TY - JOUR

T1 - A Forward Energy Flux at Submesoscales Driven by Frontogenesis

AU - Srinivasan, Kaushik

AU - Barkan, Roy

AU - McWilliams, James C.

N1 - Publisher Copyright:
© 2022 American Meteorological Society.

PY - 2023

Y1 - 2023

N2 - Submesoscale currents, comprising fronts and mixed-layer eddies, exhibit a dual cascade of kinetic energy: a forward cascade to dissipation scales at fronts and an inverse cascade from mixed-layer eddies to mesoscale eddies. Within a coarse-graining framework using both spatial and temporal filters, we show that this dual cascade can be captured in simple mathematical form obtained by writing the cross-scale energy flux in the local principal strain coordinate system, wherein the flux reduces to the sum of two terms, one proportional to the convergence and the other proportional to the strain. The strain term is found to cause the inverse energy flux to larger scales while an approximate equipartition of the convergent and strain terms captures the forward energy flux, demonstrated through model-based analysis and asymptotic theory. A consequence of this equipartition is that the frontal forward energy flux is simply proportional to the frontal con-vergence. In a recent study, it was shown that the Lagrangian rate of change of quantities like the divergence, vorticity, and horizontal buoyancy gradient are proportional to convergence at fronts, implying that horizontal convergence drives frontogenesis. We show that these two results imply that the primary mechanism for the forward energy flux at fronts is frontogenesis. We also analyze the energy flux through a Helmholtz decomposition and show that the rotational components are primarily responsible for the inverse cascade while a mix of the divergent and rotational components cause the forward cascade, consistent with our asymptotic analysis based on the principal strain framework.

AB - Submesoscale currents, comprising fronts and mixed-layer eddies, exhibit a dual cascade of kinetic energy: a forward cascade to dissipation scales at fronts and an inverse cascade from mixed-layer eddies to mesoscale eddies. Within a coarse-graining framework using both spatial and temporal filters, we show that this dual cascade can be captured in simple mathematical form obtained by writing the cross-scale energy flux in the local principal strain coordinate system, wherein the flux reduces to the sum of two terms, one proportional to the convergence and the other proportional to the strain. The strain term is found to cause the inverse energy flux to larger scales while an approximate equipartition of the convergent and strain terms captures the forward energy flux, demonstrated through model-based analysis and asymptotic theory. A consequence of this equipartition is that the frontal forward energy flux is simply proportional to the frontal con-vergence. In a recent study, it was shown that the Lagrangian rate of change of quantities like the divergence, vorticity, and horizontal buoyancy gradient are proportional to convergence at fronts, implying that horizontal convergence drives frontogenesis. We show that these two results imply that the primary mechanism for the forward energy flux at fronts is frontogenesis. We also analyze the energy flux through a Helmholtz decomposition and show that the rotational components are primarily responsible for the inverse cascade while a mix of the divergent and rotational components cause the forward cascade, consistent with our asymptotic analysis based on the principal strain framework.

KW - Ageostrophic circulations

KW - Energy transport

KW - Frontogenesis/frontolysis

KW - Fronts

KW - Ocean models

KW - Small scale processes

UR - http://www.scopus.com/inward/record.url?scp=85145018211&partnerID=8YFLogxK

U2 - 10.1175/JPO-D-22-0001.1

DO - 10.1175/JPO-D-22-0001.1

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AN - SCOPUS:85145018211

SN - 0022-3670

VL - 53

SP - 287

EP - 305

JO - Journal of Physical Oceanography

JF - Journal of Physical Oceanography

IS - 1

ER -