SPINS Science Files

SPINS comes with a variety of Science files which help with simulation data analysis. Below is a list of currently available functions with a brief description of their purpose and the assumptions behind their implementation. These Science files are in spins/src/Science.

Unless otherwise mentioned, the functions below work for both unmapped and mapped domains where the mapping is along the bottom of the domain (where the bottom is at the 0-index in the z-dimension, as opposed to at the $N_{z}-1$ index). Another way to say this is that z increases with the index.

bottom_slope.cpp

Returns the vector of the bottom slope at each x-grid point. This is used for calculating the stresses along the bottom boundary (cf. bottom_stress_x.cpp and bottom_stress_y.cpp).

bottom_stress_x.cpp

Returns the 2D vector of the x-component of stress on the bottom boundary. The z boundary condition must be no slip.

If the case is unmapped:

$t_{x}=\mu u_{z}$

where $\mu$ is the dynamic viscosity.

If the case is mapped:

$t_{x}={\frac {\mu }{\alpha ^{2}(x)}}\left(2h'(x)(w_{z}-u_{x})+(u_{z}+w_{x})(1-h'^{2}(x))\right)$

where $\alpha (x)={\sqrt {1+h'^{2}(x)}}$ and where $h'(x)$ is the bottom slope.

bottom_stress_y.cpp

Returns the 2D vector of the y-component of stress on the bottom boundary. The z boundary condition must be no slip.

If the case is unmapped:

$t_{y}=\mu v_{z}$

where $\mu$ is the dynamic viscosity.

If the case is mapped:

$t_{y}={\frac {\mu }{\alpha (x)}}\left(v_{z}-h'(x)v_{x}\right)$

where $\alpha (x)={\sqrt {1+h'^{2}(x)}}$ and where $h'(x)$ is the bottom slope.

compute_Background_PE

Returns the value of the background potential energy,

$E_{b}=g\int _{V}\rho _{*}z_{*}dV$

where $z_{*}$ is the depth of an element of the sorted density field which minimized the potential energy (ie. $\rho _{*}$). For more information see Winters et al. (1995).

compute_BPE_from_internal.cpp

Returns the rate of energy transfer from internal energy into background potential energy.

$\phi _{i}=-g\kappa \int _{A}\rho (z=z_{u})-\rho (z=z_{l})dA$

where $z_{u}$ and $z_{l}$ are the depths of the upper and lower boundaries, respectively. The integral is taken over the horizontal extent. For more information see Winters et al. (1995).

compute_quadweights.cpp

Create the quadrature weights for each dimension.

If the boundary condition is no-slip, use the Clenshaw-Curtis quadrature weights:

$w=...$

If the boundary condition is free-slip, use the trapezoid rule:

$w=L_{x}/N_{x}=\Delta x$

compute_vorticity.cpp

Compute all vorticity components.

compute_vort_x.cpp

Compute the x-component of vorticity: $\omega _{x}=w_{y}-v_{z}$

compute_vort_y.cpp

Compute the y-component of vorticity: $\omega _{y}=u_{z}-w_{x}$

compute_vort_z.cpp

Compute the z-component of vorticity: $\omega _{z}=v_{x}-u_{y}$