dg::Lamb Struct Reference

\( f(x,y) = \begin{cases} 2\lambda U J_1(\lambda r) / J_0(\gamma)\cos(\theta) \text{ for } r<R \\ 0 \text{ else} \end{cases} \) More...

Public Member Functions
	Lamb (double x0, double y0, double R, double U)
	Functor returning a Lamb-dipole. More...
DG_DEVICE double	operator() (double x, double y) const
	Return the value of the dipole. More...
double	enstrophy () const
	The total enstrophy of the dipole. More...
double	energy () const
	The total energy of the dipole. More...

Detailed Description

\( f(x,y) = \begin{cases} 2\lambda U J_1(\lambda r) / J_0(\gamma)\cos(\theta) \text{ for } r<R \\ 0 \text{ else} \end{cases} \)

with \( r = \sqrt{(x-x_0)^2 + (y-y_0)^2}\), \( \theta = \arctan_2( (y-y_), (x-x_0))\), \(J_0, J_1\) are Bessel functions of the first kind of order 0 and 1 and \(\lambda = \gamma/R\) with \( \gamma = 3.83170597020751231561\) This is the Lamb dipole

Constructor & Destructor Documentation

Lamb()

dg::Lamb::Lamb ( double  x0, double  y0, double  R, double  U  )

inline

Functor returning a Lamb-dipole.

Parameters

x0	x-center-coordinate
y0	y-center-coordinate
R	radius of the dipole
U	speed of the dipole

Member Function Documentation

energy()

double dg::Lamb::energy ( ) const

inline

The total energy of the dipole.

Analytic formula. True for periodic and dirichlet boundary conditions.

Returns

energy \( 2\pi R^2U^2\)

enstrophy()

double dg::Lamb::enstrophy ( ) const

inline

The total enstrophy of the dipole.

Analytic formula. True for periodic and dirichlet boundary conditions.

Returns

enstrophy \( \pi U^2\gamma^2\)

operator()()

DG_DEVICE double dg::Lamb::operator() ( double  x, double  y  ) const

inline

Return the value of the dipole.

Parameters

x	x - coordinate
y	y - coordinate

Returns

Lamb

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The documentation for this struct was generated from the following file:

• functors.h