vulcan::wind_shear Namespace Reference

Namespaces
namespace	roughness
namespace	exponent

Functions
template<typename Scalar>
Scalar	linear (const Scalar &altitude, double base_wind, double base_altitude, double shear_rate)
	Linear wind shear profile.
template<typename Scalar>
wind::WindVector< Scalar >	linear_vector (const Scalar &altitude, const wind::WindVector< double > &base_wind, double base_altitude, double shear_rate)
	Linear wind shear returning full wind vector.
template<typename Scalar>
Scalar	power_law (const Scalar &altitude, double ref_wind, double ref_altitude=10.0, double exponent=1.0/7.0)
	Power-law wind profile (typical for atmospheric boundary layer).
template<typename Scalar>
wind::WindVector< Scalar >	power_law_vector (const Scalar &altitude, const wind::WindVector< double > &base_wind, double ref_altitude=10.0, double exponent=1.0/7.0)
	Power-law wind profile returning full wind vector.
template<typename Scalar>
Scalar	logarithmic (const Scalar &altitude, double friction_velocity, double roughness_length, double displacement=0.0)
	Logarithmic wind profile (neutral atmospheric boundary layer).
double	friction_velocity_from_ref (double ref_wind, double ref_altitude, double roughness_length, double displacement=0.0)
	Compute friction velocity from reference wind.

Variables
constexpr double	VON_KARMAN_CONSTANT = 0.41
	von Kármán constant for atmospheric boundary layer

Function Documentation

friction_velocity_from_ref()

double vulcan::wind_shear::friction_velocity_from_ref ( double ref_wind, double ref_altitude, double roughness_length, double displacement = 0.0 )

inline

Compute friction velocity from reference wind.

Given wind speed at a reference height, compute the friction velocity for use in logarithmic profile calculations.

u* = κ * V_ref / ln((h_ref - d) / z_0)

Parameters

ref_wind	Wind speed at reference height [m/s]
ref_altitude	Reference height [m]
roughness_length	Surface roughness z_0 [m]
displacement	Zero-plane displacement d [m]

Returns

Friction velocity u* [m/s]

linear()

template<typename Scalar>

Scalar vulcan::wind_shear::linear	(	const Scalar &	altitude,
		double	base_wind,
		double	base_altitude,
		double	shear_rate )

Linear wind shear profile.

Wind = W_0 + (dW/dh) * (h - h_0)

Template Parameters

Scalar

double or casadi::MX

Parameters

altitude	Altitude [m]
base_wind	Wind at reference altitude [m/s]
base_altitude	Reference altitude [m]
shear_rate	Wind change per unit altitude [1/s], i.e., dV/dh

Returns

Wind speed at given altitude [m/s]

linear_vector()

template<typename Scalar>

wind::WindVector< Scalar > vulcan::wind_shear::linear_vector	(	const Scalar &	altitude,
		const wind::WindVector< double > &	base_wind,
		double	base_altitude,
		double	shear_rate )

Linear wind shear returning full wind vector.

Scales the base wind vector by the altitude-dependent factor. Wind direction is preserved while magnitude changes linearly.

Template Parameters

Scalar

double or casadi::MX

Parameters

altitude	Altitude [m]
base_wind	Wind vector at reference altitude
base_altitude	Reference altitude [m]
shear_rate	Wind change per unit altitude [1/s]

Returns

WindVector scaled by altitude factor

logarithmic()

template<typename Scalar>

Scalar vulcan::wind_shear::logarithmic	(	const Scalar &	altitude,
		double	friction_velocity,
		double	roughness_length,
		double	displacement = 0.0 )

Logarithmic wind profile (neutral atmospheric boundary layer).

V(h) = (u* / κ) * ln((h - d) / z_0)

Where:

• u* = friction velocity [m/s]
• κ = von Kármán constant (≈ 0.41)
• d = zero-plane displacement [m] (for vegetation/urban areas)
• z_0 = roughness length [m]

Template Parameters

Scalar

double or casadi::MX

Parameters

altitude	Altitude above ground [m]
friction_velocity	Surface friction velocity u* [m/s]
roughness_length	Surface roughness z_0 [m]
displacement	Zero-plane displacement d [m] (default: 0)

Returns

Wind speed at altitude [m/s]

power_law()

template<typename Scalar>

Scalar vulcan::wind_shear::power_law	(	const Scalar &	altitude,
		double	ref_wind,
		double	ref_altitude = 10.0,
		double	exponent = 1.0 / 7.0 )

Power-law wind profile (typical for atmospheric boundary layer).

V(h) = V_ref * (h / h_ref)^alpha

Common exponents:

• α = 1/7 (0.143) - unstable/daytime conditions
• α = 1/4 (0.25) - neutral conditions
• α = 1/3 (0.33) - stable/nighttime conditions

Template Parameters

Scalar

double or casadi::MX

Parameters

altitude	Altitude above ground [m]
ref_wind	Wind speed at reference height [m/s]
ref_altitude	Reference height [m] (typically 10m)
exponent	Power law exponent α (default: 1/7 for unstable)

Returns

Wind speed at altitude [m/s]

power_law_vector()

template<typename Scalar>

wind::WindVector< Scalar > vulcan::wind_shear::power_law_vector	(	const Scalar &	altitude,
		const wind::WindVector< double > &	base_wind,
		double	ref_altitude = 10.0,
		double	exponent = 1.0 / 7.0 )

Power-law wind profile returning full wind vector.

Template Parameters

Scalar

double or casadi::MX

Parameters

altitude	Altitude above ground [m]
base_wind	Wind vector at reference height
ref_altitude	Reference height [m] (typically 10m)
exponent	Power law exponent α

Returns

WindVector scaled by power law

Variable Documentation

VON_KARMAN_CONSTANT

double vulcan::wind_shear::VON_KARMAN_CONSTANT = 0.41

inlineconstexpr

von Kármán constant for atmospheric boundary layer