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B Previous Research
Numerical and Analytical Investigations
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analytical solution bottom friction factor boundary conditions Boundary Dam buoyancy buoyancy-driven flow closed-form solution Comparison continuity equation cooling lakes densimetric Froude number density gradients determined downflow equilibrium length expressions flow exchange friction factor ratio friction term governing equations Grashof number heat loss inertia term integrated momentum equation interfacial friction factor Jain Jain's model laminar and quasi-laminar laminar flow Laminar Regime long sidearm lower layer neglected obtained order of magnitude ordinary differential equations overpredicts partial differential equations present model present solution profile constants profile for temperature profile parameters profiles for velocity qo/kL qoAL quasi-laminar flow Quasi-Laminar Regime Reynolds number shear stress short sidearm shown in Figure sidearm circulation sidearm entrance sidearm flow Sidearm Length similarity profiles slope term Sturm and Kennedy surface cooling surface temperature temperature and velocity temperature profiles three flow regimes turbulent flow Turbulent Regime upper layer variables velocity and temperature velocity profile water-surface slope yields