### Abstract

Geostrophic turbulence near horizontal surfaces on which the vertical velocity vanishes exhibits a forward cascade of buoyancy variance, characterized by a shallow energy spectrum, secondary roll-up of filaments, and a fat-tailed vorticity probability distribution. Such surfaces occur at rigid boundaries, but also at discontinuous jumps in stratification. Here we relax this mathematical idealization and investigate geostrophic turbulence near a rapid but smooth jump in stratification, modeled by N(z) = N0[1 + αtanh (z/h)]. The rapidity of change is controlled by the length scale h and the profile approaches a step function as h → 0. The approximated Green's function for the quasigeostrophic potential vorticity (PV) is used to predict the spectral PV-streamfunction relationship, under various assumptions about the distribution of the initial PV. Numerical simulations of freely-evolving quasigeostrophic turbulence in the presence of the model stratification support the predictions and reveal that the jump has two effects: it alters the Green's function in the region of the jump and it produces a peak in PV near the jump, approaching a Dirac delta-function as the jump scale h → 0. When the Green's function is integrated against this sharp PV distribution, contributions far from the jump (|z| ≫ h) are suppressed and the flow in a region |z| ≲ O(h) exhibits surface effects. This occurs for horizontal scales L ≳ N0h/f, the deformation scale associated with the jump. These results have implications for geostrophic turbulence near the tropopause in the atmosphere and the base of the mixed layer in the ocean.

Original language | English (US) |
---|---|

Article number | 046601 |

Journal | Physics of Fluids |

Volume | 25 |

Issue number | 4 |

DOIs | |

State | Published - Apr 4 2013 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*25*(4), [046601]. https://doi.org/10.1063/1.4799470

**Geostrophic turbulence near rapid changes in stratification.** / Smith, K. S.; Bernard, E.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 25, no. 4, 046601. https://doi.org/10.1063/1.4799470

}

TY - JOUR

T1 - Geostrophic turbulence near rapid changes in stratification

AU - Smith, K. S.

AU - Bernard, E.

PY - 2013/4/4

Y1 - 2013/4/4

N2 - Geostrophic turbulence near horizontal surfaces on which the vertical velocity vanishes exhibits a forward cascade of buoyancy variance, characterized by a shallow energy spectrum, secondary roll-up of filaments, and a fat-tailed vorticity probability distribution. Such surfaces occur at rigid boundaries, but also at discontinuous jumps in stratification. Here we relax this mathematical idealization and investigate geostrophic turbulence near a rapid but smooth jump in stratification, modeled by N(z) = N0[1 + αtanh (z/h)]. The rapidity of change is controlled by the length scale h and the profile approaches a step function as h → 0. The approximated Green's function for the quasigeostrophic potential vorticity (PV) is used to predict the spectral PV-streamfunction relationship, under various assumptions about the distribution of the initial PV. Numerical simulations of freely-evolving quasigeostrophic turbulence in the presence of the model stratification support the predictions and reveal that the jump has two effects: it alters the Green's function in the region of the jump and it produces a peak in PV near the jump, approaching a Dirac delta-function as the jump scale h → 0. When the Green's function is integrated against this sharp PV distribution, contributions far from the jump (|z| ≫ h) are suppressed and the flow in a region |z| ≲ O(h) exhibits surface effects. This occurs for horizontal scales L ≳ N0h/f, the deformation scale associated with the jump. These results have implications for geostrophic turbulence near the tropopause in the atmosphere and the base of the mixed layer in the ocean.

AB - Geostrophic turbulence near horizontal surfaces on which the vertical velocity vanishes exhibits a forward cascade of buoyancy variance, characterized by a shallow energy spectrum, secondary roll-up of filaments, and a fat-tailed vorticity probability distribution. Such surfaces occur at rigid boundaries, but also at discontinuous jumps in stratification. Here we relax this mathematical idealization and investigate geostrophic turbulence near a rapid but smooth jump in stratification, modeled by N(z) = N0[1 + αtanh (z/h)]. The rapidity of change is controlled by the length scale h and the profile approaches a step function as h → 0. The approximated Green's function for the quasigeostrophic potential vorticity (PV) is used to predict the spectral PV-streamfunction relationship, under various assumptions about the distribution of the initial PV. Numerical simulations of freely-evolving quasigeostrophic turbulence in the presence of the model stratification support the predictions and reveal that the jump has two effects: it alters the Green's function in the region of the jump and it produces a peak in PV near the jump, approaching a Dirac delta-function as the jump scale h → 0. When the Green's function is integrated against this sharp PV distribution, contributions far from the jump (|z| ≫ h) are suppressed and the flow in a region |z| ≲ O(h) exhibits surface effects. This occurs for horizontal scales L ≳ N0h/f, the deformation scale associated with the jump. These results have implications for geostrophic turbulence near the tropopause in the atmosphere and the base of the mixed layer in the ocean.

UR - http://www.scopus.com/inward/record.url?scp=84877650940&partnerID=8YFLogxK

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U2 - 10.1063/1.4799470

DO - 10.1063/1.4799470

M3 - Article

AN - SCOPUS:84877650940

VL - 25

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 4

M1 - 046601

ER -