Raquel Taboada-Vázquez

TL;DR: A small adimensional parameter @e related to the depth is introduced and two new models for @e small are obtained, including a shallow water model including a new diffusion term (obtained from Navier-Stokes equations) and a shallowWater model without viscosity and explicit dependence on depth.

TL;DR: A small adimensional parameter @e related to the depth is introduced and asymptotic analysis is used to study what happens when @e becomes small to obtain a model for @e small that gives a shallow water model that considers the possibility of a non-constant bottom and the horizontal velocity components depend on z if the vorticity is not zero.

TL;DR: In this article, the authors study two-dimensional Euler equations in a domain with small depth and obtain a model for e small that, after coming back to the original domain, gives us a shallow water model that considers the possibility of a non-constant bottom, and the horizontal velocity has a dependence on the vorticity when it is not zero.

TL;DR: The authors perform some numerical computations that confirm the new model is able to approximate the solutions of Navier–Stokes equations with dependence on z (reobtaining the same velocities profile), whereas the classic model only computes the average velocity.

TL;DR: In this article, a bidimensional shallow water model with polynomial dependence on depth was obtained, where a small non-dimensional parameter e was introduced and the authors studied three-dimensional Euler equations in a domain depending on e (in such a way that, when e becomes small, the domain has small depth).