Geophysical internal equatorial waves of extreme form

Lyons, Tony

doi:10.3934/dcds.2019183

Cited by 9 publications

(5 citation statements)

References 35 publications

(79 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…for velocities u 1 which occur in realistic physical scenarios. The latter inequality and relation (39) prove ( 36) and (37). Another interesting and relevant upshot of the solutions proved to exist by Theorem 3.3 refers to the regularity of the interface defining function.…”

Section: Analysis Of the Exact Solutionsmentioning

confidence: 70%

“…An alleviation of this aspect is represented by a Bernoulli-type relation between the imposed pressure at the surface and the resulting surface distorsion; an implicit formula for the interface defining function being given by the balance of forces at the interface (5d). For a selective list of papers presenting exact solutions pertaining to geophysical fluid dynamics we refer the reader to [1,4,6,7,[11][12][13][14]16,23,24,[31][32][33]39,[42][43][44][45]48].…”

Section: Equations Of Motionmentioning

confidence: 99%

See 1 more Smart Citation

Azimuthal equatorial flows in spherical coordinates with discontinuous stratification

Martin

2021

Physics of Fluids

View full text Add to dashboard Cite

We are concerned here with an exact solution to the governing equations for geophysical fluid dynamics in spherical coordinates which incorporates discontinuous fluid stratification. This solution represents a steady, purelyazimuthal equatorial flow with an associated free-surface and an interface separating two fluid regions, each of which having its own continuous distribution of density. However, the two density functions do not match along the interface. Following the derivation of the solution we demonstrate that there is a well-defined relationship between the imposed pressure at the free-surface and the resulting distortion of the surface's shape. Moreover, imposing the continuity of the pressure along the interface generates an equation that describes (implicitly) the shape of the interface. Interestingly, it turns out that the interface defining function has infinite regularity.

show abstract

Section: Analysis Of the Exact Solutionsmentioning

confidence: 70%

Section: Equations Of Motionmentioning

confidence: 99%

Azimuthal equatorial flows in spherical coordinates with discontinuous stratification

Martin

2021

Physics of Fluids

View full text Add to dashboard Cite

show abstract

“…[31,35]). One definition of the Lambert W -function is given as the solution of the general relation x = q + re sx ⇒ x = q − 1 s W (−rse qs ) where q, r and s may complex be constants, (see [25,27] for further applications of the Lambert function in the hydrodynamic setting).…”

Section: Elliptical Pathsmentioning

confidence: 99%

Particle paths in equatorial flows

Lyons¹

2022

CPAA

Self Cite

View full text Add to dashboard Cite

<p style='text-indent:20px;'>We investigate particle trajectories in equatorial flows with geophysical corrections caused by the earth's rotation. Particle trajectories in the flows are constructed using pairs of analytic functions defined over the labelling space used in the Lagrangian formalism. Several classes of flow are investigated, and the physical regime in which each is valid is determined using the pressure distribution function of the flow, while the vorticity distribution of each flow is also calculated and found to be effected by earth's rotation.</p>

show abstract

Section: Elliptical Pathsmentioning

confidence: 99%

Particle paths in equatorial flows

Lyons

2022

Preprint

Self Cite

View full text Add to dashboard Cite

We investigate particle trajectories in equatorial flows with geophysical corrections caused by the earth's rotation. Particle trajectories in the flows are constructed using pairs of analytic functions defined over the labelling space used in the Lagrangian formalism. Several classes of flow are investigated, and the physical regime in which each is valid is determined using the pressure distribution function of the flow, while the vorticity distribution of each flow is also calculated and found to be effected by earth's rotation.

show abstract

Geophysical internal equatorial waves of extreme form

Abstract: The existence of internal geophysical waves of extreme form is confirmed and an explicit solution presented. The flow is confined to a layer lying above an eastward current while the mean horizontal flow of the solutions is westward, thus incorporating flow reversal in the fluid.

Cited by 9 publications

References 35 publications

Azimuthal equatorial flows in spherical coordinates with discontinuous stratification

Azimuthal equatorial flows in spherical coordinates with discontinuous stratification

Particle paths in equatorial flows

Particle paths in equatorial flows

Contact Info

Product

Resources

About