Flussi laminari e flussi turbolenti

Tubo di Pitot

BOTTOM DENSITY CURRENTS K-H billows develop when Fr D = U U ρ D g U D ρu ρ H 1 In a stratified flow over the bottom of the sea, the thickness of layer mixed is H 2 ρu D g( ρ ρ ) D U Mixing in negatively buoyant stratified flows happens if the velocity gradient is large (that is if the bottom is enough inclined) or near to local bottom irregularities; after this mixing, there is another stratified flow, less dense, to be mixed. COURSE B SECTION 10 SLIDE 10

BOTTOM DENSITY CURRENTS In case of free surface discharge, a stratified flow develops. Anyway the discharge is done, brine sinks toward the bottom and brine travels downslope, following bottom bathymetry, as a stratified flow. In a stratified flow, dilution is achieved with three mechanisms: molecular diffusion (very slow), dispersion by external forces (such as currents or tides, not always guaranteed) and turbulent mixing. Kelvin-Helmholtz billows COURSE B SECTION 10 SLIDE 09

I GETTI

ENTRAINMENT

DILUIZIONE Media Re

C.1.1 TURBOLENZA Turbolenza presente in molti campi dell ingegneria (aerodinamica, diluizione di inquinanti, studio della scia a valle di un corpo in movimento, miscelazione e combustione in reattori chimici, moto dell aria nell apparato respiratorio e del sangue a valle di valvole cardiache, ecc.). Turbolenza: fenomeno non totalmente compreso ma non casuale: le statistiche della separazione di coppie di particelle (~t 3 ) sono diverse da quelle dei random walks (~t 1 ) (Ottino 1990). Approccio topologico: punti critici iperbolici ed ellittici, geometria frattale e strutture ad 8 in 8 (es.: Antonia et al. 1986, Davila & Vassilicos 2003). PUNTO CRITICO ELLITTICO PUNTO CRITICO IPERBOLICO 6/ 19

C.1.2 TURBOLENZA 2D in atmosfera Turbolenza quasi-bidimensionale (Q2D): importanza teorica (semplificazione della 3D ma anche peculiarità: conservazione lagrangiana della vorticità, cascata inversa dell energia, ecc.) e pratica (es. previsioni atmosferiche, moto delle masse d acqua negli oceani e nell atmosfera). VORTICE E PUNTO CRITICO ELLITTICO GETTO 2D PUNTI CRITICI IPERBOLICI 7/ 19

C.1.2 TURBOLENZA 2D in oceano

Measurement via PTVA of the acceleration on quasi-two two-dimensional turbulent-like like flows controlled by multi-scale electromagnetic forces Simone Ferrari (1)(2), Lionel Rossi (2) and John Christos Vassilicos (2) (1) (2)

1.2. Q2D EM controlled multi-scale flows Experimental set-up: a shallow layer of brine EM forced. Topology and forcing time-dependency are known and controlled. Power-law shaped energy spectrum and Richardson-like pair dispersion properties (Rossi et al., JFM 2006) in a laminar steady flow. Experiments: constant and time-dependent forcing. Electrodes Magnets Tank size: 1700x1700 mm² Brine layer s thickness: 5 mm Electrodes Magnets size: 160 mm, 40 mm, 10 mm a b Flow visualizations with constant forcing; (a, b, c: whole field; d: SW quarter) Stirring on the SW quarter (same flow on the left) c d 4/ 17

Diluizione e turbolenza Constant forcing Time-dependent forcing

3.5 Time dependent flows Time dependent forcing with different frequencies, mean intensities and magnitudes, to excite different flow scales. A further step towards fully controlled turbulent-like flows. Mass exchange between small and medium scales is enhanced. Mass exchange between large and medium scales is enhanced. Expected time scales of the three scales of forcing t versus current I; M160, M40 and M10 refers to the magnets size; the black straight line identifies the current value over which the bottom friction is no more negligible. 15/ 17

3.1 Results: measured trajectories Trajectories are measured at all the scales of the flow (stagnation points with three different length scales). Example of measured trajectories (8 runs): on the left the whole investigation field, on the right a zoom on the SW quarter MAGNETS POSITION = hyperbolic stagnation point = elliptical stagnation point large scales medium scales small scales 10/ 17

Dal Lagrangiano all Euleriano

3.2 Results: Eulerian fields VELOCIY: hyperbolic stagnation point; ACCELERATION: source ; elliptical stagnation point sink ; spreader The mesh has 600x600 points with a mesh s size of 3x3 pixels (resolution 4 times higher than PIV) 11/ 17

Accelerazione Flusso con accelerazione locale nulla. Deformazione L accelerazione è alta dove sia la velocità che la deformazione sono alte. Accelerazione Velocità 12a/ 17

3.3 Results: Navier-Stokes equations terms A zoom on the SW quarter to highlight the physical coherence of the measures. Acceleration is much larger than viscous term everywhere but at the small scales (like in turbulent flows). Viscous term Acceleration Velocity This allows an indirect measure of the pressure gradient over all the investigation field. Acceleration and viscous term in pixel/s 2, velocity in pixel/s; 1 pixel = 0.495 mm 12b/ 17

3.4 Results: towards efficient mixing u a MAGNETS POSITION a Power input and output, in pixel 2 /s 3 ; 1 pixel = 0.495 mm Stirring intensity, in s -2 ; 1 pixel = 0.495 mm The power input-output is closely related to the pressure term. Experimental measure of a over the whole investigation field. Local maxima of a correspond to acceleration sources, local minima of a correspond to acceleration sinks. Stirring is stronger where a large and positive (Vassilicos, 2002): the points of highest stirring are not the ones connected to the largest power input. Tools to optimize the power input according to the required mixing => efficient mixing. 14/ 17

ferraris@unica.it