Changes between Version 4 and Version 5 of doc/tec/turbulence_parameterization
- Timestamp:
- Nov 20, 2018 9:46:17 AM (6 years ago)
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doc/tec/turbulence_parameterization
v4 v5 1 \varepsilon\varepsilon= Turbulence Paramereization =1 = Turbulence Parameterization = 2 2 3 [[NoteBox(warn,Page is under construction!)]] 4 5 Since r????, PALM can be operated as a RANS (Reynolds-averaged Navier-Stokes) model. 3 Since r2696, PALM can be operated as a RANS (Reynolds-averaged Navier-Stokes) model. 6 4 When running PALM as a RANS model, a different turbulence closure is used compared to the LES model where the turbulence kinetic energy (TKE) //e// is completely parameterized. 7 5 … … 11 9 which are described below. 12 10 11 Switching to the RANS parameterizaion is done by setting the namelist parameter //[/wiki/doc/app/inipar#rans_mode rans_mode] = .TRUE.//. 12 Selecting one of the available turbulence models is done via the namelist parameter [/wiki/doc/app/inipar#turbulence_closure turbulence_closure]. 13 14 13 15 == [=#tkel_model TKE-l model] == 14 16 15 The //TKE-l// model uses the following prognostic equation to calculate //e//: 17 The //TKE-l// model calculates the eddy diffusivities via the turbulence kinetic energy //e// and the mixing length //l//: 18 {{{ 19 #!Latex 20 \begin{align*} 21 K_\mathrm{m} &= c_0 \ l \ \sqrt{e}, \\ 22 K_\mathrm{h} &= \frac{K_\mathrm{m}}{\mathrm{Pr}}, 23 \end{align*} 24 }}} 25 where //Pr// denotes the Prandtl number. 26 The model constant //c//,,0,, is set to 0.55 by default, but can be altered via the namelist parameter [/wiki/doc/app/inipar#rans_const_c rans_const_c]. 27 28 The TKE is calculated using the following prognostic equation: 16 29 {{{ 17 30 #!Latex … … 22 35 - \frac{g}{\theta_{\mathrm{v},0}} K_\mathrm{h} \frac{\partial \theta_{\mathrm{v},0}}{\partial z} 23 36 + K_\mathrm{e} \frac{\partial^2 e}{\partial x_j^2} 24 - \varepsilon .37 - \varepsilon, 25 38 \end{equation*} 26 39 }}} 27 where //K//,, m,,, //K//,,h,,, and //K//,,e,, are the eddy diffusivities of momentum and heat, and the diffusivity coefficient of the TKE, respectively, which are calculated via40 where //K//,,e,, is defined as 28 41 {{{ 29 42 #!Latex 30 43 \begin{align*} 31 K_\mathrm{m} &= c_0 \ l \ \sqrt{e}, \\32 K_\mathrm{h} &= \frac{K_\mathrm{m}}{\mathrm{Pr}}, \\33 44 K_\mathrm{e} &= \frac{K_\mathrm{m}}{\sigma_e}, 34 45 \end{align*} … … 36 47 with //σ//,,e,, = 1. 37 48 This can be altered via the namelist parameter [/wiki/doc/app/inipar#rans_const_sigma rans_const_sigma]. 38 Here, //Pr// and //l// denote the Prandtl number and mixing length, respectively. 39 The model constant //c//,,0,, is set to 0.55 by default, but can be altered via the namelist parameter [/wiki/doc/app/inipar#rans_const_c rans_const_c]. 49 The dissipation rate //ε// of the TKE is calculated via 50 {{{ 51 #!Latex 52 \begin{equation*} 53 \varepsilon = c_0^3 \ e \ \frac{\sqrt{e}}{l}. 54 \end{equation*} 55 }}} 56 40 57 The mixing length is defined using the mixing length //l//,,B,, according to Blackadar (1962) and the Dyer-Businger function Φ,,m,, 41 58 {{{ … … 49 66 }}} 50 67 where //κ//, //f//, //U//,,g,,, //L//, and //z// denote the von-Karman constant, the Coriolis parameter, the geostrophic wind, the Monin-Obukhov length, and the height, respectively. 68 //l//,,wall,, defines an upper limit of the mixing length as the distance to the nearest solid surface (wall). 51 69 52 The dissipation rate of the TKE, ε, is calculated via53 {{{54 #!Latex55 \begin{equation*}56 \varepsilon = c_0^3 \ e \ \frac{\sqrt{e}}{l}.57 \end{equation*}58 }}}59 70 60 71 == [=#tkee_model TKE-ε model] == 61 72 62 The TKE-ε model uses an additional prognostic equation to calculate the dissipation rate ε of the TKE: 73 The //TKE-ε// model calculates the eddy diffusivities via the turbulence kinetic energy //e// and the dissipation rate //ε// of the TKE: 74 {{{ 75 #!Latex 76 \begin{align*} 77 K_\mathrm{m} &= c_0^4 \ \frac{e^2}{\varepsilon}, \\ 78 K_\mathrm{h} &= \frac{K_\mathrm{m}}{\mathrm{Pr}}, 79 \end{align*} 80 }}} 81 where //Pr// denotes the Prandtl number. 82 The model constant //c//,,0,, is set to 0.55 by default, but can be altered via the namelist parameter [/wiki/doc/app/inipar#rans_const_c rans_const_c]. 83 84 The TKE is calculated using the same prognostic equation as the //TKE-l// model. 85 The dissipation rate //ε// is calculated via the following prognostic equation: 63 86 {{{ 64 87 #!Latex … … 69 92 - c_3 \frac{\varepsilon}{e} \frac{g}{\theta_{\mathrm{v},0}} K_\mathrm{h} \frac{\partial \theta_{\mathrm{v},0}}{\partial z} 70 93 + K_\varepsilon \frac{\partial^2 \varepsilon}{\partial x_j^2} 71 - c_2 \frac{\varepsilon^2}{e} .94 - c_2 \frac{\varepsilon^2}{e}, 72 95 \end{equation*} 73 96 }}} 74 The diffusivity coefficient//K//,,ε,, is defined as97 where //K//,,ε,, is defined as 75 98 {{{ 76 99 #!Latex … … 81 104 with //σ//,,ε,, = 1.3. 82 105 This can be altered via the namelist parameter [/wiki/doc/app/inipar#rans_const_sigma rans_const_sigma]. 106 The model constants //c//,,1,,, //c//,,2,,, and //c//,,3,, are set to 1.44, 1.92, and 1.44, respectively. 107 These values can be altered via the namelist parameter [/wiki/doc/app/inipar#rans_const_c rans_const_c].
