Lines Matching refs:kappa

232 …assically defined by $\mathrm{Pe}_h = \lVert \bm u \rVert h / (2 \kappa)$ where $\kappa$ is the di…
236 \mathrm{Pe} = \frac{\lVert \bm u \rVert^2}{\lVert \bm u_{\bm X} \rVert \kappa}.
286 + \frac{\kappa^2 \Vert \bm g \Vert_F ^2}{C_d} \right]^{-1/2}
525 \frac{\partial E}{\partial t} + \nabla \cdot (\bm{u} E ) - \kappa \nabla E = 0 \, ,
528 with $\bm{u}$ the vector velocity field and $\kappa$ the diffusion coefficient.
682 …enter velocity, $T_w$ is the temperature at the wall, $Pr=\frac{\mu}{c_p \kappa}$ is the Prandlt n…
726 \bm{v}' &= 2 \sqrt{3/2} \sum^N_{n=1} \sqrt{q^n(\bm{x})} \bm{\sigma}^n \cos(\kappa^n \bm{d}^n \cdot …
727 \bm{\hat{x}}^n &= \left[(x - U_0 t)\max(2\kappa_{\min}/\kappa^n, 0.1) , y, z  \right]^T
734 wavemode amplitude $q^n$, wavemode frequency $\kappa^n$, and $\kappa_{\min} =
748 \kappa^n = \kappa_{\min} (1 + \alpha)^{n-1} \ , \quad \forall n=1, 2, ... , N
751 The wavemode amplitudes $q^n$ are defined by a model energy spectrum $E(\kappa)$:
754 q^n = \frac{E(\kappa^n) \Delta \kappa^n}{\sum^N_{n=1} E(\kappa^n)\Delta \kappa^n} \ ,\quad \Delta \…
757 $$ E(\kappa) = \frac{(\kappa/\kappa_e)^4}{[1 + 2.4(\kappa/\kappa_e)^2]^{17/6}} f_\eta f_{\mathrm{cu…
760 f_\eta = \exp \left[-(12\kappa /\kappa_\eta)^2 \right], \quad
761 f_\mathrm{cut} = \exp \left( - \left [ \frac{4\max(\kappa-0.9\kappa_\mathrm{cut}, 0)}{\kappa_\mathr…
862 | $\{\kappa^n\}_{n=1}^N$                         | k^n      | No             | Yes       |