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the vertical vorticity. Equation (6) highlights the various phenomena that can result in restratification (or destratification) of the ocean: frontogenesis or frontolysis (FRONT), advection of PV (ADV), friction (FRIC), and diabatic processes (DIA). If the vertical levels z t and z b do not intersect surface and benthic boundary layers, then advection of PV through the bounding surfaces dominates over the other three terms: diabatic and frictional effects are weak away from boundaries, while
the vertical vorticity. Equation (6) highlights the various phenomena that can result in restratification (or destratification) of the ocean: frontogenesis or frontolysis (FRONT), advection of PV (ADV), friction (FRIC), and diabatic processes (DIA). If the vertical levels z t and z b do not intersect surface and benthic boundary layers, then advection of PV through the bounding surfaces dominates over the other three terms: diabatic and frictional effects are weak away from boundaries, while
velocity at the tropopause, except for the last one ( Keyser and Shapiro 1986 ). The particular characteristic of a narrower trough implies horizontally confluent flow along the uptrough sector and diffluent flow downtrough. From the classical perspective of strain-induced frontogenesis ( Hoskins and Bretherton 1972 ), we can therefore expect frontogenesis and frontolysis, respectively, in these sectors. The other shape characteristics have not been assessed for their SCFT implications. We now define
velocity at the tropopause, except for the last one ( Keyser and Shapiro 1986 ). The particular characteristic of a narrower trough implies horizontally confluent flow along the uptrough sector and diffluent flow downtrough. From the classical perspective of strain-induced frontogenesis ( Hoskins and Bretherton 1972 ), we can therefore expect frontogenesis and frontolysis, respectively, in these sectors. The other shape characteristics have not been assessed for their SCFT implications. We now define
buoyancy flux [ EBF = ( τ w × z ^ / f ρ 0 ) ⋅ ∇ h b | z = 0 ] ( Thomas et al. 2013 ). In the upper ocean where eddies are most active, elongated surface density fronts and filaments are sharpened by the strain from larger-scale flows that enhance lateral buoyancy gradients via strain-induced frontogenesis (e.g., McWilliams et al. 2009a ; Gula et al. 2014 ). The horizontal strain rate arising from frontogenesis/frontolysis is given by the following expression: (5) St = ( u x − υ y ) 2 + ( υ
buoyancy flux [ EBF = ( τ w × z ^ / f ρ 0 ) ⋅ ∇ h b | z = 0 ] ( Thomas et al. 2013 ). In the upper ocean where eddies are most active, elongated surface density fronts and filaments are sharpened by the strain from larger-scale flows that enhance lateral buoyancy gradients via strain-induced frontogenesis (e.g., McWilliams et al. 2009a ; Gula et al. 2014 ). The horizontal strain rate arising from frontogenesis/frontolysis is given by the following expression: (5) St = ( u x − υ y ) 2 + ( υ
of the Shapiro–Keyser cyclone model shortly after its introduction, writing that the warm-frontal and polar-cold-frontal gradients of temperature distinctly separated (i.e., fractured) south of the cyclone triple point (junction of the cyclone’s warm and cold fronts). Horizontal frontogenesis diagnostics from a numerical simulation of this storm…show weak frontolysis...in this fracture region, and distinctly separated regions of warm and cold frontogenesis to the north and south. The Bergen
of the Shapiro–Keyser cyclone model shortly after its introduction, writing that the warm-frontal and polar-cold-frontal gradients of temperature distinctly separated (i.e., fractured) south of the cyclone triple point (junction of the cyclone’s warm and cold fronts). Horizontal frontogenesis diagnostics from a numerical simulation of this storm…show weak frontolysis...in this fracture region, and distinctly separated regions of warm and cold frontogenesis to the north and south. The Bergen
comparison, the ratio of the color scales among the three plots are chosen as the same as the bottom panels of Fig. 3 . Region 3 has the strongest buoyancy conversion among the three subdomains and displays a clear winter maximum which corresponds to the seasonal phase of the MLD and F s ( Figs. 3j and 5c ). This suggests that both mixed layer instability and strain-induced frontogenesis are at work in this region. It is interesting to note that intense frontolysis occurs beneath the mixed layer
comparison, the ratio of the color scales among the three plots are chosen as the same as the bottom panels of Fig. 3 . Region 3 has the strongest buoyancy conversion among the three subdomains and displays a clear winter maximum which corresponds to the seasonal phase of the MLD and F s ( Figs. 3j and 5c ). This suggests that both mixed layer instability and strain-induced frontogenesis are at work in this region. It is interesting to note that intense frontolysis occurs beneath the mixed layer
direct circulation was observed at the Antarctic Polar Front ( Naveira Garabato et al. 2001 ) and the Azores Front ( Rudnick 1996 ), which points to the importance of baroclinic instability in driving frontolysis, restratification, and net subduction at ocean fronts. The thermohaline intrusion descended along the 26.3 kg m −3 isopycnal surface, which is in the seasonal pycnocline that capped the EDW at this early stage in the winter season. The pycnostad to the south of the Gulf Stream’s center was
direct circulation was observed at the Antarctic Polar Front ( Naveira Garabato et al. 2001 ) and the Azores Front ( Rudnick 1996 ), which points to the importance of baroclinic instability in driving frontolysis, restratification, and net subduction at ocean fronts. The thermohaline intrusion descended along the 26.3 kg m −3 isopycnal surface, which is in the seasonal pycnocline that capped the EDW at this early stage in the winter season. The pycnostad to the south of the Gulf Stream’s center was
fluctuations extract energy mostly from the 2D frontal flow, increasingly with t 0 . This indicates that fluctuations play some role in retarding frontogenesis (often referred to as frontolysis) at least in an integral sense. Here we refine that characterization by examining the frontogenetic tendency balance ( Giordani and Caniaux 2001 ) derived from the alongfront-averaged buoyancy conservation equation including the nonlinear eddy flux. For simplicity we write it in untransformed coordinates (also used
fluctuations extract energy mostly from the 2D frontal flow, increasingly with t 0 . This indicates that fluctuations play some role in retarding frontogenesis (often referred to as frontolysis) at least in an integral sense. Here we refine that characterization by examining the frontogenetic tendency balance ( Giordani and Caniaux 2001 ) derived from the alongfront-averaged buoyancy conservation equation including the nonlinear eddy flux. For simplicity we write it in untransformed coordinates (also used
contribution by Ω k j , typically referred to as the (horizontal) rotation tensor, cancels out. Because F hor b in Eq. (A3) is written as a tensor dot product, it is in coordinate invariant form. Furthermore, Eq. (A3) illustrates that the components of the horizontal strain-rate tensor determine the rate of frontogenesis of frontolysis. The nondimensional S k j and b , k b , j subject to the scaling in Eq. (7) are (A4) S k j = [ Ro u x 1 2 ( υ x + ε Ro u y ) 1 2 ( υ x + ε Ro u y ) ε υ y
contribution by Ω k j , typically referred to as the (horizontal) rotation tensor, cancels out. Because F hor b in Eq. (A3) is written as a tensor dot product, it is in coordinate invariant form. Furthermore, Eq. (A3) illustrates that the components of the horizontal strain-rate tensor determine the rate of frontogenesis of frontolysis. The nondimensional S k j and b , k b , j subject to the scaling in Eq. (7) are (A4) S k j = [ Ro u x 1 2 ( υ x + ε Ro u y ) 1 2 ( υ x + ε Ro u y ) ε υ y
accompanied by northeast–southwest-tilted broadening troughs wrapping themselves up cyclonically and poleward. Shapiro et al. (1999) further added the term LC3 for the life cycle of the cyclone simulated in anticyclonic background shear. The location of cyclones relative to the region of strong environmental temperature gradient is also closely related to the warm and cold frontal structures. When a cyclone is located over a region of strong environmental horizontal temperature gradient, frontogenesis
accompanied by northeast–southwest-tilted broadening troughs wrapping themselves up cyclonically and poleward. Shapiro et al. (1999) further added the term LC3 for the life cycle of the cyclone simulated in anticyclonic background shear. The location of cyclones relative to the region of strong environmental temperature gradient is also closely related to the warm and cold frontal structures. When a cyclone is located over a region of strong environmental horizontal temperature gradient, frontogenesis
the location of the large positive values of . The large negative values of in those figures match well with the location of weakening gradient of (i.e., a site of frontolysis). In contrast, Fig. 11a reveals that the match between the location of the ULF and the pattern of positive values of is poor, where stands for horizontal gradient. Similar results are found in the simulation with diabatic heating. Unfortunately, in the original comment, Buzzi (2016) neither comments on the logic
the location of the large positive values of . The large negative values of in those figures match well with the location of weakening gradient of (i.e., a site of frontolysis). In contrast, Fig. 11a reveals that the match between the location of the ULF and the pattern of positive values of is poor, where stands for horizontal gradient. Similar results are found in the simulation with diabatic heating. Unfortunately, in the original comment, Buzzi (2016) neither comments on the logic
