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Exact solutions and stability analysis of a nonlinear model of Open-Ocean deep convection that allows multiple steady states. / Bashmachnikov, Igor L.; Kovalevsky, Dmitry V.

In: Discontinuity, Nonlinearity, and Complexity, Vol. 8, No. 2, 01.01.2019, p. 169-186.

Research output: Contribution to journal › Article › peer-review

Harvard

Bashmachnikov, IL & Kovalevsky, DV 2019, 'Exact solutions and stability analysis of a nonlinear model of Open-Ocean deep convection that allows multiple steady states', Discontinuity, Nonlinearity, and Complexity, vol. 8, no. 2, pp. 169-186. https://doi.org/10.5890/DNC.2019.06.005

APA

Bashmachnikov, I. L., & Kovalevsky, D. V. (2019). Exact solutions and stability analysis of a nonlinear model of Open-Ocean deep convection that allows multiple steady states. Discontinuity, Nonlinearity, and Complexity, 8(2), 169-186. https://doi.org/10.5890/DNC.2019.06.005

Vancouver

Bashmachnikov IL, Kovalevsky DV. Exact solutions and stability analysis of a nonlinear model of Open-Ocean deep convection that allows multiple steady states. Discontinuity, Nonlinearity, and Complexity. 2019 Jan 1;8(2):169-186. https://doi.org/10.5890/DNC.2019.06.005

Author

Bashmachnikov, Igor L. ; Kovalevsky, Dmitry V. / Exact solutions and stability analysis of a nonlinear model of Open-Ocean deep convection that allows multiple steady states. In: Discontinuity, Nonlinearity, and Complexity. 2019 ; Vol. 8, No. 2. pp. 169-186.

BibTeX

@article{6b8580c90a1e48bc94aaf35f88a6497a,
title = "Exact solutions and stability analysis of a nonlinear model of Open-Ocean deep convection that allows multiple steady states",
abstract = "We present analytical solutions of the two-basin model of open-ocean deep convection. Originally suggested by Whitehead [Whitehead, J.A. (2000), Stratified convection with multiple states, Ocean Modelling, 2(3-4), 109- 121], the model allows regimes with multiple steady states (multiple equilibria). We provide the full analytical description of the steady states for the particular case of constant surface heat flux from the ocean to the atmosphere, and explore analytically stability of the equilibria within the Lyapunov theory. The results show that, for this particular case, the steady state is unique and stable for all dynamic flow regimes. We also present analytical expressions for dependence of critical values of sea-surface heat flux, at which transitions between the dynamic regimes occur, on the model parameters.",
keywords = "Multiple steady states, Nonlinearity, Open-ocean deep convection, Stability of equilibria",
author = "Bashmachnikov, {Igor L.} and Kovalevsky, {Dmitry V.}",
year = "2019",
month = jan,
day = "1",
doi = "10.5890/DNC.2019.06.005",
language = "English",
volume = "8",
pages = "169--186",
journal = "Discontinuity, Nonlinearity, and Complexity",
issn = "2164-6376",
publisher = "L & H Scientific Publishing, LLC",
number = "2",

}

RIS

TY - JOUR

T1 - Exact solutions and stability analysis of a nonlinear model of Open-Ocean deep convection that allows multiple steady states

AU - Bashmachnikov, Igor L.

AU - Kovalevsky, Dmitry V.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We present analytical solutions of the two-basin model of open-ocean deep convection. Originally suggested by Whitehead [Whitehead, J.A. (2000), Stratified convection with multiple states, Ocean Modelling, 2(3-4), 109- 121], the model allows regimes with multiple steady states (multiple equilibria). We provide the full analytical description of the steady states for the particular case of constant surface heat flux from the ocean to the atmosphere, and explore analytically stability of the equilibria within the Lyapunov theory. The results show that, for this particular case, the steady state is unique and stable for all dynamic flow regimes. We also present analytical expressions for dependence of critical values of sea-surface heat flux, at which transitions between the dynamic regimes occur, on the model parameters.

AB - We present analytical solutions of the two-basin model of open-ocean deep convection. Originally suggested by Whitehead [Whitehead, J.A. (2000), Stratified convection with multiple states, Ocean Modelling, 2(3-4), 109- 121], the model allows regimes with multiple steady states (multiple equilibria). We provide the full analytical description of the steady states for the particular case of constant surface heat flux from the ocean to the atmosphere, and explore analytically stability of the equilibria within the Lyapunov theory. The results show that, for this particular case, the steady state is unique and stable for all dynamic flow regimes. We also present analytical expressions for dependence of critical values of sea-surface heat flux, at which transitions between the dynamic regimes occur, on the model parameters.

KW - Multiple steady states

KW - Nonlinearity

KW - Open-ocean deep convection

KW - Stability of equilibria

UR - http://www.scopus.com/inward/record.url?scp=85067289734&partnerID=8YFLogxK

U2 - 10.5890/DNC.2019.06.005

DO - 10.5890/DNC.2019.06.005

M3 - Article

AN - SCOPUS:85067289734

VL - 8

SP - 169

EP - 186

JO - Discontinuity, Nonlinearity, and Complexity

JF - Discontinuity, Nonlinearity, and Complexity

SN - 2164-6376

IS - 2

ER -

ID: 42996264