commit d56d6a44e424f1229908669101f6dbbd0c1e67bc
parent 028a90c6e8e30d05fcdc917534a1dfdaff1d914e
Author: Ivan Gankevich <igankevich@ya.ru>
Date: Mon, 29 May 2017 17:34:05 +0300
Edit pressure sections of related work.
Diffstat:
| arma.org | | | 32 | ++++++++++++++++---------------- |
1 file changed, 16 insertions(+), 16 deletions(-)
diff --git a/arma.org b/arma.org
@@ -176,18 +176,18 @@ multi-dimensional stochastic process that is real only statistically.
** Pressure field determination formulae
**** Small amplitude waves theory.
-In\nbsp{}cite:stab2012,degtyarev1998modelling,degtyarev1997analysis the
-authors propose a solution for inverse problem of hydrodynamics of potential
-flow in the framework of small-amplitude wave theory (under assumption that wave
-length is much larger than height: \(\lambda \gg h\)). In that case inverse
-problem is linear and reduces to Laplace equation with mixed boundary
-conditions, and equation of motion is solely used to determine pressures for
-calculated velocity potential derivatives. The assumption of small amplitudes
-means the slow decay of wind wave coherence function, i.e. small change of local
-wave number in time and space compared to the wavy surface elevation (\(z\)
-coordinate). This assumption allows to calculate elevation \(z\) derivative as
-\(\zeta_z=k\zeta\), where \(k\) is wave number. In two-dimensional case the
-solution is written explicitly as
+In\nbsp{}cite:stab2012,degtyarev1998modelling,degtyarev1997analysis the authors
+propose a solution for inverse problem of hydrodynamics of potential flow within
+the framework of small-amplitude wave theory (under assumption that wave length
+is much larger than height: \(\lambda{}\gg{}h\)). In that case inverse problem
+is linear and reduces to Laplace equation with mixed boundary conditions, and
+equation of motion is solely used to determine pressures for calculated velocity
+potential derivatives. The assumption of small amplitudes means the slow decay
+of wind wave coherence function, i.e.\nbsp{}small change of local wave number in
+time and space compared to the wavy surface elevation (\(z\) coordinate). This
+assumption allows to calculate elevation \(z\) derivative as \(\zeta_z=k\zeta\),
+where \(k\) is wave number. In two-dimensional case the solution is written
+explicitly as
\begin{align}
\left.\frac{\partial\phi}{\partial x}\right|_{x,t}= &
-\frac{1}{\sqrt{1+\alpha^{2}}}e^{-I(x)}
@@ -217,10 +217,10 @@ the form of elliptic partial differential equation (PDE):
The authors suggest transforming this equation to finite differences and solve
it numerically.
-As will be shown in [[#sec:compare-formulae]] that eqref:eq-old-sol-2d diverges when
-attempted to calculate velocity field for large-amplitude waves, and this is the
-reason that it can not be used together with ARMA model, that generates
-arbitrary-amplitude waves.
+As will be shown in sec.\nbsp{}[[#sec:compare-formulae]]
+that\nbsp{}eqref:eq-old-sol-2d diverges when attempted to calculate velocity
+field for large amplitude waves, and this is the reason that it can not be used
+together with ARMA model, that generates arbitrary amplitude waves.
**** Linearisation of boundary condition.
:PROPERTIES:
