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Nonlinear Stability of Ekman Boundary Layers in Rotation Stratified Fluids

2014-10-03 Fluid mechanics
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Release : 2014-10-03
Genre : Fluid mechanics
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Book Rating : 856/5 ( reviews)

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Book Synopsis Nonlinear Stability of Ekman Boundary Layers in Rotation Stratified Fluids by : Hajime Koba

Download or read book Nonlinear Stability of Ekman Boundary Layers in Rotation Stratified Fluids written by Hajime Koba. This book was released on 2014-10-03. Available in PDF, EPUB and Kindle. Book excerpt: A stationary solution of the rotating Navier-Stokes equations with a boundary condition is called an Ekman boundary layer. This book constructs stationary solutions of the rotating Navier-Stokes-Boussinesq equations with stratification effects in the case when the rotating axis is not necessarily perpendicular to the horizon. The author calls such stationary solutions Ekman layers. This book shows the existence of a weak solution to an Ekman perturbed system, which satisfies the strong energy inequality. Moreover, the author discusses the uniqueness of weak solutions and computes the decay rate of weak solutions with respect to time under some assumptions on the Ekman layers and the physical parameters. The author also shows that there exists a unique global-in-time strong solution of the perturbed system when the initial datum is sufficiently small. Comparing a weak solution satisfying the strong energy inequality with the strong solution implies that the weak solution is smooth with respect to time when time is sufficiently large.

Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids

2014-03-05 Mathematics
Download Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids PDF Online Free

Author :
Release : 2014-03-05
Genre : Mathematics
Kind : eBook
Book Rating : 332/5 ( reviews)

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Book Synopsis Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids by : Hajime Koba

Download or read book Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids written by Hajime Koba. This book was released on 2014-03-05. Available in PDF, EPUB and Kindle. Book excerpt: A stationary solution of the rotating Navier-Stokes equations with a boundary condition is called an Ekman boundary layer. This book constructs stationary solutions of the rotating Navier-Stokes-Boussinesq equations with stratification effects in the case when the rotating axis is not necessarily perpendicular to the horizon. The author calls such stationary solutions Ekman layers. This book shows the existence of a weak solution to an Ekman perturbed system, which satisfies the strong energy inequality. Moreover, the author discusses the uniqueness of weak solutions and computes the decay rate of weak solutions with respect to time under some assumptions on the Ekman layers and the physical parameters. The author also shows that there exists a unique global-in-time strong solution of the perturbed system when the initial datum is sufficiently small. Comparing a weak solution satisfying the strong energy inequality with the strong solution implies that the weak solution is smooth with respect to time when time is sufficiently large.

The Theory of Rotating Fluids

1990 Science
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Release : 1990
Genre : Science
Kind : eBook
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Book Synopsis The Theory of Rotating Fluids by : Harvey Philip Greenspan

Download or read book The Theory of Rotating Fluids written by Harvey Philip Greenspan. This book was released on 1990. Available in PDF, EPUB and Kindle. Book excerpt:

Boundary and Shear Layers in Rotating and Stratified Fluids

1973 Boundary layer
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Release : 1973
Genre : Boundary layer
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Book Synopsis Boundary and Shear Layers in Rotating and Stratified Fluids by : Yves Jean François Desaubies

Download or read book Boundary and Shear Layers in Rotating and Stratified Fluids written by Yves Jean François Desaubies. This book was released on 1973. Available in PDF, EPUB and Kindle. Book excerpt:

Rotating Fluids in Geophysics

1978 Science
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Release : 1978
Genre : Science
Kind : eBook
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Book Synopsis Rotating Fluids in Geophysics by : Paul Harry Roberts

Download or read book Rotating Fluids in Geophysics written by Paul Harry Roberts. This book was released on 1978. Available in PDF, EPUB and Kindle. Book excerpt: The subject of rotating fluids is worth studying for many reasons, not least of which is that all large scale motions of the Earth's atmosphere, oceans and core are dominated by its rotation. Trade winds follow lines of latitude because of rotation: the effect of these winds upon the Atlantic generates, in gyroscopic fashion, the intense northerly flowing Gulf Stream: and evidence of the impact of rotation on the Earth's core is seen in the northwardd pointing compass. However, the study of rotating fluids has also been characterized by the power, elegance and ingenuity of the experimental and theoretical tools which have been brought to bear on it - tools of which every fluid mechanist ought to be aware. This book is devoted primarily to a theoretical exposition of the subject, although several sections are centred on experimental and numerical techniques in their applications to the atmosphere, oceans and core of the Earth. A theme running through the book is waves and stability, supported by a brief section expounding hydrodynamic stability theory.

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