Research papersTransformation of internal breathers in the idealised shelf sea conditions

- Evolution of a Gardner breather along sloping bottom numerically replicated.
- Numerical solutions for weakly and fully nonlinear (Euler) equations compared.
- Narrow-banded breathers are insensitive with respect to Earth's rotation.
- Breathers with a wide spectrum are strongly affected by background rotation.

We address the propagation and transformation of long internal breather-like wave in an idealised but realistic stratification and in the conditions matching the average summer stratification in the southern part of the Baltic Sea. The focus is on changes in the properties of the breather when the water depth increases and the coefficient at the cubic nonlinear term changes its sign, equivalently, the breather cannot exist anymore. The simulations are performed in parallel in the framework of weakly nonlinear Gardner equation and using fully nonlinear Euler equations. The amplitudes of breathers in these frameworks have slightly different courses in idealised conditions (when Earth's rotation is neglected) whereas a decrease in the amplitude is faster in the fully nonlinear simulation. The impact of the background (Earth's) rotation substantially depends on the spectral width of the initial breather. The evolution of narrow-banded breathers is almost the same for rotating and non-rotating situations but amplitudes of breathers with a wide spectrum experience substantial changes in realistic situation with the background rotation. The propagation of a narrow-banded breather along a path in the Baltic Sea over a location where the cubic nonlinear term changes its sign reveals fast disintegration of the breather into a precursor soliton and a transient dispersive wave group.