Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A comparative theorem for surface waves

Sommario

L'Autore mostra che alcuni tipi di onde rotazionali possono essere rappresentati nella forma:

$$\Delta _2 \Psi = \alpha ^2 \Psi ,$$
((a))
$$\Delta _2 \Psi = - \alpha ^2 \Psi ,$$
((a'))
$$\Delta _2 \Psi = - 2R_0 (conR_0 = cost)$$
((b))

Si ha

$$\frac{{\partial \Psi }}{{\partial x}} = - v,\frac{{\partial \Psi }}{{\partial y}} = u$$

con u e v componenti della velocità. Le onde del tipo (a) e (b) (con R0>0) hanno il rotore nello stesso senso della propagazione, le onde del tipo (a′) e (b) (con R0<0) hanno il rotore in senso opposto alla propagazione. Si dimostra il seguente teorema. L'onda si appiattisce quando il rotore ha la stessa direzione della propagazione mentre diviene più ripida se il rotore ha senso opposto alla propagazione.

Summary

Author shows that some class of rotational waves may be obtained in the form:

$$\Delta _2 \Psi = \alpha ^2 \Psi ,$$
((a))
$$\Delta _2 \Psi = - \alpha ^2 \Psi ,$$
((a'))
$$\Delta _2 \Psi = - 2R_0 (conR_0 = cost)$$
((b))

It is

$$\frac{{\partial \Psi }}{{\partial x}} = - v,\frac{{\partial \Psi }}{{\partial y}} = u (with u and v = velocities)$$

The waves (a) and (b) (with R0>0) have the rotation in the same direction of the propagation, while the waves (a′) and (b) (with R0<0) have the rotation opposite to the propagation. The following theorem may be proved. The waves is flattening when the rotation has the same direction of the propagation, but it becomes steeper if the rotation is opposite to it.

This is a preview of subscription content, log in to check access.

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Supino, G. A comparative theorem for surface waves. Meccanica 12, 140–143 (1977). https://doi.org/10.1007/BF02179927

Download citation

Keywords

  • Mechanical Engineer
  • Civil Engineer
  • Surface Wave
  • Alla
  • Comparative Theorem