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, and p ′ and w ′ 0 are perturbations of the surface pressure and velocity component normal to the surface. The second and third terms on the right-hand side of Eq. (1) represent wind stress work on the surface waves, which is discussed in a separate study by Wang and Huang (2004) . The first term on the right-hand side of Eq. (1) is the wind stress work on the quasi-steady currents on the surface, and quasi steadiness is defined in comparison with the time scale of typical surface waves
, and p ′ and w ′ 0 are perturbations of the surface pressure and velocity component normal to the surface. The second and third terms on the right-hand side of Eq. (1) represent wind stress work on the surface waves, which is discussed in a separate study by Wang and Huang (2004) . The first term on the right-hand side of Eq. (1) is the wind stress work on the quasi-steady currents on the surface, and quasi steadiness is defined in comparison with the time scale of typical surface waves
1112 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUIv!E22Analysis of Seasonal Current Variations in the Westeru Equatorial Indian Ocean: Direct Measurements and GFDL Model Comparison MARTIN VISBECK AND FRIEDRICH SCHOTTInstitut fitr Meereskunde an der Universitdt Kiel, Klel, Federal Republic of Germany(Manuscript received 27 September 1990, in final form 19 November 1991) The seasonal
1112 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUIv!E22Analysis of Seasonal Current Variations in the Westeru Equatorial Indian Ocean: Direct Measurements and GFDL Model Comparison MARTIN VISBECK AND FRIEDRICH SCHOTTInstitut fitr Meereskunde an der Universitdt Kiel, Klel, Federal Republic of Germany(Manuscript received 27 September 1990, in final form 19 November 1991) The seasonal
time-explicit solution 4~ defined by (3.9) and(3.10). This led to (3.11) which is nonlinear in the presence of measurements of some worth (w > 0). In comparison, the time-implicit but optimal solution ~k defined by (2.5)-(2.9) and (3.5)-(3.8) can have. only linearstructure near the data point at x = 0. This matter isdiscussed further elsewhere.d. Weaker forms of regularity The purpose of data assimilation is the creation oi~a field ,or "map" which is a satisfactory estimate ofsome quantity of
time-explicit solution 4~ defined by (3.9) and(3.10). This led to (3.11) which is nonlinear in the presence of measurements of some worth (w > 0). In comparison, the time-implicit but optimal solution ~k defined by (2.5)-(2.9) and (3.5)-(3.8) can have. only linearstructure near the data point at x = 0. This matter isdiscussed further elsewhere.d. Weaker forms of regularity The purpose of data assimilation is the creation oi~a field ,or "map" which is a satisfactory estimate ofsome quantity of
. The ship was north of Kane Basin during 3–12 August. The scene for 12 August in Fig. 2 is typical of the ice conditions encountered. The Healy was outfitted with hull-mounted ADCP to measure current profiles, swath-scanning sonar to map the seafloor, and thermosalinograph for continuous measurement of near-surface temperature and salinity. We used a conductivity–temperature–depth (CTD) probe and rosette sampling system to profile water properties at specific stations. Meteorological sensors
. The ship was north of Kane Basin during 3–12 August. The scene for 12 August in Fig. 2 is typical of the ice conditions encountered. The Healy was outfitted with hull-mounted ADCP to measure current profiles, swath-scanning sonar to map the seafloor, and thermosalinograph for continuous measurement of near-surface temperature and salinity. We used a conductivity–temperature–depth (CTD) probe and rosette sampling system to profile water properties at specific stations. Meteorological sensors
(exponential in time) separation between neighboring fluid particle trajectories. 1 As in the case of the polar vortex, the generation of small scales is controlled by long-lived, coherent structures, and the stirring process is therefore referred to as chaotic advection. By “long lived,” one generally assumes that the coherent structures remain intact over a time period long in comparison with the typical parcel winding time. It is not uncommon for flows undergoing chaotic advection to contain “barriers
(exponential in time) separation between neighboring fluid particle trajectories. 1 As in the case of the polar vortex, the generation of small scales is controlled by long-lived, coherent structures, and the stirring process is therefore referred to as chaotic advection. By “long lived,” one generally assumes that the coherent structures remain intact over a time period long in comparison with the typical parcel winding time. It is not uncommon for flows undergoing chaotic advection to contain “barriers
, as a first approximation, we expect P ≃ ε. In this paper we present and compare what we believe to be the first series of simultaneous and independent measurements of P and ε covering a large proportion of the water column, at a site with a strong tidal flow where the water column can be considered to be well mixed. It is widely recognized that production and dissipation will balance and so the experiment provides a critical comparison of the two profile methods employed. We shall identify
, as a first approximation, we expect P ≃ ε. In this paper we present and compare what we believe to be the first series of simultaneous and independent measurements of P and ε covering a large proportion of the water column, at a site with a strong tidal flow where the water column can be considered to be well mixed. It is widely recognized that production and dissipation will balance and so the experiment provides a critical comparison of the two profile methods employed. We shall identify
vortex-gas model; Gallet and Ferrari 2020 , 2021 ; Thompson and Young 2006 ). In this study, we take on the cascade viewpoint as a followup of Chen (2023) , but comparisons with the vortex-gas model will be made. The theories targeting asymptotic scaling behaviors clearly will encounter problems when applying to transitions where bottom drag and β influences are both at work. An apparent need for a more complete theory has motivated further developments. Recently, Chang and Held (2021
vortex-gas model; Gallet and Ferrari 2020 , 2021 ; Thompson and Young 2006 ). In this study, we take on the cascade viewpoint as a followup of Chen (2023) , but comparisons with the vortex-gas model will be made. The theories targeting asymptotic scaling behaviors clearly will encounter problems when applying to transitions where bottom drag and β influences are both at work. An apparent need for a more complete theory has motivated further developments. Recently, Chang and Held (2021
boundary layer eddy. d. Comparison of Monin–Obukhov scaling with observations According to MOST, the temperature difference between any two levels z i , z j in the surface layer should be (12) Δ θ ¯ i j = θ ¯ ( z i ) − θ ¯ ( z j ) = ∫ z j z i ϕ h ( | z | L ) θ * κ | z | d z , where | z i | and | z j | are the nominal sensor depths along the mooring line, and the universal function ϕ h used here is based on the results [Eqs. (3) ] from the Kansas experiment. These theoretical predictions
boundary layer eddy. d. Comparison of Monin–Obukhov scaling with observations According to MOST, the temperature difference between any two levels z i , z j in the surface layer should be (12) Δ θ ¯ i j = θ ¯ ( z i ) − θ ¯ ( z j ) = ∫ z j z i ϕ h ( | z | L ) θ * κ | z | d z , where | z i | and | z j | are the nominal sensor depths along the mooring line, and the universal function ϕ h used here is based on the results [Eqs. (3) ] from the Kansas experiment. These theoretical predictions
realistic upper boundary condition, the so-called “natural” boundary condition on salinity. Due to the restraint of the free surface requirement, this kind of boundary condition is not discussed here, but in terms of the scaling argument below it should be similar to the virtual salt flux case. For simplicity, wind stress effects are neglected in the scaling argument and in most of the numerical experiments. We call the combination of (1) and (2) “relaxation” boundary conditions and, in comparison
realistic upper boundary condition, the so-called “natural” boundary condition on salinity. Due to the restraint of the free surface requirement, this kind of boundary condition is not discussed here, but in terms of the scaling argument below it should be similar to the virtual salt flux case. For simplicity, wind stress effects are neglected in the scaling argument and in most of the numerical experiments. We call the combination of (1) and (2) “relaxation” boundary conditions and, in comparison
solution has severalfeatures. It is clear that the surface density must increasemonotonically poleward to avoid singularities in (3.10).As a corollary, there can be no closed contours of(shown more generally by Killworth, 1979). The gyreboundary is located where A vanishes for this solution,and bears little resemblance to maps of either wE orPs. The solution is nonunique because the constantK can be chosen arbitrarily within the limits givenby (3.8). Because B tends to zero at depth, so do u and v(algebraically
solution has severalfeatures. It is clear that the surface density must increasemonotonically poleward to avoid singularities in (3.10).As a corollary, there can be no closed contours of(shown more generally by Killworth, 1979). The gyreboundary is located where A vanishes for this solution,and bears little resemblance to maps of either wE orPs. The solution is nonunique because the constantK can be chosen arbitrarily within the limits givenby (3.8). Because B tends to zero at depth, so do u and v(algebraically
