Preprints
https://doi.org/10.5194/egusphere-2023-819
https://doi.org/10.5194/egusphere-2023-819
02 May 2023
 | 02 May 2023

Geostrophic adjustment on the mid-latitude β-plane

Itamar Yacoby, Nathan Paldor, and Hezi Gildor

Abstract. Analytical and numerical solutions of the Linearized Rotating Shallow Water Equations are combined to study the geostrophic adjustment on the mid-latitude β-plane. The adjustment is examined in zonal periodic channels of width Lᵧ = 4Rd (‘narrow’ channel, where Rd is the radius of deformation) and Lᵧ=60Rd (‘wide’ channel) for the particular initial conditions of a resting fluid with a step-like height distribution, η₀. In the one-dimensional case, where η₀ = η₀(y) we find that: (i) β affects the geostrophic state (determined from the conservation of the meridional vorticity gradient) only when b = cot (Φ₀) Rd /R ≥ 0.5 (where Φ₀ is the channel’s central latitude and R is Earth’s radius); (ii) The energy conversion ratio varies by less than 10 % when b increases from 0 to 1; (iii) In ‘wide’ channels, β affects the waves significantly even for small b (e.g. b = 0.005). (iv) For b = 0.005, harmonic waves approximate the waves in ‘narrow’ channels, and trapped waves approximate the waves in ‘wide’ channels. In the two-dimensional case, where η₀ = η₀(x) we find that: (i) At short times the spatial structure of the steady solution is similar to that on the f-plane, while at long times the steady state drifts westward at the speed of Rossby waves – harmonic Rossby waves in ‘narrow’ channels and trapped Rossby waves in ‘wide’ channels; (ii) In ‘wide’ channels, trapped wave dispersion causes the equatorward segment of the wavefront to move faster than the northern segment; (iii) The energy of Rossby waves on the β-plane approaches that of the steady-state on the f-plane; (iv) The results outlined in (iii) and (iv) of the one-dimensional case also hold in the two-dimensional case.

Journal article(s) based on this preprint

03 Aug 2023
Geostrophic adjustment on the midlatitude β plane
Itamar Yacoby, Nathan Paldor, and Hezi Gildor
Ocean Sci., 19, 1163–1181, https://doi.org/10.5194/os-19-1163-2023,https://doi.org/10.5194/os-19-1163-2023, 2023
Short summary

Itamar Yacoby et al.

Interactive discussion

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-819', Anonymous Referee #1, 06 Jun 2023
    • AC1: 'Reply on RC1', Nathan Paldor, 27 Jun 2023
  • RC2: 'Comment on egusphere-2023-819', Anonymous Referee #2, 15 Jun 2023
    • AC2: 'Reply on RC2', Nathan Paldor, 27 Jun 2023
  • EC1: 'Comment on egusphere-2023-819', Karen J. Heywood, 27 Jun 2023
    • AC3: 'Reply on EC1', Nathan Paldor, 28 Jun 2023
      • EC2: 'Reply on AC3', Karen J. Heywood, 28 Jun 2023

Interactive discussion

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-819', Anonymous Referee #1, 06 Jun 2023
    • AC1: 'Reply on RC1', Nathan Paldor, 27 Jun 2023
  • RC2: 'Comment on egusphere-2023-819', Anonymous Referee #2, 15 Jun 2023
    • AC2: 'Reply on RC2', Nathan Paldor, 27 Jun 2023
  • EC1: 'Comment on egusphere-2023-819', Karen J. Heywood, 27 Jun 2023
    • AC3: 'Reply on EC1', Nathan Paldor, 28 Jun 2023
      • EC2: 'Reply on AC3', Karen J. Heywood, 28 Jun 2023

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload
AR by Nathan Paldor on behalf of the Authors (28 Jun 2023)  Author's response   Author's tracked changes   Manuscript 
ED: Publish as is (28 Jun 2023) by Karen J. Heywood
AR by Nathan Paldor on behalf of the Authors (29 Jun 2023)  Manuscript 

Journal article(s) based on this preprint

03 Aug 2023
Geostrophic adjustment on the midlatitude β plane
Itamar Yacoby, Nathan Paldor, and Hezi Gildor
Ocean Sci., 19, 1163–1181, https://doi.org/10.5194/os-19-1163-2023,https://doi.org/10.5194/os-19-1163-2023, 2023
Short summary

Itamar Yacoby et al.

Itamar Yacoby et al.

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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.

Short summary
The transition from an arbitrary initial sea surface height to a geostrophic balance in which the velocity is steady was solved last century for constant Coriolis frequency, f(y) where y is the latitude. This study extends the theory to the realistic case in which f(y) is linear with y. We find that the variation of f(y) simply translates the steady geostrophic state westward as low frequency Rossby waves that are harmonic in narrow domains and trapped near the equatorward boundary in wide ones.