On the Water Exchange and the Current in Hamana Lake in Relation to Occurrences of Toxic Shellfish

Abstract

Since 1949 hydrographical surveys^{1), 2), 3), 4)} have been conducted by the Hamana Lake Branch, Shizuoka Fisheries Experimental Station, in the lake in order to find out causes of poisonous shell-fish encountered there from time to time. Using data obtained from the surveys the author has calculated the amounts of water exchange, which was caused by vertical mixing between the upper and lower parts of the lake, by the inflows from the open sea and of terrestrial water. Thereupon has been introduced the following new simultaneous equations
{A(T"_a-T'_a)=Q₁(T₁- _??_ ₀)-Q₂(T₀- _??_ _s)-M _??_ X _??_ +DA,
A (Cl"_a-Cl'_a)=Q₁(Cl₁-Cl₀)-Q₂ (Cl₀-Cl_s)-M _??_ Y _??_,
B (T"_b-T'_b)= Q₂(T₂-T₃)+M _??_ X _??_ +D' B,
B (Cl"_b-Cl'_b)= Q₂(Cl₂-Cl_s)+M _??_ Y _??_, where _??_ X _??_ =[Δ T"-Δ T'/Δσ _t "-Δσ _t'+Δ T'•Δσ_t"-Δ T"•Δσ'_t/(Δσ"_t-Δσ'_t)²logΔσ"_t/Δσ'_t],
_??_ Y _??_ =[ΔCl"-ΔCl'/Δσ"_t-Δσ'_t+ΔCl'•Δσ_t"-ΔCl"•Δσ_t'/(Δσ"_t-Δσ'_t)²logΔσ"_t/Δσ_t'],
A, B=volumes of water in the upper and lower parts of lake,
T_a, Cl_a=mean values of temperature and chlorinity of the upper part,
T_b, Cl_b= _??_ _??_ _??_ of the lower part,
Q₁, Q₂=volumes of terrestrial water and open sea water flowing in during a certain period,
T₁, Cl ₁=mean values of temperature and chlorinity of terrestrial water,
T₂, Cl₂= _??_ _??_ _??_ of open sea water,
T₀, Cl₀=temperature and chlorinity of the upper layer in the upper part,
T₃, Cl₃= _??_ _??_ _??_ in the lower part,
DA=differential amount of heat exchange between the surrounding areas and the upper part,
D' B= _??_ _??_ _??_ and the lower part,
T=T"+T'/2, Δ T=T_a-T_b, Δσ_t=σ_tb-σ_ta(represents stability between the upper and lower parts),
M=m(t"-t'), c=m/σ_tb-σ_ta,
c is volume of exchanged water by vertical mixing between the upper and lower parts at unit time, and notations " and ' represent the values at time t" and t' respectively.