21 research outputs found
A one-dimensional model of vertical stratification of Lake Shira focussed on winter conditions and ice cover
Change in the circulation regime in the stratified saline Lake Shira (Siberia, Republic of Khakassia)
Π§ΠΈΡΠ»Π΅Π½Π½ΠΎΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ Π³ΠΈΠ΄ΡΠΎΡΠ΅ΡΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ΅ΠΆΠΈΠΌΠ° ΠΡΠ°ΡΠ½ΠΎΡΡΡΠΊΠΎΠ³ΠΎ Π²ΠΎΠ΄ΠΎΡ ΡΠ°Π½ΠΈΠ»ΠΈΡΠ°
Mathematical models of hydrothermal processes for stratified flows in flow-through reservoirs are con-
sidered in the paper. Models are based on the equations of fluid mechanics and heat transfer. They are
applied to describe the hydrothermal regime of the Krasnoyarsk Reservoir. It is assumed that the reservoir
depth is varied continuously, and the reservoir width is varied in a stepwise way. A numerical algorithm
to study two-dimensional vertically stratified flows in terms of the streamfunction and the vorticity is con-
sidered. Parametrization of coefficients of the vertical turbulent exchange is proposed. Numerical results
for currents at the dam area of the Krasnoyarsk reservoir are presented. The numerical model allows
one to determine the temperature of water entering the intake openings in relation to the stratification,
the position of water intake and the flow rate of waterΠΠ»Ρ ΠΎΠΏΠΈΡΠ°Π½ΠΈΡ ΡΡΡΠ°ΡΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΠ΅ΡΠ΅Π½ΠΈΠΉ Π² ΠΏΡΠΎΡΠΎΡΠ½ΡΡ
Π²ΠΎΠ΄ΠΎΠ΅ΠΌΠ°Ρ
ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡΡΡ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π³ΠΈΠ΄ΡΠΎΡΠ΅ΡΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² Π² Π²ΠΎΠ΄ΠΎΠ΅ΠΌΠ°Ρ
Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΠΌΠ΅Ρ
Π°Π½ΠΈΠΊΠΈ ΠΆΠΈΠ΄ΠΊΠΎΡΡΠΈ
ΠΈ ΡΠ΅ΠΏΠ»ΠΎΠΏΠ΅ΡΠ΅Π½ΠΎΡΠ° Ρ ΡΡΠ΅ΡΠΎΠΌ ΡΠΏΠ΅ΡΠΈΡΠΈΠΊΠΈ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΠΌΡΡ
Π·Π°Π΄Π°Ρ. ΠΠ»Ρ ΡΠΈΡΠ»Π΅Π½Π½ΠΎΠ³ΠΎ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π³ΠΈΠ΄ΡΠΎΡΠ΅ΡΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ΅ΠΆΠΈΠΌΠ° ΠΡΠ°ΡΠ½ΠΎΡΡΡΠΊΠΎΠ³ΠΎ Π²ΠΎΠ΄ΠΎΡ
ΡΠ°Π½ΠΈΠ»ΠΈΡΠ° ΠΏΡΠΈΠΌΠ΅Π½ΡΠ΅ΡΡΡ ΡΡ
Π΅ΠΌΠ° Π»ΠΎΠΆΠ° Π²ΠΎΠ΄ΠΎΡ
ΡΠ°Π½ΠΈΠ»ΠΈΡΠ° Π² Π²ΠΈΠ΄Π΅ ΡΠ°ΠΉΠΎΠ½ΠΎΠ² Ρ Π½Π΅ΠΏΡΠ΅ΡΡΠ²Π½ΡΠΌ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ΠΌ Π³Π»ΡΠ±ΠΈΠ½Ρ ΠΈ ΡΠΊΠ°ΡΠΊΠΎΠΎΠ±ΡΠ°Π·Π½ΡΠΌ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ΠΌ ΡΠΈΡΠΈΠ½Ρ.
Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ ΡΠΈΡΠ»Π΅Π½Π½ΡΠΉ Π°Π»Π³ΠΎΡΠΈΡΠΌ Π΄Π»Ρ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π΄Π²ΡΠΌΠ΅ΡΠ½ΡΡ
Π² Π²Π΅ΡΡΠΈΠΊΠ°Π»ΡΠ½ΠΎΠΉ ΠΏΠ»ΠΎΡΠΊΠΎΡΡΠΈ
ΡΡΡΠ°ΡΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΠ΅ΡΠ΅Π½ΠΈΠΉ Π² ΠΏΡΠΎΡΠΎΡΠ½ΡΡ
Π²ΠΎΠ΄ΠΎΠ΅ΠΌΠ°Ρ
Π² ΠΏΠ΅ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ
ΡΡΠ½ΠΊΡΠΈΠΈ ΡΠΎΠΊΠ°. ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π° ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈΠ·Π°ΡΠΈΡ ΠΊΠΎΡΡΡΠΈΡΠΈΠ΅Π½ΡΠΎΠ² Π²Π΅ΡΡΠΈΠΊΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΡΡΡΠ±ΡΠ»Π΅Π½ΡΠ½ΠΎΠ³ΠΎ ΠΎΠ±ΠΌΠ΅Π½Π°. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΠΏΡΠΈΠΌΠ΅ΡΡ
ΡΠ°ΡΡΠ΅ΡΠΎΠ² ΡΠ΅ΡΠ΅Π½ΠΈΠΉ Π½Π° ΠΏΡΠΈΠΏΠ»ΠΎΡΠΈΠ½Π½ΠΎΠΌ ΡΡΠ°ΡΡΠΊΠ΅ ΠΡΠ°ΡΠ½ΠΎΡΡΡΠΊΠΎΠ³ΠΎ Π²ΠΎΠ΄ΠΎΡ
ΡΠ°Π½ΠΈΠ»ΠΈΡΠ°. Π§ΠΈΡΠ»Π΅Π½Π½Π°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ
ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΠΈΡΡ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΡ Π²ΠΎΠ΄Ρ, ΠΏΠΎΡΡΡΠΏΠ°ΡΡΠ΅ΠΉ Π² Π²ΠΎΠ΄ΠΎΠ·Π°Π±ΠΎΡΠ½ΡΠ΅ ΠΎΡΠ²Π΅ΡΡΡΠΈΡ, Π² Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΠΎΡ ΡΡΡΠ°ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ, ΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ Π²ΠΎΠ΄ΠΎΠ·Π°Π±ΠΎΡΠ°, ΡΠ°ΡΡ
ΠΎΠ΄Π° Π²ΠΎΠ΄
Π§ΠΈΡΠ»Π΅Π½Π½ΠΎΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ Π³ΠΈΠ΄ΡΠΎΡΠ΅ΡΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ΅ΠΆΠΈΠΌΠ° ΠΡΠ°ΡΠ½ΠΎΡΡΡΠΊΠΎΠ³ΠΎ Π²ΠΎΠ΄ΠΎΡ ΡΠ°Π½ΠΈΠ»ΠΈΡΠ°
Mathematical models of hydrothermal processes for stratified flows in flow-through reservoirs are con-
sidered in the paper. Models are based on the equations of fluid mechanics and heat transfer. They are
applied to describe the hydrothermal regime of the Krasnoyarsk Reservoir. It is assumed that the reservoir
depth is varied continuously, and the reservoir width is varied in a stepwise way. A numerical algorithm
to study two-dimensional vertically stratified flows in terms of the streamfunction and the vorticity is con-
sidered. Parametrization of coefficients of the vertical turbulent exchange is proposed. Numerical results
for currents at the dam area of the Krasnoyarsk reservoir are presented. The numerical model allows
one to determine the temperature of water entering the intake openings in relation to the stratification,
the position of water intake and the flow rate of waterΠΠ»Ρ ΠΎΠΏΠΈΡΠ°Π½ΠΈΡ ΡΡΡΠ°ΡΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΠ΅ΡΠ΅Π½ΠΈΠΉ Π² ΠΏΡΠΎΡΠΎΡΠ½ΡΡ
Π²ΠΎΠ΄ΠΎΠ΅ΠΌΠ°Ρ
ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡΡΡ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π³ΠΈΠ΄ΡΠΎΡΠ΅ΡΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² Π² Π²ΠΎΠ΄ΠΎΠ΅ΠΌΠ°Ρ
Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΠΌΠ΅Ρ
Π°Π½ΠΈΠΊΠΈ ΠΆΠΈΠ΄ΠΊΠΎΡΡΠΈ
ΠΈ ΡΠ΅ΠΏΠ»ΠΎΠΏΠ΅ΡΠ΅Π½ΠΎΡΠ° Ρ ΡΡΠ΅ΡΠΎΠΌ ΡΠΏΠ΅ΡΠΈΡΠΈΠΊΠΈ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΠΌΡΡ
Π·Π°Π΄Π°Ρ. ΠΠ»Ρ ΡΠΈΡΠ»Π΅Π½Π½ΠΎΠ³ΠΎ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π³ΠΈΠ΄ΡΠΎΡΠ΅ΡΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ΅ΠΆΠΈΠΌΠ° ΠΡΠ°ΡΠ½ΠΎΡΡΡΠΊΠΎΠ³ΠΎ Π²ΠΎΠ΄ΠΎΡ
ΡΠ°Π½ΠΈΠ»ΠΈΡΠ° ΠΏΡΠΈΠΌΠ΅Π½ΡΠ΅ΡΡΡ ΡΡ
Π΅ΠΌΠ° Π»ΠΎΠΆΠ° Π²ΠΎΠ΄ΠΎΡ
ΡΠ°Π½ΠΈΠ»ΠΈΡΠ° Π² Π²ΠΈΠ΄Π΅ ΡΠ°ΠΉΠΎΠ½ΠΎΠ² Ρ Π½Π΅ΠΏΡΠ΅ΡΡΠ²Π½ΡΠΌ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ΠΌ Π³Π»ΡΠ±ΠΈΠ½Ρ ΠΈ ΡΠΊΠ°ΡΠΊΠΎΠΎΠ±ΡΠ°Π·Π½ΡΠΌ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ΠΌ ΡΠΈΡΠΈΠ½Ρ.
Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ ΡΠΈΡΠ»Π΅Π½Π½ΡΠΉ Π°Π»Π³ΠΎΡΠΈΡΠΌ Π΄Π»Ρ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π΄Π²ΡΠΌΠ΅ΡΠ½ΡΡ
Π² Π²Π΅ΡΡΠΈΠΊΠ°Π»ΡΠ½ΠΎΠΉ ΠΏΠ»ΠΎΡΠΊΠΎΡΡΠΈ
ΡΡΡΠ°ΡΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΠ΅ΡΠ΅Π½ΠΈΠΉ Π² ΠΏΡΠΎΡΠΎΡΠ½ΡΡ
Π²ΠΎΠ΄ΠΎΠ΅ΠΌΠ°Ρ
Π² ΠΏΠ΅ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ
ΡΡΠ½ΠΊΡΠΈΠΈ ΡΠΎΠΊΠ°. ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π° ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈΠ·Π°ΡΠΈΡ ΠΊΠΎΡΡΡΠΈΡΠΈΠ΅Π½ΡΠΎΠ² Π²Π΅ΡΡΠΈΠΊΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΡΡΡΠ±ΡΠ»Π΅Π½ΡΠ½ΠΎΠ³ΠΎ ΠΎΠ±ΠΌΠ΅Π½Π°. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΠΏΡΠΈΠΌΠ΅ΡΡ
ΡΠ°ΡΡΠ΅ΡΠΎΠ² ΡΠ΅ΡΠ΅Π½ΠΈΠΉ Π½Π° ΠΏΡΠΈΠΏΠ»ΠΎΡΠΈΠ½Π½ΠΎΠΌ ΡΡΠ°ΡΡΠΊΠ΅ ΠΡΠ°ΡΠ½ΠΎΡΡΡΠΊΠΎΠ³ΠΎ Π²ΠΎΠ΄ΠΎΡ
ΡΠ°Π½ΠΈΠ»ΠΈΡΠ°. Π§ΠΈΡΠ»Π΅Π½Π½Π°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ
ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΠΈΡΡ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΡ Π²ΠΎΠ΄Ρ, ΠΏΠΎΡΡΡΠΏΠ°ΡΡΠ΅ΠΉ Π² Π²ΠΎΠ΄ΠΎΠ·Π°Π±ΠΎΡΠ½ΡΠ΅ ΠΎΡΠ²Π΅ΡΡΡΠΈΡ, Π² Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΠΎΡ ΡΡΡΠ°ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ, ΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ Π²ΠΎΠ΄ΠΎΠ·Π°Π±ΠΎΡΠ°, ΡΠ°ΡΡ
ΠΎΠ΄Π° Π²ΠΎΠ΄