kitagawa (version 3.1.2)

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

Value

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

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..

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

A. J. Barbour <[e-mail]>

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: $$D \equiv \frac{T}{S}$$

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.