Eulerian and Lagrangian studies in surface flow turbulence

Cressman, John R.; Davoudi, Jahanshah; Goldburg, W. I.; Schumacher, Jörg

doi:10.1088/1367-2630/6/1/053

Cited by 71 publications

(130 citation statements)

References 42 publications

Supporting

Mentioning

117

Contrasting

Order By: Relevance

“…Hence, the shallow flow is dominated by bottom friction and as has been shown by Duran-Matute et al 8 for flows in the regime determined by (22), the vertical structure quickly relaxes to Poiseuille-like profile. This a posteriori justifies the presumed Poiseuille-like vertical structure of the horizontal flow (see (3) and Ref. 9).…”

Section: Quasi-linear Theory Of Secondary Motion In Q2d Shallow Fsupporting

confidence: 72%

“…This compressibility leads to inhomogeneous distributions of Lagrangian tracers on such surface flows resulting in a clustering of the tracers in ridge-like structures and meandering streams. [2][3][4] In the present paper, we will quantitatively relate magnitude and spatial distribution of vertical motion inside a shallow fluid layer to the local distribution of strain and vorticity of the surface flow. Furthermore, the compressibility of this surface flow is also quantified in terms of the local strainvorticity balance in the horizontal flow field as described by the Okubo-Weiss function.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Strain-vorticity induced secondary motion in shallow flows

Kamp

2012

Physics of Fluids

View full text Add to dashboard Cite

Deviations from two-dimensionality of a shallow flow that is dominated by bottom friction are quantified in terms of the spatial distribution of strain and vorticity as described by the Okubo-Weiss function. This result is based on a Poisson equation for the pressure in a quasi-horizontal (primary) flow. It is shown that the Okubo-Weiss function specifies vertical pressure gradients, which for their part drive vertical (secondary) motion. An asymptotic expansion of these gradients based on the smallness of the vertical to horizontal scale ratio demonstrates that the sign and magnitude of secondary circulation inside the fluid layer is dictated by the signs and magnitude of the Okubo-Weiss function. As a consequence of this, secondary motion as well as nonzero horizontal divergence do also depend on the strength, i.e., the Reynolds number of the primary flow. The theory is exemplified by two generic vortical structures (monopolar and dipolar structures). Most importantly, the theory can be applied to more complicated turbulent shallow flows in order to assess the degree of two-dimensionality using measurements of the free-surface flow only.

show abstract

Section: Quasi-linear Theory Of Secondary Motion In Q2d Shallow Fsupporting

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Strain-vorticity induced secondary motion in shallow flows

Kamp

2012

Physics of Fluids

View full text Add to dashboard Cite

show abstract

“…(8.12) compared to the pure 2D case (Bec et al 2004;Kalda 2007). For a review of relevant laboratory experiments see Cressman et al (2004). For realistic geophysical flows one might expect quite a large variation in the range of 1.5 ≤ b < ∞ of this exponent.…”

Section: Spreading Rates In the Uppermost Layer Of The Gulf Of Finlandmentioning

confidence: 99%

Evaluation and Tuning of Model Trajectories and Spreading Rates in the Baltic Sea Using Surface Drifter Observations

Kjellsson

Döös

Soomere

2013

Preventive Methods for Coastal Protection

View full text Add to dashboard Cite

Results from experiments with surface drifters in the Baltic Sea in 2010-2011 are presented and discussed. In a first experiment, 12 SVP-B (Surface Velocity Program, with Barometer) drifters with a drogue at 12-18 m depth were deployed in the Baltic Sea. In a second experiment, shallow drifters extending to a depth of 1.5 m were deployed in the Gulf of Finland. Results from the SVP-B drifter experiment are compared to results from a regional ocean model and a trajectory code. Differences between the observed SVP-B drifters and simulated drifters are found for absolute dispersion (i.e., squared displacement from initial position) and relative dispersion (i.e., squared distance between two initially paired drifters). The former is somewhat underestimated since the simulated currents are neither as fast nor as variable as those observed. The latter is underestimated both due to the abovementioned reasons and due to the resolution of the ocean model.For the shallower drifters, spreading in the upper 1-2 m of the Gulf of Finland is investigated. The spreading rate is about 200 m/day for separations <0.5 km, 500 m/day for separations below 1 km and in the range of 0.5-3 km/day for separations in the range of 1-4 km. The spreading rate does not follow Richardson's law. The initial spreading, up to a distance of about d = 100-150 m, is governed by the power law d ∼ t 0.27 whereas for larger separations the distance increases as d ∼ t 2.5 .

show abstract

“…References [5,6] summarise results of direct numerical simulations of tracers floating on the surface of turbulent flows, and characterise the resulting fractal patterns in terms of their Lyapunov dimensions.…”

mentioning

confidence: 99%

Lyapunov Exponents for Particles Advected in Compressible Random Velocity Fields at Small and Large Kubo Numbers

Gustavsson

Mehlig

2013

J Stat Phys

View full text Add to dashboard Cite

We calculate the Lyapunov exponents describing spatial clustering of particles advected in one-and two-dimensional random velocity fields at finite Kubo numbers Ku (a dimensionless parameter characterising the correlation time of the velocity field). In one dimension we obtain accurate results up to Ku ∼ 1 by resummation of a perturbation expansion in Ku. At large Kubo numbers we compute the Lyapunov exponent by taking into account the fact that the particles follow the minima of the potential function corresponding to the velocity field. The Lyapunov exponent is always negative. In two spatial dimensions the sign of the maximal Lyapunov exponent λ 1 may change, depending upon the degree of compressibility of the flow and the Kubo number. For small Kubo numbers we compute the first four non-vanishing terms in the small-Ku expansion of the Lyapunov exponents. By resumming these expansions we obtain a precise estimate of the location of the path-coalescence transition (where λ 1 changes sign) for Kubo numbers up to approximately Ku = 0.5. For large Kubo numbers we estimate the Lyapunov exponents for a partially compressible velocity field by assuming that the particles sample those stagnation points of the velocity field that have a negative real part of the maximal eigenvalue of the matrix of flow-velocity gradients.

show abstract

Eulerian and Lagrangian studies in surface flow turbulence

Cited by 71 publications

References 42 publications

Strain-vorticity induced secondary motion in shallow flows

Strain-vorticity induced secondary motion in shallow flows

Evaluation and Tuning of Model Trajectories and Spreading Rates in the Baltic Sea Using Surface Drifter Observations

Lyapunov Exponents for Particles Advected in Compressible Random Velocity Fields at Small and Large Kubo Numbers

Contact Info

Product

Resources

About