Asset Details
Do you wish to reserve the book?
The Matsuno–Gill model on the sphere
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
The Matsuno–Gill model on the sphere
Do you wish to request the book?
The Matsuno–Gill model on the sphere
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
The Matsuno–Gill model on the sphere
2023
Overview
We extend the Matsuno–Gill model, originally developed on the equatorial $\\beta$-plane, to the surface of the sphere. While on the $\\beta$-plane the non-dimensional model contains a single parameter, the damping rate $\\gamma$, on a sphere the model contains a second parameter, the rotation rate $\\epsilon ^{1/2}$ (Lamb number). By considering the different combinations of damping and rotation, we are able to characterize the solutions over the $(\\gamma, \\epsilon ^{1/2})$ plane. We find that the $\\beta$-plane approximation is accurate only for fast rotation rates, where gravity waves traverse a fraction of the sphere's diameter in one rotation period. The particular solutions studied by Matsuno and Gill are accurate only for fast rotation and moderate damping rates, where the relaxation time is comparable to the time on which gravity waves traverse the sphere's diameter. Other regions of the parameter space can be described by different approximations, including radiative relaxation, geostrophic, weak temperature gradient and non-rotating approximations. The effect of the additional parameter introduced by the sphere is to alter the eigenmodes of the free system. Thus, unlike the solutions obtained by Matsuno and Gill, where the long-term response to a symmetric forcing consists solely of Kelvin and Rossby waves, the response on the sphere includes other waves as well, depending on the combination of $\\gamma$ and $\\epsilon ^{1/2}$. The particular solutions studied by Matsuno and Gill apply to Earth's oceans, while the more general $\\beta$-plane solutions are only somewhat relevant to Earth's troposphere. In Earth's stratosphere, Venus and Titan, only the spherical solutions apply.
Publisher
Cambridge University Press
Subject
