fronts.D.brooks_and_corey
- fronts.D.brooks_and_corey(n, l=1.0, alpha=1.0, Ks=None, k=None, nu=1e-06, g=9.81, theta_range=(0.0, 1.0))
Return a Brooks and Corey moisture diffusivity function.
Given the saturated hydraulic conductivity \(K_S\) and parameters \(\alpha\), n, l, \(\theta_r\) and \(\theta_s\), the Brooks and Corey moisture diffusivity function D is defined as:
\[D(\theta) = \frac{K_S S_e^{1/n + l + 1}} {\alpha n (\theta_s-\theta_r)}\]where:
\[S_e = \frac{\theta-\theta_r}{\theta_s-\theta_r}\]and \(\theta\) is water content.
- Parameters:
n (float) – n parameter.
l (float, optional) – l parameter. The default is 1.
alpha (float, optional) – \(\alpha\) parameter. The default is 1. Must be positive.
Ks (None or float, optional) – \(K_S\), the saturated hydraulic conductivity. Must be positive. If neither Ks nor k are given, the saturated hydraulic conductivity is assumed to be 1.
k (None or float, optional) – Intrinsic permeability of the porous medium. Can be given in place of Ks, which results in the saturated hydraulic conductivity being computed using \(K_S = kg/\nu\). Must be positive.
nu (float, optional) – \(\nu\), the kinematic viscosity of the wetting fluid. Only used if k is passed instead of Ks. Must be positive. Defaults to 1e-6, approximately the kinematic viscosity of water at 20°C in SI units.
g (float, optional) – Magnitude of the gravitational acceleration. Only used if k is passed instead of Ks. Must be positive. Defaults to 9.81, the gravity of Earth in SI units.
theta_range (sequence of two floats, optional) – (\(\theta_r\), \(\theta_s\)), where \(\theta_r\) is the minimum (also known as residual) water content and \(\theta_s\) is the maximum water content. The default is (0, 1). \(\theta_s\) must be greater than \(\theta_r\).
- Returns:
D –
Function to evaluate \(D\) and its derivatives:
D(theta)
evaluates and returns \(D\) attheta
D(theta, 1)
returns both the value of \(D\) and its first derivative attheta
D(theta, 2)
returns the value of \(D\), its first derivative, and its second derivative attheta
In all cases, the argument
theta
may be a single float or a NumPy array.- Return type:
callable
References
[1] BROOKS, R.; COREY, T. Hydraulic properties of porous media. Hydrology Papers, Colorado State University, 1964, vol. 24, p. 37.