ave_linear_eos

type, public, extends(equation_of_state) :: ave_linear_eos

A linearised implementation of the equation of state which has been horizontally-integrated. The basic equation of stateis $\rho(x,y) = \rho_0[1-\beta_T(T(x,y)-T_0) + \beta_S(S(x,y)-S_0)].$

Inherits

Help

Components

Type	Visibility		Name		Initial
real(kind=r8),	private	::	ref_rho	=	1.0_r8	The density for the temperature and salinity about which the equation of state was linearised, $\rho_0$ .
real(kind=r8),	private	::	ref_t	=	0.0_r8	The temperature about which the equation of state was linearised, $T_0$ .
real(kind=r8),	private	::	ref_s	=	0.0_r8	The salinity about which the equation of state was linearised, $S_0$ .
real(kind=r8),	private	::	beta_t	=	0.0_r8	The thermal contraction coefficient, $\beta_T$ .
real(kind=r8),	private	::	beta_s	=	1.0_r8	The haline contraction coefficient, $\beta_S$ .
real(kind=r8),	private	::	a_DS	=	1.0_r8	The shape coefficient for a horizontally-integrated model. It is defined as $\alpha_{DS} = \frac{1}{y_2 - y_1} \int^{y_2}_{y_1} f_{D}f_S dy,$ where $f_{D}(y)$ and $f_S(y)$ are the shapes of the variables $D$ and $S$ in the transverse direction.
real(kind=r8),	private	::	a_DT	=	1.0_r8	The shape coefficient for a horizontally-integrated model. It is defined as $\alpha_{DT} = \frac{1}{y_2 - y_1} \int^{y_2}_{y_1} f_{D}f_T dy,$ where $f_{D}(y)$ and $f_T(y)$ are the shapes of the variables $D$ and $T$ in the transverse direction.
real(kind=r8),	private	::	a_DS_t	=	1.0_r8	The shape coefficient for a horizontally-integrated model. It is defined as $\tilde{\alpha}_{DS} = \frac{1}{\alpha_{D^2}(y_2 - y_1)} \int^{y_2}_{y_1} f^2_{D}f_S dy,$ where $f_{D}(y)$ and $f_S(y)$ are the shapes of the variables $D$ and $S$ in the transverse direction and $\alpha_{D^2} = \frac{1}{y_2 - y_1}\int^{y_2}_{y_1}f_D^2dy.$
real(kind=r8),	private	::	a_DT_t	=	1.0_r8	The shape coefficient for a horizontally-integrated model. It is defined as $\tilde{\alpha}_{DT} = \frac{1}{\alpha_{D^2}(y_2 - y_1)} \int^{y_2}_{y_1} f^2_{D}f_T dy,$ where $f_{D}(y)$ and $f_T(y)$ are the shapes of the variables $D$ and $T$ in the transverse direction and $\alpha_{D^2} = \frac{1}{y_2 - y_1}\int^{y_2}_{y_1}f_D^2dy.$

Constructor

public interface ave_linear_eos

private pure function constructor(ref_rho, ref_t, ref_s, beta_t, beta_s, a_DS, a_DT, a_DS_t, a_DT_t) result(this)

Arguments

Type	Intent	Optional		Name
real(kind=r8),	intent(in)		::	ref_rho	The density for the temperature and salinity about which the equation of state was linearised, $\rho_0$ .
real(kind=r8),	intent(in)		::	ref_t	The temperature about which the equation of state was linearised, $T_0$ .
real(kind=r8),	intent(in)		::	ref_s	The salinity about which the equation of state was linearised, $S_0$ .
real(kind=r8),	intent(in)		::	beta_t	The thermal contraction coefficient, $\beta_T$ .
real(kind=r8),	intent(in)		::	beta_s	The haline contraction coefficient, $\beta_S$ .
real(kind=r8),	intent(in),	optional	::	a_DS	The shape coefficient for a horizontally-integrated model. It is defined as $\alpha_{DS} = \frac{1}{y_2 - y_1} \int^{y_2}_{y_1} f_{D}f_S dy,$ where $f_{D}(y)$ and $f_S(y)$ are the shapes of the variables $D$ and $S$ in the transverse direction. Defualt value is 1.
real(kind=r8),	intent(in),	optional	::	a_DT	The shape coefficient for a horizontally-integrated model. It is defined as $\alpha_{DT} = \frac{1}{y_2 - y_1} \int^{y_2}_{y_1} f_{D}f_T dy,$ where $f_{D}(y)$ and $f_T(y)$ are the shapes of the variables $D$ and $T$ in the transverse direction. Defualt value is 1.
real(kind=r8),	intent(in),	optional	::	a_DS_t	The shape coefficient for a horizontally-integrated model. It is defined as $\tilde{\alpha}_{DS} = \frac{1}{\alpha_{D^2}(y_2 - y_1)} \int^{y_2}_{y_1} f^2_{D}f_S dy,$ where $f_{D}(y)$ and $f_S(y)$ are the shapes of the variables $D$ and $S$ in the transverse direction and $\alpha_{D^2} = \frac{1}{y_2 - y_1}\int^{y_2}_{y_1}f_D^2dy.$ Defualt value is 1.
real(kind=r8),	intent(in),	optional	::	a_DT_t	The shape coefficient for a horizontally-integrated model. It is defined as $\tilde{\alpha}_{DT} = \frac{1}{\alpha_{D^2}(y_2 - y_1)} \int^{y_2}_{y_1} f^2_{D}f_T dy,$ where $f_{D}(y)$ and $f_T(y)$ are the shapes of the variables $D$ and $T$ in the transverse direction and $\alpha_{D^2} = \frac{1}{y_2 - y_1}\int^{y_2}_{y_1}f_D^2dy.$ Defualt value is 1.

Return Value type(ave_linear_eos)

Type-Bound Procedures

procedure, public :: water_density => linear_water_density

private function linear_water_density(this, temperature, salinity) result(density)

Author: Chris MacMackin
Date: August 2018

Calculates the density of the water from the temperature and salinity, using a linear equation of state, $\rho(x,y) = \rho_0[1-\beta_T(T(x,y)-T_0) + \beta_S(S(x,y)-S_0)].$

Arguments

Type	Intent		Name
class(ave_linear_eos),	intent(in)	::	this
class(scalar_field),	intent(in)	::	temperature	A field containing the temperature of the water
class(scalar_field),	intent(in)	::	salinity	A field containing the salinity of the water

Return Value class(scalar_field), pointer

A field containing the density of the water

procedure, public :: water_density_ave1 => linear_water_density_ave1

private function linear_water_density_ave1(this, temperature, salinity) result(density)

Author: Chris MacMackin
Date: August 2018

Calculates one form of the horizontally-averaged density of the water from the temperature and salinity, using a linear equation of state, $\bar{rho}(x) = \rho_0[1-\beta_T(\alpha_{DT}T(x)-T_0) + \beta_S(\alpha_{DS}S(x)-S_0)].$

Arguments

Type	Intent		Name
class(ave_linear_eos),	intent(in)	::	this
class(scalar_field),	intent(in)	::	temperature	A field containing the temperature of the water
class(scalar_field),	intent(in)	::	salinity	A field containing the salinity of the water

Return Value class(scalar_field), pointer

A field containing the density of the water

procedure, public :: water_density_ave2 => linear_water_density_ave2

private function linear_water_density_ave2(this, temperature, salinity) result(density)

Author: Chris MacMackin
Date: August 2018

Calculates another form of the horizontally-averaged density of the water from the temperature and salinity, using a linear equation of state, $\tilde{\rho}(x) = \rho_0[1-\beta_T(\tilde{\alpha}_{DT}T(x)-T_0) + \beta_S(\tilde{\alpha}_{DS}S(x)-S_0)].$

Arguments

Type	Intent		Name
class(ave_linear_eos),	intent(in)	::	this
class(scalar_field),	intent(in)	::	temperature	A field containing the temperature of the water
class(scalar_field),	intent(in)	::	salinity	A field containing the salinity of the water

Return Value class(scalar_field), pointer

A field containing the density of the water

procedure, public :: water_density_derivative => linear_water_deriv

private function linear_water_deriv(this, temperature, d_temperature, salinity, d_salinity, dir) result(d_density)

Author: Chris MacMackin
Date: August 2018

Calculates the derivative of the average water density from the temperature and salinity, using a linear equation of state with the second type of averaging, $\tilde{\rho} = \rho_0[1-\beta_T(\tilde{\alpha}_{DT}T-T_0) + \beta_S(\tilde{\alpha}_{DS}S-S_0)].$

Arguments

Type	Intent		Name
class(ave_linear_eos),	intent(in)	::	this
class(scalar_field),	intent(in)	::	temperature	A field containing the temperature of the water
class(scalar_field),	intent(in)	::	d_temperature	A field containing the derivative of the temperature of the water, in teh same direction as `dir`
class(scalar_field),	intent(in)	::	salinity	A field containing the salinity of the water
class(scalar_field),	intent(in)	::	d_salinity	A field containing the derivative of the salinity of the water, in the same direction as `dir`
integer,	intent(in)	::	dir	The direction in which to take the derivative

Return Value class(scalar_field), pointer

A field containing the density of the water

procedure, public :: haline_contraction => linear_haline_contraction

private function linear_haline_contraction(this, temperature, salinity) result(coef)

Author: Chris MacMackin
Date: August 2018

Returns the haline contraction coefficient.

Arguments

Type	Intent		Name
class(ave_linear_eos),	intent(in)	::	this
class(scalar_field),	intent(in)	::	temperature
class(scalar_field),	intent(in)	::	salinity

Return Value class(scalar_field), allocatable

procedure, public :: thermal_contraction => linear_thermal_contraction

private function linear_thermal_contraction(this, temperature, salinity) result(coef)

Author: Chris MacMackin
Date: August 2018

Returns the thermal contraction coefficient.

Arguments

Type	Intent		Name
class(ave_linear_eos),	intent(in)	::	this
class(scalar_field),	intent(in)	::	temperature
class(scalar_field),	intent(in)	::	salinity

Return Value class(scalar_field), allocatable

Source Code

  type, extends(equation_of_state), public :: ave_linear_eos
    !* Author: Chris MacMackin
    !  Date: August 2018
    !
    ! A linearised implementation of the equation of state which has
    ! been horizontally-integrated. The basic equation of stateis $$
    ! \rho(x,y) = \rho_0[1-\beta_T(T(x,y)-T_0) +
    ! \beta_S(S(x,y)-S_0)]. $$
    !
    private
    real(r8) :: ref_rho = 1.0_r8
      !! The density for the temperature and salinity about which the
      !! equation of state was linearised, \(\rho_0\).
    real(r8) :: ref_t = 0.0_r8
      !! The temperature about which the equation of state was
      !! linearised, \(T_0\).
    real(r8) :: ref_s = 0.0_r8
      !! The salinity about which the equation of state was
      !! linearised, \(S_0\).
    real(r8) :: beta_t = 0.0_r8
      !! The thermal contraction coefficient, \(\beta_T\).
    real(r8) :: beta_s = 1.0_r8
      !! The haline contraction coefficient, \(\beta_S\).
    real(r8) :: a_DS = 1.0_r8
      !! The shape coefficient for a horizontally-integrated model. It
      !! is defined as $$\alpha_{DS} = \frac{1}{y_2 - y_1}
      !! \int^{y_2}_{y_1} f_{D}f_S dy, $$ where \(f_{D}(y)\) and
      !! \(f_S(y)\) are the shapes of the variables \(D\) and \(S\) in
      !! the transverse direction.
    real(r8) :: a_DT = 1.0_r8
      !! The shape coefficient for a horizontally-integrated model. It
      !! is defined as $$\alpha_{DT} = \frac{1}{y_2 - y_1}
      !! \int^{y_2}_{y_1} f_{D}f_T dy, $$ where \(f_{D}(y)\) and
      !! \(f_T(y)\) are the shapes of the variables \(D\) and \(T\) in
      !! the transverse direction.
    real(r8) :: a_DS_t = 1.0_r8
      !! The shape coefficient for a horizontally-integrated model. It
      !! is defined as $$\tilde{\alpha}_{DS} =
      !! \frac{1}{\alpha_{D^2}(y_2 - y_1)} \int^{y_2}_{y_1} f^2_{D}f_S
      !! dy, $$ where \(f_{D}(y)\) and \(f_S(y)\) are the shapes of
      !! the variables \(D\) and \(S\) in the transverse direction and
      !! $$\alpha_{D^2} = \frac{1}{y_2 -
      !! y_1}\int^{y_2}_{y_1}f_D^2dy.$$
    real(r8) :: a_DT_t = 1.0_r8
      !! The shape coefficient for a horizontally-integrated model. It
      !! is defined as $$\tilde{\alpha}_{DT} =
      !! \frac{1}{\alpha_{D^2}(y_2 - y_1)} \int^{y_2}_{y_1} f^2_{D}f_T
      !! dy, $$ where \(f_{D}(y)\) and \(f_T(y)\) are the shapes of
      !! the variables \(D\) and \(T\) in the transverse direction and
      !! $$\alpha_{D^2} = \frac{1}{y_2 -
      !! y_1}\int^{y_2}_{y_1}f_D^2dy.$$
  contains
    procedure :: water_density => linear_water_density
    procedure :: water_density_ave1 => linear_water_density_ave1
    procedure :: water_density_ave2 => linear_water_density_ave2
    procedure :: water_density_derivative => linear_water_deriv
    procedure :: haline_contraction => linear_haline_contraction
    procedure :: thermal_contraction => linear_thermal_contraction
  end type ave_linear_eos

ave_linear_eos Derived Type

Contents

Variables

Constructor

Type-Bound Procedures

Source Code

type, public, extends(equation_of_state) :: ave_linear_eos

Inherits

Contents

Variables

Constructor

Type-Bound Procedures

Source Code

Components

Constructor

public interface ave_linear_eos

private pure function constructor(ref_rho, ref_t, ref_s, beta_t, beta_s, a_DS, a_DT, a_DS_t, a_DT_t) result(this)

Arguments

Return Value type(ave_linear_eos)

Type-Bound Procedures

procedure, public :: water_density => linear_water_density

private function linear_water_density(this, temperature, salinity) result(density)

Arguments

Return Value class(scalar_field), pointer

procedure, public :: water_density_ave1 => linear_water_density_ave1

private function linear_water_density_ave1(this, temperature, salinity) result(density)

Arguments

Return Value class(scalar_field), pointer

procedure, public :: water_density_ave2 => linear_water_density_ave2

private function linear_water_density_ave2(this, temperature, salinity) result(density)

Arguments

Return Value class(scalar_field), pointer

procedure, public :: water_density_derivative => linear_water_deriv

private function linear_water_deriv(this, temperature, d_temperature, salinity, d_salinity, dir) result(d_density)

Arguments

Return Value class(scalar_field), pointer

procedure, public :: haline_contraction => linear_haline_contraction

private function linear_haline_contraction(this, temperature, salinity) result(coef)

Arguments

Return Value class(scalar_field), allocatable

procedure, public :: thermal_contraction => linear_thermal_contraction

private function linear_thermal_contraction(this, temperature, salinity) result(coef)

Arguments

Return Value class(scalar_field), allocatable

Source Code