Lines Matching refs:kappa

236 …assically defined by $\mathrm{Pe}_h = \lVert \bm u \rVert h / (2 \kappa)$ where $\kappa$ is the di…
240 \mathrm{Pe} = \frac{\lVert \bm u \rVert^2}{\lVert \bm u_{\bm X} \rVert \kappa}.
292 …\tau = \textrm{minreg}_2 \left\{\frac{\Delta t}{2 C_t},\ \frac{h}{aC_a}, \ \frac{h^2}{\kappa C_d} …
301 …_t}, \frac{1}{C_a \sqrt{\bm u \cdot (\bm u \cdot  \bm g)}}, \frac{1}{C_d \kappa \Vert \bm g \Vert_…
302 …{\Delta t}\right)^2 + C_a^2 \bm u \cdot (\bm u \cdot  \bm g) + \left(C_d \kappa\right)^2 \Vert \bm…
520 \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 …
521 \bm{\hat{x}}^n &= \left[(x - U_0 t)\max(2\kappa_{\min}/\kappa^n, 0.1) , y, z  \right]^T
525 …T$ ), bulk velocity $U_0$, wavemode amplitude $q^n$, wavemode frequency $\kappa^n$, and $\kappa_{\…
537 \kappa^n = \kappa_{\min} (1 + \alpha)^{n-1} \ , \quad \forall n=1, 2, ... , N
540 The wavemode amplitudes $q^n$ are defined by a model energy spectrum $E(\kappa)$:
543 q^n = \frac{E(\kappa^n) \Delta \kappa^n}{\sum^N_{n=1} E(\kappa^n)\Delta \kappa^n} \ ,\quad \Delta \…
546 $$ E(\kappa) = \frac{(\kappa/\kappa_e)^4}{[1 + 2.4(\kappa/\kappa_e)^2]^{17/6}} f_\eta f_{\mathrm{cu…
549 f_\eta = \exp \left[-(12\kappa /\kappa_\eta)^2 \right], \quad
550 f_\mathrm{cut} = \exp \left( - \left [ \frac{4\max(\kappa-0.9\kappa_\mathrm{cut}, 0)}{\kappa_\mathr…
641 | $\{\kappa^n\}_{n=1}^N$                         | k^n      | No             | Yes       |