Kinetic Energy Equation
Kinetic Energy Equation#
\(-c_3\mathrm{f}_1\boldsymbol{v}\cdot\boldsymbol{\nabla}\left(\frac{P}{\mathrm{f}_1}\right)\) |
1901 |
press_work |
\(-c_3\mathrm{f}_1\boldsymbol{v'}\cdot\boldsymbol{\nabla}\left(\frac{P'}{\mathrm{f}_1}\right)\) |
1902 |
press_work_pp |
\(-c_3\mathrm{f}_1\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\left(\frac{\overline{P}}{\mathrm{f}_1}\right)\) |
1903 |
press_work_mm |
\(c_2v_r\mathrm{f}_2\Theta\) |
1904 |
buoy_work |
\(c_2v'_r\mathrm{f}_2\Theta'\) |
1905 |
buoy_work_pp |
\(c_2\overline{v_r}\mathrm{f}_2\overline{\Theta}\) |
1906 |
buoy_work_mm |
\(c_5\boldsymbol{v}\cdot\left[\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal{D}}\right]\) |
1907 |
visc_work |
\(c_5\boldsymbol{v'}\cdot\left[\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal{D'}}\right]\) |
1908 |
visc_work_pp |
\(c_5\overline{\boldsymbol{v}}\cdot\left[\boldsymbol{\nabla}\cdot\overline{\boldsymbol{\mathcal{D}}}\right]\) |
1909 |
visc_work_mm |
\(\mathrm{f}_1\boldsymbol{v}\cdot\left[\boldsymbol{v}\cdot\boldsymbol{\nabla}\boldsymbol{v}\right]\) |
1910 |
advec_work |
\(\mathrm{f}_1\boldsymbol{v'}\cdot\left[\boldsymbol{v'}\cdot\boldsymbol{\nabla}\boldsymbol{v'}\right]\) |
1911 |
advec_work_ppp |
\(\mathrm{f}_1\overline{\boldsymbol{v}}\cdot\left[\boldsymbol{v'}\cdot\boldsymbol{\nabla}\boldsymbol{v'}\right]\) |
1912 |
advec_work_mpp |
\(\mathrm{f}_1\boldsymbol{v'}\cdot\left[\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\boldsymbol{v'}\right]\) |
1913 |
advec_work_pmp |
\(\mathrm{f}_1\boldsymbol{v'}\cdot\left[\boldsymbol{v'}\cdot\boldsymbol{\nabla}\overline{\boldsymbol{v}}\right]\) |
1914 |
advec_work_ppm |
\(\mathrm{f}_1\overline{\boldsymbol{v}}\cdot\left[\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\overline{\boldsymbol{v}}\right]\) |
1915 |
advec_work_mmm |
\(c_4\boldsymbol{v}\cdot\left[\left(\boldsymbol{\nabla}\times\boldsymbol{B}\right)\times\boldsymbol{B}\right]\) |
1916 |
mag_work |
\(c_4\boldsymbol{v'}\cdot\left[\left(\boldsymbol{\nabla}\times\boldsymbol{B'}\right)\times\boldsymbol{B'}\right]\) |
1918 |
mag_work_ppp |
\(c_4\overline{\boldsymbol{v}}\cdot\left[\left(\boldsymbol{\nabla}\times\boldsymbol{B'}\right)\times\boldsymbol{B'}\right]\) |
1919 |
mag_work_mpp |
\(c_4\boldsymbol{v'}\cdot\left[\left(\boldsymbol{\nabla}\times\overline{\boldsymbol{B}}\right)\times\boldsymbol{B'}\right]\) |
1920 |
mag_work_pmp |
\(c_4\boldsymbol{v'}\cdot\left[\left(\boldsymbol{\nabla}\times\boldsymbol{B'}\right)\times\overline{\boldsymbol{B}}\right]\) |
1921 |
mag_work_ppm |
\(c_4\overline{\boldsymbol{v}}\cdot\left[\left(\boldsymbol{\nabla}\times\overline{\boldsymbol{B}}\right)\times\overline{\boldsymbol{B}}\right]\) |
1922 |
mag_work_mmm |
\(\frac{1}{2}\mathrm{f}_1v_r\,v^2\) |
1923 |
ke_flux_radial |
\(\frac{1}{2}\mathrm{f}_1v_\theta\,v^2\) |
1924 |
ke_flux_theta |
\(\frac{1}{2}\mathrm{f}_1v_\phi\,v^2\) |
1925 |
ke_flux_phi |
\(\frac{1}{2}\mathrm{f}_1\,\overline{v_r}\,\overline{v}^2\) |
1926 |
mke_mflux_radial |
\(\frac{1}{2}\mathrm{f}_1\,\overline{v_\theta}\,\overline{v}^2\) |
1927 |
mke_mflux_theta |
\(\frac{1}{2}\mathrm{f}_1\,\overline{v_\phi}\,\overline{v}^2\) |
1928 |
mke_mflux_phi |
\(\frac{1}{2}\mathrm{f}_1\,\overline{v_r}\,{v'}^2\) |
1929 |
pke_mflux_radial |
\(\frac{1}{2}\mathrm{f}_1\,\overline{v_\theta}\,{v'}^2\) |
1930 |
pke_mflux_theta |
\(\frac{1}{2}\mathrm{f}_1\,\overline{v_\phi}\,{v'}^2\) |
1931 |
pke_mflux_phi |
\(\frac{1}{2}\mathrm{f}_1\,v'_r\,{v'}^2\) |
1932 |
pke_pflux_radial |
\(\frac{1}{2}\mathrm{f}_1\,v'_\theta\,{v'}^2\) |
1933 |
pke_pflux_theta |
\(\frac{1}{2}\mathrm{f}_1\,v'_\phi\,{v'}^2\) |
1934 |
pke_pflux_phi |
\(c_5\left[\boldsymbol{v}\cdot\boldsymbol{\mathcal{D}} \right]_r\) |
1935 |
visc_flux_r |
\(c_5\left[\boldsymbol{v}\cdot\boldsymbol{\mathcal{D}} \right]_\theta\) |
1936 |
visc_flux_theta |
\(c_5\left[\boldsymbol{v}\cdot\boldsymbol{\mathcal{D}} \right]_\phi\) |
1937 |
visc_flux_phi |
\(c_5\left[\boldsymbol{v'}\cdot\boldsymbol{\mathcal{D'}} \right]_r\) |
1938 |
visc_fluxpp_r |
\(c_5\left[\boldsymbol{v'}\cdot\boldsymbol{\mathcal{D'}} \right]_\theta\) |
1939 |
visc_fluxpp_theta |
\(c_5\left[\boldsymbol{v'}\cdot\boldsymbol{\mathcal{D'}} \right]_\phi\) |
1940 |
visc_fluxpp_phi |
\(c_5\left[\boldsymbol{\overline{v}}\cdot\boldsymbol{\overline{\mathcal{D}}} \right]_r\) |
1941 |
visc_fluxmm_r |
\(c_5\left[\boldsymbol{\overline{v}}\cdot\boldsymbol{\overline{\mathcal{D}}} \right]_\theta\) |
1942 |
visc_fluxmm_theta |
\(c_5\left[\boldsymbol{\overline{v}}\cdot\boldsymbol{\overline{\mathcal{D}}} \right]_\phi\) |
1943 |
visc_fluxmm_phi |
\(-c_3v_r P\) |
1944 |
press_flux_r |
\(-c_3v_\theta P\) |
1945 |
press_flux_theta |
\(-c_3v_\phi P\) |
1946 |
press_flux_phi |
\(-c_3v'_r P'\) |
1947 |
press_fluxpp_r |
\(-c_3v'_\theta P'\) |
1948 |
press_fluxpp_theta |
\(-c_3v'_\phi P'\) |
1949 |
press_fluxpp_phi |
\(-c_3\overline{v_r}\, \overline{P}\) |
1950 |
press_fluxmm_r |
\(-c_3\overline{v_\theta}\, \overline{P}\) |
1951 |
press_fluxmm_theta |
\(-c_3\overline{v_\phi}\, \overline{P}\) |
1952 |
press_fluxmm_phi |
\(--\) |
1953 |
production_shear_ke |
\(--\) |
1954 |
production_shear_pke |
\(--\) |
1955 |
production_shear_mke |