On the amplification of convergences in coastal currents and the formation of squirts

We consider the temporal evolution of a slow downstream decrease in the velocity of a coastal current contained in the light upper layer of the ocean. The quasi-geostrophic model consists of two piecewise uniform potential vorticity regions separated horizontally by a free interface ( front ) which intersects the vertical coastal wall in a nose region. As time increases, the slope of the front increases in this region, and the magnitude of the downstream convergence also increases, according to a nonlinear long-wave theory. At the time when this theory becomes invalid, the calculation is continued by numerical integration of the contour dynamical equations. This shows a continuation of the increase of the slope of the front near the nose, provided the total geostrophic transport is nonzero. (The case of zero transport is also discussed.) As time increases, a plume forms near the nose of the front, thereby transporting coastal water to very large offshore distances. It is suggested that this effect is responsible for some of the cold water plumes which extend to large distances from the coast of California. The cause of the small finite initial convergence (not implicit in our simple model) is attributed to differential upwelling or to a current instability

Initiation of a doubly diffusive convection in a stable halocline

A vertically stable density stratification with temperature gradient Tz \u3c 0, salinity gradient Sz \u3c 0, and with density compensating horizontal T/S gradients is unstable to lateral intrusions because the molecular heat diffusivity is much larger than the salt diffusivity. Previous marginal instability theory is extended to the supercritical regime. The fastest growing vertical wavelength (δz) is obtained in a model of a T/S front with finite lateral width (L*) and lateral salinity variation (ΔS). The value of δz ≈ ΔS/|Sz| varies only slightly with the parameters, and this result is applied to the smallest step size observed in the main thermocline of the Weddell Sea. Nonlinear considerations show that the laterally divergent heat/salt flux produced by the instability forces a mean vertical circulation which enhances the compensating lateral T/S gradients, thereby accelerating the intrusive instability, and eventually producing local density ratios sufficient to initiate strong vertical convection. This suggests that weak isopycnal T/S gradients are necessary to initiate the steps which subsequently merge into larger layers

Interaction of inertia-gravity waves with the wind

An inertia-gravity wave which propagates upwind and upward in the thermocline has a reflection coefficient r which is greater than unity ( overreflection ) as a result of the wave current interaction in the mixed layer which overlies the thermocline…

The 1962 Summer Program in Geophysical Fluid Dynamics

Originally issued as Reference No. 62-38, series later renamed WHOI-.Includes the preprint "Mixing-length Analyses of Turbulent Thermal Convection at Arbitrary Prandtl Number" - R. Kraichnan (1962). N.Y.U. Research Report No. HSN-6.National Science Foundation under Research Grant NSF2233

Minimal properties of planetary eddies

An isolated barotropic eddy on the β-plane can be in equilibrium only if it is composed of a coupled cyclone-anticyclone system, only if it is separated by a vorticity discontinuity (free streamline) from the surrounding fluid..

Direct Numerical Simulation of 3D Salt Fingers: From Secondary Instability to Chaotic Convection

The amplification and equilibration of three-dimensional salt fingers in unbounded uniform vertical gradients of temperature and salinity is modeled with a Direct Numerical Simulation in a triply periodic computational domain. A fluid dynamics video of the simulation shows that the secondary instability of the fastest growing square-planform finger mode is a combination of the well-known vertical shear instability of two-dimensional fingers [Holyer, 1984] and a new horizontal shear mode.Comment: APS DFD Gallery of Fluid Motion 200

Salt fingers in three dimensions

Three dimensional (3D) numerical calculations are made for a vertically unbounded fluid with initially uniform vertical gradients of sugar ( S ) and salt ( T ), where τ = κS/κT = 1/3 is the diffusivity ratio, and the molecular viscosity is ν \u3e\u3e κT. The latter inequality allows us to neglect the nonlinear term in the momentum equation, while retaining such terms in the T-S equations. The discrete 3D Fourier spectrum resolves the fastest growing horizontal wavelength, as well as the depth independent Fourier component. Unlike previous calculations for the pure 2D case the finite amplitude equilibration in 3D is primarily due to the instability of the lateral S-gradients in the fingers, and the consequent transfer of energy to vertical scales comparable with the finger width. It is shown that finite amplitude two-dimensional disturbances are unstable and give way to three dimensional fingers with much larger fluxes. Calculations are also made for rigid boundary conditions at z = (0,L) in order to make a rough quantitative comparison with previous lab experiments wherein a finger layer of finite thickness is sandwiched between two well-mixed (T,S) reservoirs. The flux ratio is in good agreement, and the fluxes agree within a factor of two even though the thin interfacial boundary layer between the reservoir and the fingers is not quite rigid because sheared fingers pass through it. It is suggested that future experiments be directed toward the much simpler unbounded gradient model, for which flux and variance laws are given herein

The salt finger amplitude in unbounded T-S gradient layers

Finite amplitude numerical calculations are made for a completely unbounded salt finger domain whose overall vertical property gradients (Tz and Sz) are uniform and remain unaltered in time. For diffusivity ratio τ = κS/κT = O (1), Prandtl number ν/κT \u3e\u3e 1, and density ratio R = Tz/Sz \u3e 1 this regime corresponds to a double gradient sugar (S)—salt (T) experiment. Two-dimensional pseudo-spectral calculations are made in the vicinity of the minimum critical condition for salt finger instability, viz., small ε ≡ (Rτ)-1 - 1 \u3e 0; the allowed spectrum includes the fastest growing wave of linear theory. When the vertical wavelength of the fundamental Fourier component is systematically increased the solution changes from a single steady vertical mode to a multi-modal statistically steady chaotic state. Each of the long vertical modes can be amplified by the (unchanging overall) gradient Sz, and can be stabilized by the induced vertical T, S gradients on the same scale as the modes; nonlinear triad interactions in the T - S equations can also lead to amplitude equilibration even though ε, κT/ν, and the Reynolds number are extremely small. When subharmonics of the horizonal wavelength of maximum growth are introduced into the numerical calculations the new wave amplifies (via Sz) and produces a quantitative change in the time average fluxes. Experimentally testable values of heat flux and rms horizontal T-fluctuations are computed in the range 2.8 \u3e R \u3e1.6 for τ = 1/3. Asymptotic similarity laws ε → 0 are also presented

1979 summer study program in geophysical fluid dynamics : the Woods Hole Oceanographic Institution : notes on polar oceanography

The emphasis in this year's GFD program has been somewhat different from the past. We have tried to expose a theoretically oriented audience to the new body of observations pertaining to the Arctic and Antarctic circulation. We have, however, not departed from our traditional goal of encouraging broad based inquiries into the field of Geophysical Fluid Dynamics. We would like to believe that the breadth of interest and enthusiasm exhibited in these reports will stimulate future work in Polar Oceanography and Fluid Dynamics.Office of Naval Research under Contract N00014-79-C-067

Mechanism of eddy separation from coastal currents

A series of multi-layer numerical experiments show that classical finite amplitude instabilities in boundary currents are not sufficient to account for the pinched-off eddies observed in the ocean and in laboratory experiments. These instabilities (barotropic or baroclinic) are shown to lead to an entrainment of offshore fluid into the boundary currents. Eddy separation, on the other hand, requires an additional process, such as a larger scale of motion containing a downstream velocity convergence of finite amplitude; this might be produced by long period fluctuations in the discharge from an upstream source region which controls the boundary current, or by topographic features. In our spatially idealized model, we numerically computed the temporal evolution of an assumed initial state consisting of a fast moving upstream region separated by a potential vorticity front from a slow moving downstream region. We verify long-wave theories which show that this initial state indeed leads to frontal steepening and to a blocking wave. This eventually produces large transverse velocities followed by complete detrainment of eddies without any entrainment into the residual boundary current