108
V. Liapidevskii and N. Gavrilov
13. Gavrilyuk, S. L., Liapidevskii, V. Yu., & Chesnokov, A. A. (2016). Spilling breakers in shallow
water: Applications to Favre waves and to the shoaling and breaking of solitary waves. Journal
of Fluid Mechanics, 808, 441–468.
14. Helfrich, K. R., & Melville, W. K. (2006). Long nonlinear internal waves. Annual Review of
Fluid Mechanics, 38, 395–425.
15. Lamb, K. G. (2003). Shoaling solitary internal waves: On a criterion for the formation of waves
with trapped cores. Journal of Fluid Mechanics, 478, 81–100.
16. Lamb, K. G., & Farmer, D. (2011). Instabilities in an internal solitary-like wave on the Oregon
Shelf. Journal of Physical Oceanography, 41, 67–87.
17. Liapidevskii, V. Yu., & Teshukov, V. M. (2000). Mathematical models of long-wave propagation in an inhomogeneous fluid. Novosibirsk: Publishing House of the Siberian Branch of the
Russian Academy of Sciences (in Russian).
18. Liapidevskii, V. Yu., Kukarin, V. F., Navrotsky, V. V., & Khrapchenkov, F. F. (2013). Evolution
of large amplitude internal waves of in a swash zone. Fundam. prikl. gidrofiz., 6, 35–45 (in
Russian).
19. Liapidevskii, V. Yu., Novotryasov, V. V., Khrapchenkov, F. F., & Yaroshchuk, I. O. (2017).
Internal undular bore in a shelf zone. Journal of Applied Mechanics and Technical Physics,
58(5), 809–818.
20. Lien, R Ch., Henyey, F., Ma, B., & Yang, Y. J. (2014). Large-amplitude internal solitary
waves observed in the northern South China sea: Properties and energetic. Journal of Physical
Oceanography, 44(4), 1095–1115.
21. Le Metayer, O., Gavrilyuk, S., & Hank, S. (2010). A numerical scheme for the Green-Naghdi
model. Journal of Computational Physics, 229, 2034–2045.
22. Maxworthy, T. (1980). On the formation of nonlinear internal waves from the gravitational
collapse of mixing regions in two and three dimensions. Journal of Fluid Mechanics, 96, 47–
64.
23. Moum, J. N., Farmer, D. M., Smyth, W. D., Armi, L., & Vagle, S. (2003). Structure and generation of turbulence at interfaces strained by internal solitary waves propagating shoreward
over the continental shelf. Journal of Physical Oceanography, 33, 2093–2112.
24. Moum, J. N., & Nash, J. D. (2005). River plumes as a source of large amplitude internal waves
in the coastal ocean. Nature, 437, 400–403.
25. Serre, F. (1953). Contribution a l’etude des ecoulements permanents et variables dans les
canaux. Houille Blanche, 8(3), 374–388 (in French).
26. Stamp, A. P., & Jacka, M. (1995). Deep-water internal solitary waves. Journal of Fluid
Mechanics, 305, 347–371.
27. Tung, K. K., Chan, T. F., & Kubota, T. (1982). Large amplitude internal waves of permanent
form. Studies in Applied Mathematics, 66, 1–44.
28. Vlasenko, V., & Hutter, K. (2002). Numerical experiments on the breaking of solitary internal
waves over a slope-shelf topography. Journal of Physical Oceanography, 32, 1779–1793.
V. Liapidevskii and N. Gavrilov
13. Gavrilyuk, S. L., Liapidevskii, V. Yu., & Chesnokov, A. A. (2016). Spilling breakers in shallow
water: Applications to Favre waves and to the shoaling and breaking of solitary waves. Journal
of Fluid Mechanics, 808, 441–468.
14. Helfrich, K. R., & Melville, W. K. (2006). Long nonlinear internal waves. Annual Review of
Fluid Mechanics, 38, 395–425.
15. Lamb, K. G. (2003). Shoaling solitary internal waves: On a criterion for the formation of waves
with trapped cores. Journal of Fluid Mechanics, 478, 81–100.
16. Lamb, K. G., & Farmer, D. (2011). Instabilities in an internal solitary-like wave on the Oregon
Shelf. Journal of Physical Oceanography, 41, 67–87.
17. Liapidevskii, V. Yu., & Teshukov, V. M. (2000). Mathematical models of long-wave propagation in an inhomogeneous fluid. Novosibirsk: Publishing House of the Siberian Branch of the
Russian Academy of Sciences (in Russian).
18. Liapidevskii, V. Yu., Kukarin, V. F., Navrotsky, V. V., & Khrapchenkov, F. F. (2013). Evolution
of large amplitude internal waves of in a swash zone. Fundam. prikl. gidrofiz., 6, 35–45 (in
Russian).
19. Liapidevskii, V. Yu., Novotryasov, V. V., Khrapchenkov, F. F., & Yaroshchuk, I. O. (2017).
Internal undular bore in a shelf zone. Journal of Applied Mechanics and Technical Physics,
58(5), 809–818.
20. Lien, R Ch., Henyey, F., Ma, B., & Yang, Y. J. (2014). Large-amplitude internal solitary
waves observed in the northern South China sea: Properties and energetic. Journal of Physical
Oceanography, 44(4), 1095–1115.
21. Le Metayer, O., Gavrilyuk, S., & Hank, S. (2010). A numerical scheme for the Green-Naghdi
model. Journal of Computational Physics, 229, 2034–2045.
22. Maxworthy, T. (1980). On the formation of nonlinear internal waves from the gravitational
collapse of mixing regions in two and three dimensions. Journal of Fluid Mechanics, 96, 47–
64.
23. Moum, J. N., Farmer, D. M., Smyth, W. D., Armi, L., & Vagle, S. (2003). Structure and generation of turbulence at interfaces strained by internal solitary waves propagating shoreward
over the continental shelf. Journal of Physical Oceanography, 33, 2093–2112.
24. Moum, J. N., & Nash, J. D. (2005). River plumes as a source of large amplitude internal waves
in the coastal ocean. Nature, 437, 400–403.
25. Serre, F. (1953). Contribution a l’etude des ecoulements permanents et variables dans les
canaux. Houille Blanche, 8(3), 374–388 (in French).
26. Stamp, A. P., & Jacka, M. (1995). Deep-water internal solitary waves. Journal of Fluid
Mechanics, 305, 347–371.
27. Tung, K. K., Chan, T. F., & Kubota, T. (1982). Large amplitude internal waves of permanent
form. Studies in Applied Mathematics, 66, 1–44.
28. Vlasenko, V., & Hutter, K. (2002). Numerical experiments on the breaking of solitary internal
waves over a slope-shelf topography. Journal of Physical Oceanography, 32, 1779–1793.