omega_constants: Calculate any constants that depend on angular frequency...

View source: R/omega_constants.R

omega_constantsR Documentation

Calculate any constants that depend on angular frequency \omega

Description

This function accesses the appropriate method to calculate the \omega-dependent constant associated with the choice of c.type.

This function is not likely to be needed by the user.

Usage

omega_constants(omega = 0, c.type = c("alpha", "diffusivity_time"), ...)

## Default S3 method:
omega_constants(omega = 0, c.type = c("alpha", "diffusivity_time"), ...)

Arguments

omega

frequency, [rad/sec]

c.type

the constant to calculate

...

additional params passed to calculator. In the case of ctype="alpha", set S., T., Rs.; and, in the case of ctype="diffusivity_time", set D. or S., T..

Details

What is "omega"?

The name is in reference to radial frequency \omega, which is defined as

\omega \equiv 2 \pi / \tau

where \tau is the period of oscillation.

What is the "alpha" calculation?

The parameter \alpha is defined as

\alpha \equiv r_w \sqrt{\omega S / T}

where r_w is the radius of the well, where S is the storativity, and T is transmissivity. See the parameter ... for details on how to pass these values.

This definition is common to many papers on the topic. For example, it corresponds to Equation 12 in Kitagawa et al (2011). Because the computation of \alpha depends also on physical properties, additional parameters can be passed through (e.g. the transmissivity).

What is the "diffusivity_time" calculation?

This is a similar calculation to omega_norm. It uses the effective hydraulic diffusivity D, which is defined in this case as the ratio of transmissivity to storativity:

D \equiv \frac{T}{S}

Value

Values of the constant represented by c.type for the given parameters

Warnings Issued

In the case c.type='alpha', the parameters S., T., and Rs. should be passed; otherwise, values are assumed to ensure the calculation does not fail, and the results are essentially meaningless.

Warnings will be issued if any necessary parameters are missing, indicating default values were used.

Author(s)

A. J. Barbour <andy.barbour@gmail.com>

See Also

alpha_constants, well_response, and kitagawa-package for references and more background.

Other ConstantsCalculators: alpha_constants(), kitagawa-constants

Examples

# alpha
omega_constants() # default is alpha, but will give warnings about S., T., Rs.
omega_constants(T.=1,S.=1,Rs.=1)  # 0, no warnings
omega_constants(1:10)  # sequence, with warnings about S., T., Rs.
omega_constants(1:10,T.=1,S.=1,Rs.=1) # sequence, no warnings
# diffusivity time
omega_constants(c.type="diffusivity_time", D.=1)  # 0, no warnings
omega_constants(c.type="diff", D.=1)  # 0, no warnings (arg matching)
omega_constants(c.type="diff")  # 0, warnings about S., T. because no D.
omega_constants(c.type="diff", S.=1)  # 0, warnings about T. because no D. or S.

abarbour/kitagawa documentation built on Feb. 1, 2024, 2:49 p.m.