Internal tide energetics in Internal tide energetics in the Sicilian Strait and the Sicilian Strait and

Adjacent areasAdjacent areas

Jihène Abdennadher and Moncef BoukthirUR1304, Institut Préparatoire aux Etudes

d’Ingénieur de Tunis, Tunisia

ROMS_Workshop 2008

ObjectivesObjectives

Characterize the internal tides Characterize the internal tides generation and propagation in the generation and propagation in the Sicilian Strait and in the adjacent areasSicilian Strait and in the adjacent areas

Estimate MEstimate M22 and K and K11 internal tide internal tide energeticsenergetics

Evaluate the contribution of the internal Evaluate the contribution of the internal tide into the mixingtide into the mixing

Model domain and configuration (ROMS)Model domain and configuration (ROMS)

• 1/32° x 1/32° (gebco 1/32° x 1/32° (gebco 1min resolution)1min resolution)

• 30 vertical levels30 vertical levels

• Realistic summer Realistic summer stratification (MEDAR)stratification (MEDAR)

• Forcing at the open Forcing at the open boundaries by tides boundaries by tides elevation of Melevation of M22 S S22 K K11 and and OO11 (Mog2d) (Mog2d)

• Mellor turbulent closure Mellor turbulent closure schemaschema

• 0.5° sponge layers0.5° sponge layers

Bathymetry of the model domain deduced from Gebco 1 minute resolution. Depths are in m.

Tunisia

Sicily

Adventure Bank

Messina strait

InternalInternal tidetide budget budget

12 20

0

'' .( )

2 2i

bt i i

u g dg w p u D A

t dzConversion rate Flux divergence

Internal energy density

is the background basic density stratification,0is the reference water density, 0

is the water density perturbation, 'is the pressure perturbation,ip

η z z(1 s) u v

t x ybtw

is the vertical velocity induced by the barotropic flow,

is the horizontal internal velocity,iu

The governing equation for the baroclinic energy is given by

Assuming that the advection of the baroclinic energy is negligible, the dissipation of the baroclinic energy averaged over a tidal period (denoted by an overbar) can be evaluated by

' bt i i

V V S

D dV gw dV p u dS ;;;;;;;;;;;;;;

Spatial distribution of:•a) Depth integrated Conversion rate of energy (W.m-2) ;•b) Depth integrated energy flux divergence (W.m-2) ;•c) Depth integrated dissipation rate (W.m-2).

(a)

(c)

The highest values of conversion occur at the western edge of the Adventure Bank, the western Sicilian Shelf and in the NW of Pantelleria isle. Strong local dissipation near the generation sites.

M2

M2 internal tide in theSicilian Strait

(b)

(a)

The Messina strait is a potential region of M2 internal tide generation.

M2 internal tide in the Messina Strait

Model-predicted distribution of the depth-integrated conversion rate from the M2 surface to internal tide.Integrated M2 baroclinic energy flux across the bounding transects is given in MW. Conversion(CRE), dissipation (DIS) and flux divergence (DIV) are given in MW.

M2 internal tide Energy budget

•The M2 conversion from surface to internal tide in the model domain amounts to 68 MW, 70% of which are in the Sicilian strait and 18 % in the Messina strait.• The Messina strait seems to be more dissipative (92 % of the available energy is dissipated) than the Sicilian strait (83 %).

The M2 mode conversion integrated over these prominent topographic features sums up to 35.6 MW, which is 75% of that

integrated over the Sicilian strait

42 % of the M2 baroclinic energy generated in the Sicilian strait is dissipated in close proximity to the baroclinic M2 generation sites.

M2

Model-predicted distribution of the depth-integrated conversion rate from the M2 surface to internal tide. Integrated M2 baroclinic energy flux across the bounding transects is given in MW. Conversion(CRE), dissipation (DIS) and flux divergence (DIV) are given in MW.

5.5

3.0

0.3 0.6

M2 Depth integrated internal energy flux (W.m-1)

Horizontal section at 100 m depth of the reconstructed vertical velocity at the M2 frequency(m/s) (Wavelet decomposition).

Vertical section at the west shelf Vertical section at the west shelf break of the Adventure Bankbreak of the Adventure Bank

This transect corresponds to the prominent direction of propagation of the M2 internal tides from the most efficient generation site

• Strong conversion occurs over the steepest parts of the continental slope (shelf edge of the AB) which is characterized by a supercritical slope as reveals the plot of the internal generation criteria parameter.

M2 Internal conversion rate of energy (10-6 W.m-3)

M2 Internal vertical displacement amplitude (m) (IDA)

M2 internal energy density (J.m-3)

M2 depth integrated internal energy flux along (Fxbar) and across (Fybar) component (W.m-1)

The cross and along shelf components of the M2 depth integrated energy flux reveal a seaward propagation as suggested by Sherwin (1991) and the ray theory of Baines (1982).

Internal generation criteria parameter

2 2

2 2; H

γ = fN f

•M2 internal vertical displacement amplitudes (IDA) in excess of 24 m are reached near the seabed.

• The largest value of internal energy density (7 J.m-3) is also located at the shelf break. Elsewhere, the internal energy is concentrated at the surface layers and is almost negligible in the bottom layers.

Hovmuller diagram related to the vertical velocity w at the surface.

TM2

x 10-5

T

ime

elap

sed

in d

ays

Distance from the transect origin (km)

Double periodicity of the internal tide, the temporal one is within M2 period and the spatial wavelength () is within the second barcolinic mode of propagation (68 km).

Internal mode of the M2 internal tide

K1

The depth-integrated K1 baroclinic energy flux and the depth integrated conversion rate (W.m-2)

K1 Internal tide generation

• The K1 internal tide is generated over the Adventure Bank’s edge, the surrounding of Pantelleria isle and the south east of the Malta plateau.

Model-predicted distribution of the depth-integrated conversion rate from the K1 surface to internal tide. Integrated K1 baroclinic energy flux across the bounding transects is given in MW. Conversion (CRE), dissipation (DIS) and flux divergence (DIV) are given in MW.

The total conversion over the model domain is 46.4 MW , 65 %65 % of which is in the Sicilian strait and 19 % in the south east of Malta plateau.

The energy converted over the model domain and in the subregions are totally lost which is coherent with the fact that K1 frequency is subinertial at these latitudes and so cannot propagate. K1

K1 internal tide Energy budget

Sensibility to initial Sensibility to initial stratificationstratification

x 10-3

Depth integrated energy flux and the depth integrated conversion (W.m-2) using initiala) Summer stratificationb) Winter stratificationc) Climatology stratification

(a) (c)

(b)

• Enhanced conversion in summer conditions in the Sicilian Strait.• No change in the K1 direction of the internal energy fluxes.

K1

x 10-3

(a) (c)

(b)

Depth integrated energy flux and the depth integrated conversion (W.m-2) using initial a) Summer stratificationb) Winter stratificationc) Climatology stratification

M2

•Enhanced conversion in summer conditions in the all generation sites.• Change in the orientation of energy fluxes which is coherent with the fact that energy ray slope is influenced by the stratification.

(a)

(b)

(c)

Depth integrated energy flux and depth integrated flux divergence (10-3 W.m-2) using initial : a) Summer stratification b) Winter stratification c) Climatology stratification

Sicilian strait Reduction of the conversion with respect to that obtained in summer solution

M2 K1

Winter 18 % 30 %

Climatology 11 % 21 %

Sicilian strait % of the dissipation to conversion

M2

Summer 84

Winter 93

Climatology 91

Internal tide MixingInternal tide Mixingqualitative approachqualitative approach

Bottom internal currents in the straits of Sicily (left) and Messina (Right) (cm.s-1)

Surface internal currents in the straits of Sicily (left) and Messina (Right) (cm.s-1)

The strong gradient between the surface internal current and the bottom one essentially at the A.B and in the narrow passage of the Messina strait may lead to strong mixing at these areas.

Turbulent Kinetic energy (cm2.s-2) at the bottom averaged over a tidal cycle in the straits of Sicily (left) and Messina (right).

ValidationValidation

M2

S2

K1

O1

53 m 93 m 285 m 380 m

C01

M2

S2

K1

O1

46 m 103 m 289 m 408 m

C02

• The M2 internal tide prevails over K1 at all depths• The internal signal is more important at C01 stationOur results are coherent with the measurements of Gasparini et al. (2004).

Internal density energy (J.m-3)CO1

CO2

ConclusionsConclusions M2 internal tide is generated over the western

shelf edge of the Adventure Bank, at the NW of Sicily and in the NW of the Pantelleria isle.

From the most efficient site the internal energy propagates toward the north and to the Tunisian coasts. The propagation from the Pantelleria isle is mainly toward the Tunisian coasts.

The M2 conversion of energy in the whole domain is 68 MW, 70 % of which are found in the Sicilian strait where strong dissipation occur in close proximity to the generation sites.

The K1 internal tide is less energetic than M2. Moreover, the K1 converted energy is totally dissipated in close proximity of the generation sites.

The generation sites appear as independents from the initial stratification, but the M2 conversion of energy as well as the propagation direction are strongly influenced by the initial stratification.

The NE of the Adventure Bank and the Messina strait are found to be strong mixing areas.

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