recent years, the decrease in dissolved oxygen at the bottom ofthe northern part of the Lake Biwa, the largest freshwater lake in Japan, has been observed. The main cause ofthis is considered to be the change in stratification, which depends on weather and climate conditions. In thepresent study, numerical simulations were carried out to investigate the effect of strong wind on the structure ofstratification in Lake Biwa. The baseline simulation was conducted using actual meteorological data, andexperimental simulations were conducted using meteorological data with modified wind speed and direction.The numerical experiments showed that if the magnitude of the wind is strong enough, the stratificationcollapses and the wind can enhance the vertical mixing in the bottom layer even in the summer season withstrong thermal stratification. In a stratified season, when the strong wind blows predominantly in one direction,the rate of the vertical mixing changes by the wind direction. Moreover, as the duration of the strong windextends, vertical mixing easily occurs.

Pull-down basin in the central part of Japan due to subduction-induced mantle flow

We tested the hypothesis that dissolved organic matter (DOM) is delivered to deep layers by convective mixing in winter, where it contributes to the mineralization of C, N, and P in the oxygenated hypolimnion of large (surface area 674 km2, maximum depth 104 m), monomictic Lake Biwa. Basin-scale, seasonal measurements of DOM concentrations revealed that dissolved organic carbon (DOC) and nitrogen (DON) accumulated in the epilimnion during warm seasons and were redistributed into the deeper layer during winter overturn. Hypolimnetic DOC and DON decreased in concentration over the stratification period, indicating mineralization; the contributions of DOM to the total mineralization of C and N were 8% and 30%, respectively. Higher contribution of N relative to C suggests that the N-rich DOM was mineralized at depth. We failed to detect a significant contribution of dissolved organic phosphorus to P mineralization in the hypolimnion, which could be explained by substantial depletion in P relative to C and N of DOM; C: P and N: P ratios were 1,978 and 147, respectively. The data suggest that convective mixing in this monomictic basin delivers DOM to hypolimnetic depths, where it is mineralized during subsequent periods of stratification.

This paper describes the fundamental characteristics of the numerical experiments on thermal convection carried out under the condition of the northern part of Lake Biwa. Since the temporal change of vertical distribution of water temperature during the cooling period can be reproduced by means of a simple simulation model of thermal convection in the previous study, the numerical results of thermal convection simulation was firstly shown under wide range of cooling rates at water surface. We considered to clarify the basic features of these numerical data on thermal convection using a stochastic model and its mean field approximation. It was shown through the comparison of theoretical results to numerical results that the mean field approximation with some refinement is applicable to the numerical experiments to some extent.

Applicability of Mean Field Approximation to Numerical Experiments of Thermal Convection during the Cooling Period of Lake Biwa

This paper describes the fundamental characteristics of vertical heat transfer due to thermal convection during the cooling period (September to February) in the northern part of Lake Biwa. It is well known that the thermal convection during the cooling period is the main mechanisms of DO transfer from the water surface to the bottom of lake. The mixing mechanism caused by thermal convection is investigated numerically using 3-D CFD model. It is shown that thermal convection cells are observed in the computational domain, changing the positions of submerging portion temporally. Then, a stochastic model with Monte-Carlo simulation is proposed to consider the results of numerical experiments. It is pointed out that the characteristics of the spatial flow patterns with Fractal structure are reproduced by the model.