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TABLE II.

Values and physical meanings of the variables in Eqs. (9) and (10).

Variable	Calculation formula	Physical meaning
μ_t	$ρ c_{μ} \frac{k^{2}}{ε}$	Turbulent viscosity
M_t	$\sqrt{k / a^{2}}$	Turbulent Mach number
G_k	$μ_{t} (\frac{\partial v_{i}}{\partial x_{j}} + \frac{\partial v_{j}}{\partial x_{i}}) \frac{\partial v_{i}}{\partial x_{j}}$	Turbulent kinetic energy produced by the average velocity gradient
G_b	$β g \frac{μ_{t}}{P r_{t}} \frac{\partial T}{\partial y}$	Turbulent kinetic energy produced by the buoyancy force
Y_M	$2 ρ ε M_{t}^{2}$	Fluctuation effect on the total dissipation rate in a compressible flow
σ_k	1	Model constant
σ_ε	1.2	Model constant
c₁	$max (0.43, \frac{η}{η + 5})$	Model constant
η	$\frac{k}{ε} \sqrt{(2 S_{i j} \cdot S_{i j})}$	Turbulent time scale divided by the time-averaged strain rate of air
S_ij	$\frac{1}{2} (\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}})$	Time-averaged strain rate of air
c₂	1.9	Model constant
c_1ε	1.44	Model constant
c_3ε	$tanh (V_{⊥ g} / v)$	Buoyancy effect on ε

Variable	Calculation formula	Physical meaning
μ_t	$ρ c_{μ} \frac{k^{2}}{ε}$	Turbulent viscosity
M_t	$\sqrt{k / a^{2}}$	Turbulent Mach number
G_k	$μ_{t} (\frac{\partial v_{i}}{\partial x_{j}} + \frac{\partial v_{j}}{\partial x_{i}}) \frac{\partial v_{i}}{\partial x_{j}}$	Turbulent kinetic energy produced by the average velocity gradient
G_b	$β g \frac{μ_{t}}{P r_{t}} \frac{\partial T}{\partial y}$	Turbulent kinetic energy produced by the buoyancy force
Y_M	$2 ρ ε M_{t}^{2}$	Fluctuation effect on the total dissipation rate in a compressible flow
σ_k	1	Model constant
σ_ε	1.2	Model constant
c₁	$max (0.43, \frac{η}{η + 5})$	Model constant
η	$\frac{k}{ε} \sqrt{(2 S_{i j} \cdot S_{i j})}$	Turbulent time scale divided by the time-averaged strain rate of air
S_ij	$\frac{1}{2} (\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}})$	Time-averaged strain rate of air
c₂	1.9	Model constant
c_1ε	1.44	Model constant
c_3ε	$tanh (V_{⊥ g} / v)$	Buoyancy effect on ε