CELT Model
The Coupling Equations for linear tides (CELT) model computes internal-wave scattering over a series of topographic steps. It is a flexible model that can include (i) an arbitrary number of steps, (ii) realistic stratification that varies with horizontal location, (iii) forcing by either an incoming internal wave or a barotropic transport, (iv) vertical viscosity, and (v) the Coriolis force. Matlab functions I have written to solve the equations are:
Which can be tested using the example script:
test.mPlease contact me if you have questions or concerns about the functions. Details of the model are presented in
Kelly, S. M., N. L. Jones, and J. D. Nash (2013), A coupled model for the vertical modes of Laplace's tidal equation in a two-dimension fluid of variable depth, J. Phys. Oceanogr., 43, 1780-1797, doi:10.1175/JPO-D-12-0147.1.
The model was also used in:
Kelly, S. M., N. L. Jones, J. D. Nash and A. F. Waterhouse (2013), The geography of mode-1 internal tide energy loss, Geophys. Res. Lett., 40, 4689-4693, doi:10.1002/grl.50872.
T. M. S. Johnston, D. L. Rudnick, and S. M. Kelly, (2015), Standing Internal Tides in Tasman Sea Observed by Gliders, J. Phys. Oceanogr., 45, 2715-237, doi:10.1175/JPO-D-15-0038.1.
Klymak J. M., H. L. Simmons, D. Braznikov, S. M. Kelly, J. A. MacKinnon, M. H. Alford, R. Pinkel, and J. D. Nash (2016), Refection of linear internal tides from realistic topography: The Tasman continental slope, J. Phys. Oceanogr., 46, 3321-3337, doi: 10.1175/JPO-D-16-0061.1
Marques, O. B., M. H. Alford, R. Pinkel, J. A. MacKinnon, J. M. Klymak, J. D. Nash, A. F. Waterhouse, S. M. Kelly, H. L. Simmons, and D. Braznikov (2021), Internal Tide Structure and Temporal Variability on the Reflective Continental Slope of Southeastern Tasmania J. Phys. Oceanogr., 51, 611-631, 10.1175/JPO-D-20-0044.1.
CSW Model
The source code for the global model is available at:
https://bitbucket.org/smkelly/
The model equations were derived and applied regionally in:
Savage, A. C., A. F. Waterhouse, and S. M. Kelly (2020), Internal tide nonstationarity and wave-mesoscale interactions in the Tasman Sea J. Phys. Oceanogr., 50, 2931–2951, 10.1175/JPO-D-19-0283.1.
Kelly, S. M., P. F. J. Lermusiaux, T. F. Duda, and P. J. Haley Jr. (2016), A Coupled-mode Shallow Water model for tidal analysis: Internal-tide reflection and refraction by the Gulf Stream, J. Phys. Oceanogr., 46, 3661-3679, doi: 10.1175/JPO-D-16-0018.1.
Global results were presented in:
Kelly, S. M., A. F. Waterhouse, and A. C. Savage (2021), Global dynamics of the stationary M2 Mode-1 internal tide Geophys. Res. Lett., 48, e2020GL091692. 10.1029/2020GL091692.
Other Matlab functions
Some useful functions for analyzing internal tides are:
MODES.m uses a finite-difference algorithm to compute hydrostatic normal vertical modes with a rigid lid, flat bottom, and arbitrary stratification. MODES_FS.m uses a spectral algorithm to compute hydrostatic normal vertical modes with a free-surface (or rigid-lid), flat bottom, and arbitrary stratification. MODES_FAST.m solves the rigid-lid problem very quickly by using the Fast Fourier Transform (FFT) and analytical solutions to the coupling integrals. POTENTIAL.m computes the tidal potential and equilibrium tide using the methods of
Munk, W. H., and D. E. Cartwright (1966), Tidal spectroscopy and prediction, Phil. Trans. Roy. Soc. London A, 259, 533-581.
MODES.m and POTENTIAL.m were used in
Kelly, S. M., N. L. Jones, G. N. Ivey, and R. J. Lowe (2015), Internal tide spectroscopy and prediction in the Timor Sea, J. Phys. Oceanogr., 45, e-View, doi:10.1175/JPO-D-14-0007.1.
The spectral algorithm used in MODES_FS.m is derived and tested in
Kelly, S. M. (2016), The Vertical Mode Decomposition of Tides in the Presence of a Free Surface and Arbitrary Topography, J. Phys. Oceanogr., Submitted.