Effect of Structure of Internal Waves on Energy Transfer and Flow Control Between South and Middle Basins of Caspian Sea

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1 Modern Appled Scence; Vol. 10, No. 3; 016 ISSN E-ISSN Publshed by Canadan Center of Scence and Educaton Effect of Structure of Internal Waves on Energy Transfer and Flow Control Between South and Mddle Basns of Caspan Sea Ashrafoalsadat Shekarbaghan 1 1 Organzaton for Educatonal Research and plannng(oerp), Iran Correspondence: Ashrafoalsadat Shekarbaghan, Assstant Professor n Physcs Department of Scence & Mathematcs Educaton, of Educaton Studes Research Center, Organzaton for Educatonal Research and plannng(oerp), Iran, Tehran. E-mal: a0.baghan@gmal.com Receved: December 10, 015 Accepted: January 10, 016 Onlne Publshed: January 13, 016 do: /mas.v10n3p33 URL: Abstract In ths study, role of nternal waves n controllng stratfed exchange flows between south and mddle basns of Caspan Sea and energy transfer have been studed. The studes have been conducted based on feld and theoretcal studes based on numercal calculatons. In ths nvestgaton, Caspan Sea has been consdered as stratfed and Boussnesq approxmaton has been consdered. In equatons governng the movement, coheson and compressblty have been neglected. In the feld studes, nvestgaton of densty profles ndcate sgns of stratfed structure whch so far has been attrbuted to dual dstrbuton convecton phenomenon, but by consderng densty rato profle and values of densty rato whch are mostly negatve numbers, the factor causng stratfed structure of Caspan Sea can be attrbuted to exstence of nternal waves. Densty feld n these two basns ndcate that the mddle basn has hgher average densty compared to the south basn, ths fact can cause creaton of a gravty exchange flow. Ths exchange flow causes creaton of nternal waves n ths sea that can have a modal structure towards vertcal drecton. In theoretcal studes, the two mddle and south basns of Caspan Sea are networked n two dmenson x-z systems and equatons governng movement are solved through a numercal method by usng fnte dfference method and the vertcal velocty values obtaned n 90 ponts of the network was almost 10-6 to 10-4 m/s, meanng that vertcal movements are much smaller. Values obtaned for horzontal velocty are almost 10-3 to 10-1 m/s. Vertcal and horzontal velocty profles obtaned from soluton of these equatons and also densty profle obtaned n four ntegraton perods ndcate that as a result of passage of gravty flow between the two basns, densty n varous ponts of the two basns change. The structure created from nternal waves on the crest causes creaton of shear strata observed. Ths structure can be effectve n exchange of the two basns. Therefore, n transfer and energy converson, dentfcaton of the created strata s of a hgh mportance. Keywords: nternal waves, normal modes, dstrbuton convecton, gravty flow, Caspan Sea 1. Introducton Observatons ndcate exstence of stratfed structure n seas; so that the way of creaton of stratfed structure has always been a queston. Dfferent mechansms such as dual dstrbuton, nternal waves, and turbulent mxng have been proposed for creaton of them []. Ruddck [199] beleves that exstence of stratfed structure depends on dual dstrbuton [3], but n the Caspan Sea the condtons of creaton of dual dstrbuton are less observed. Hence, exstence of nternal waves should cause creaton of stratfed structure. Therefore, mechansms of nternal waves are more acceptable for creaton of a stratfed structure. Exstence of nternal waves n stratfed envronments such as sea s very common. These waves have a more effectve role n transferrng the momentum n sea [4, 5]. Normal modes of these waves cause creaton of shear layers whch have also been observed n expermental medums [6]. The stratfed structure related to normal modes of these waves can be mportant n vertcal and horzontal transfer n marne envronments or dffuson of sound waves whch are usually used for searchng n seas. Wong et al. (001) ndcated that n closed envronments, flows due to plumes that move n the bottom of the closed basn have caused nternal waves that ther phase velocty s towards down and ther group velocty s towards up drectons. Equalty of ther phase velocty wth advecton velocty due to plume wth fllng box 33

2 Modern Appled Scence Vol. 10, No. 3; 016 mechansm, cause creaton of sem-statonary modal structure. Also ths structure has caused creaton of shear strata (5 to 7) whch are effectve n creaton of stratfed structure of physcal quanttes such as salnty and temperature [6]. Vertcal structure of physcal propertes such as salnty and temperature n lakes also ndcate these strata. For nstance, Boehrer (000) by nvestgatng vertcal structure of salnty and temperature n Constance Lake ndcated that regular strata are observed n them so that nternal waves can be analyzed nto modes that each can transfer ndependently, consderng ths fact that ndependent waves n lakes can be observed wth hgher probablty. Therefore, the hypothess that n lakes, all water motons end n nternal waves s a reasonable hypothess. Hence, he attrbuted the profle of flow velocty n Constance Lake to the velocty obtaned from solvng equatons of nternal waves and by proposng an analytc model of normal modes of nternal waves, justfed them [7]. Hogg et al. (000) nvestgated role of nternal waves n controllng stratfed exchange flows between two closed marne basns by solvng equatons governng movement wth numercal methods by determnng Egen value matrx. At frst, created nternal waves n an expermental smulaton n order to create exchange flow n a reservor ncludng the two basns, then by examnng waves n terms of locaton and tme, calculated propagaton velocty. After ths operaton, based on theory of hydraulc control n stratfed current conservaton, flud velocty n defned and separate strata that ther nteracton occurs only n lmted condtons was calculated and then compared wth velocty of nternal waves n the water column [8]. Bans and Turner (1969) ndcated that gravty flows cause modal movements (together wth nternal waves) [9]. Hydrographcal structure of Caspan Sea whch s a closed lake s n such a way that can be consdered n two mddle and south basns. Exstence of a mound between mddle and south basns of Caspan Sea whch s almost located besde Abshouran pennsula, causes that flow exchange between the two basns from top of the mound, cause creaton of nternal waves. Meanng that the gravty flow between the two basns especally on the bottom towards the south basn from top of the mound n the stratfed area, causes creaton of such waves. On the other hand, modal structure of these waves should be effectve n the way of flow exchange between these two basns. In ths research an analytc (numercal) model has been proposed and compared wth feld observatons and the obtaned results are dscussed. These results can be compared wth those obtaned from studes conducted by Boehrer and Hogg et al., and t s found that there s an approprate consstency between these results. Several studes have been conducted on coastal areas and waves caused by wnds n the Caspan Sea, however, few studes have been conducted on marne physcs of varous parts of Caspan Sea. Therefore, t seems that the present study s a new approach n terms of ssues of marne physcs related to nternal parts of the Caspan Sea especally n Abshouran regon.. Feld Study In ths research, the obtaned data by CTD measurements have been used for provdng σ t profle. Plan of the Caspan Sea and CTD measurement statons have been ndcated n the frst research tour of the Internatonal Atomc Energy Agency n fgure 1 [1]. Feld observatons ndcate σ t profle of stratfed structure of the Caspan Sea n fgure 3. σ t values n these waters are often negatve and less than one. 3. Analytc Model Internal waves n an area wth densty stratfcaton can be obtaned by analyss of the movement equatons. In small movements, ampltude of pressure and densty changes are as follows, respectvely: PP(z)+P (x,y,z,t) ρρ(z)+ρ (x,y,z,t) Where, P(Z) s hydrostatc dstrbuton of pressure n water column and P' represents fluctuatons of pressure, ρ(z) s vertcal dstrbuton of densty feld and ρ s also changes related to densty feld. Horzontal components of flud's movement are as follows: ρ(ut-fv)-p'x (1) ρ(vt-fu)-p'y And ts vertcal component s: ρ(wt) -P z - gρ () 34

3 Modern Appled Scence Vol. 10, No. 3; 016 And the ndexes are ndcatng the partal dervatve (for example Ut u t ). Also f Ω snφ s the Corols parameter so that φs the lattude and Ωs the angular velocty of the ground. Mass contnuty equaton for ncompressble condtons s also as follows: u x +v y +w z 0 (3) Also buoyancy conservaton equaton s: 0 d ρ t +w ρ (4) dz The equaton ndcates local changes of densty due to vertcal movements of the flud n densty feld wth vertcal gradent. By combnng these equatons an equaton based on vertcal component of the velocty of flud movement can be obtaned [10]: w N H w f w t z Where N s frequency of buoyancy of the envronment and s: N ρ ρ z, g H + x y Equaton 5 has a wave soluton. For nstance, for small ampltude movements n a flud wth stable densty stratfcaton, ths soluton can be n the followng form: kx ( + ly ωt) w wˆ( z) e (6) Where wz ˆ( ) s vertcal structure of ampltude of vertcal movements that can nclude multple modes of Wn (n0, 1,, 3, 4, ). These modes are orthogonal functons and are known as normal modes. K and L are horzontal components of vector of turbulence wave number andω s turbulence frequency and exponental part of ths term ndcates tme horzontal structure of the turbulence. Ampltude of the vertcal movement of partcles of the flud proportonal to w n s h n and n case where Boussnesq approxmaton s applcable, by replacng equaton 6 nto equaton 5, t can be ndcated that vertcal structure of normal modes s as the followng relaton [10]: d w ˆ ( N ω )( k + l + ) w ˆ 0 (7) dz ω So that for fxed and postve values of N has trgonometrc soluton as follows: Also we have: ( N ω )( k + l ) wˆ sn( ( z+ H) ω (5) n d h dz N + hn 0 Cn (8) Where C n s phase velocty of mode "n" and we have C n ghe n whch e H s the equvalent heght [10]. For n0, movement mode s the same barotropc mode whch ts phase velocty s gh and H s heght of the stratum. For n>0, modes are related to baroclnc movements and 1 C n s the especal value accordng to 35

4 Modern Appled Scence Vol. 10, No. 3; 016 especal functons of h ( z ). For a medum wth fxed N, soluton of equaton 8 wth boundary condtons h 0 n z 0, H s as follows: n n n d h N + hn 0 (9) dz Cn Boundary condtons of h n 0 n surface of the flud stratum ndcates rgd ld approxmaton. Structure of these functons for varous modes s n a way that for n1, the functon has one peak and for n, the functon has two peaks, and etc. By havng w n n accordance wth h n, horzontal veloctes of u n can also be obtaned by usng conservaton equaton [6]. Of course, n the model proposed by Wong et al., effect of molecular coheson has also been consdered whch ndcates that vertcal structure of normal modes have attenuaton. Ths effect (attenuaton) can also be observed n feld and expermental observatons (fgure 6) [11]. Due to exstence of densty dfference between two ponts of the same heght from two basns of the Caspan Sea and also densty dfference between two ponts n the same dstance from coast and of dfferent heghts, value of N s varable. Therefore, there s no analytc soluton for equaton 7 and numercal method should be appled. For ths purpose, frst the two basns n the Caspan Sea are networked and then the equaton governng nternal waves on ponts of the network are solved. Equaton of nternal waves wll be wrtten n drectons of x (along north-south drecton of the Caspan Sea) and z (along vertcal drecton from surface to bottom of the sea) n D coordnate system accordng to equaton 5 by consderng assumptons of ncompressblty and non-cohesveness of the flud and usng Boussnesq approxmaton as follows [10]: w N w t x z x After nettng the basn, orgn of the coordnate s assumed on the southern coast of the Caspan Sea (Nowshahar Cty), then general answer of the equaton s defned as follows [7]: wxzt (,, ) { aw j j( z).cos( kx ω jt) } (11) Consderng boundary condtons for all "J", the followng relaton exsts: j W (0) W ( H) 0 j By replacng equaton 11 n equaton 10, the followng equaton s obtaned: { cos( kx ωjt) a j( W j ωj + W jk ( N ω j) } 0 (1) j j j ωj j ωj (10) W + W k ( N ) 0 (13) u w Consderng conservaton equaton of + 0 x z, we have: 1 uxzt (,, ) Σj{ aw j j ( z) sn( kx ω jt)} k 1 U j Wj (15) k Frst, Wj, vertcal velocty of nternal waves, s obtaned n the J defned n equaton 13, then Uj whch s horzontal velocty of nternal waves n the J defned n equaton 15 s obtaned. (14) For calculatng Wj, equaton 13 s solved by usng fnte dfference method whch means the term z w to the defned and lmted value. For ths purpose, backward dfference method s used whch means the dervatve s 36

5 Modern Appled Scence Vol. 10, No. 3; 016 stuated as functon n varous ponts, n fact dervatve s made separated by Taylor Seres: W W + W j, j,( 1) j,( ) Δz j, 1 dw dz (16) By replacng equaton 16 n equaton 13, the followng relaton s obtaned: Wj, Wj,( 1) + W j,( ) N j,( 1) + k 1 W j,( 1) 0 Δz ω j, K s wavenumber and L s wavelength. If wavelength s assumed to be one eghth of length of the regon, by usng relaton of the wavenumber; (17) π k (18) L wavenumber value for calculatons obtaned as equal to 5 1 π 10 m. N s the buoyancy frequency, ω s wave frequency, C s wave propagaton velocty, g' s the reduced gravty ntensty, and h s the heght of water from sea level, then the followng relatons are obtaned: N Δρ. g Δ z ρ N j,( 1) ρ ρ ρ g + ρ Δz j,( 1) j, j,( 1) j, (19) ω kc 1/ ω j ( 1) kgh ( ) (0) ω j,( 1) k ρ ρ ρ j,( 1) j, + ρ j,( 1) j, gh N ( j, 1) 1 ω ( j, 1) k Δzh (1) It s observed that for solvng these equatons, frst j and should be defned n the regon beng studed. Hence, networkng method should be used. W j, ndcates vertcal velocty n specfc and j whch are stuated n a specfc pont, Wj, 1 ndcates vertcal velocty n a pont wth dstance Δx from the coast and wth heght dfference equal to Δ z before the pont (,j), and Wj,( ) ndcates vertcal velocty n a pont wth Δx dstance from the coast and heght dfference equal to Δ z before the pont (,j). 3.1 Networkng Method In order to calculate W, the regon of the study should be networked n terms of and j.for ths purpose, accordng to fgure, we dvde X axs nto 1 equal dvsons wth 70 km dstance from each other, ndcate j on the X axs so that we would have ponts from 1 to 13 and we dvde Z axs nto 40 equal dvsons wth 0 km dstance from each other, ndcate on Z axs so that we would have from 1 to 40. In ths case, j1 and 1 are related to orgn ofd coordnate system, so for and j we wll have: j1,, 3, 4,,13 37

6 Modern Appled Scence Vol. 10, No. 3; 016 1,, 3, 4,,40 Therefore, dstance between two successve j parameter s 70km and the dstance between two successve parameters s 0km. Dstance between two successve parameters s equal to Δz between the two pontsand h value whch s heght from sea level s equal to ( 1) Δ z: h ( 1) Δ z 0( 1) () 3. Calculaton of Vertcal Velocty Accordng to the networkng method, frst we compare varous ponts of the network wth frst tour research statons of the Internatonal Atomc Energy Agency: j1 s located n margn of south coast of the Caspan Sea and border of the south basn s northern coast of Iran, n ths pont velocty s equal to zero, whch means: W(1, ) 0 j s located between the south coast of Caspan Sea and staton 1 of frst marne tour of Internatonal Atomc Energy Agency. For calculatng data related to ths pont, nterpolaton method s used and the data related to j whch extends n 70km dstance from coast of Caspan Sea s obtaned from surface to bottom of the sea. j3 s almost located on staton 1 of frst marne tour of Internatonal Atomc Energy Agency. The data of CTD of the staton can be used for j3 whch extends n 140km dstance from coast of Caspan Sea from surface to bottom of the sea. Accordngly, the pont j4 s almost located on staton, the pont j5 s almost located on staton 3, the pont j6 s almost located on staton 4, the pont j7 s almost located on staton 5, the pont j8 s almost located on staton 6, the pont j9 s almost located on staton 7, the pont j10 s almost located on staton 8, the pont j11 s almost located on staton 9, and the pont j13 s almost located on staton 11, so that we can apply the measurements related to marne frst tour statons as the mentoned order for ponts wth specfc J. But j1 s almost located on staton 11 of frst marne tour of Internatonal Atomc Energy Agency so that was deleted because of low depth of measurements of frst tour of Internatonal Atomc Energy Agency, so the requred data for j1 whch have been obtaned by nterpolaton are used. Therefore, ponts j1 and j13 are located n northern part of the Caspan Sea and these regons have low depth, then because of low depth we can assume the velocty n pont 13 as zero: W(13, ) 0 So for solvng equaton 13 we can apply the followng hypothess as one of the boundary condtons: W(1, ) W(13, ) 0 Also vertcal velocty n bottom of the sea s equal to zero. Therefore, for each specfc j, consderng topography of bottom of the Caspan Sea, when reachng bottom of the sea, vertcal velocty of the sad pont becomes zero. Equaton 13 after replacement and smplfcaton s wrtten as below: 1 8 Wj, π 10 Wj,( 1) + Wj,( ) 0 1 (3) We solve equaton 3 by usng MATLAB.6 software, we obtan vertcal velocty n each node, meanng that we obtan W j n certan j wth dfferent parameters and hence, frst we obtan W j n 1,,. We follow the same process for all dfferent j parameters so that W j profles are respectvely depcted. Profles of vertcal velocty n statons 4, 5, and 6 are observed n fgure 4. In fact these profles ndcate vertcal modes of nternal waves. 3.3 Calculaton of Horzontal Velocty After calculatng W j, we fnd values of U j, and snce U j, ndcates horzontal velocty n pont (,j), for calculatng U j, we use the followng relatons: U U 1 W k W, k z j, j, j, 1 j 38

7 Modern Appled Scence Vol. 10, No. 3; 016 W j, ku j, z Hence, by applyng fnte dfference method through backward Euler method, equaton 4 s solved: W U j, j, 1 j, (4) W ku j, Δz ( Wj, Wj, 1) (5) 0k Therefore, by havng values of Wj, and Wj, 1, we can obtan U j, n each pont. Lke calculaton of W j,, we also fnd U j, n the certan j for parameters exsted, then U j profle lke W j profle s drawn n varous j parameters. Profles of horzontal velocty n statons 4, 5, and 6 are ndcated n fgure 5. In fact these profles ndcate vertcal and horzontal modes of nternal waves. 3.4 Densty Calculaton Method After calculatng U and W, densty value wll be consdered. Accordng to mass conservaton equaton we have: ρ u ρ + + w ρ 0 (6) t x z We use fnte dfference method by usng backward Euler method for smplfyng equaton 6, so that we have: ρ x j, ρ ρ j, ( j 1), Δx (7) ρ z j, ρ ρ j, j,( 1) Δz (8) We replace equatons 7 and 8 n equaton 6 and obtan equaton 9: ρ ρj, ρ( j 1), ρj, ρj,( 1) U j, Wj, t Δx Δz (9) 4 Δ x 7 10 m Δ z 0m Hence, equaton 9 s solved and value of ρ t for certan and j can be obtaned. Also t can be noted that: ρ Δρ t Δt ρ Δρ Δt t (30) when we have Δ t assumed as regulaton tme or collapse tme of mxed water column after mxng. Consderng the dstance between the frst two ponts symmetry to each other n two sdes of the crest between south and mddle basns whch have notceable densty dfference, we obtan value of L from equaton 31, then by consderng propertes related to these ponts whch one belongs to j6 and the other one belongs to j8 (j7 s above the stuated obstacle), we can obtan Δ t whch s collapse tme [1]. L Δ t 1/ ( gh ) (31) Value of Δt s obtaned almost as equal to 9300 sec, value of Δρ s obtaned n each staton for less values 39

8 Modern Appled Scence Vol. 10, No. 3; 016 than ths tme as 800sec, and more values of tme as 45600sec and sec and sec. Also we have: ρ ρ0 + ρ That also can be wrtten as follows: ρ ρ0 +Δ ρ (3) Therefore, by havng Δρ and ρ0 we obtan value of ρ for the sad tmes so that we can compare densty profles obtaned wth the prmary densty profle (drawn by data resulted from fst research tour measurements of UNESCO). Accordng to the comparson t can be observed that the calculated densty profle has an approprate coordnaton wth the prmary densty profle (fgures 6). Meanng that nternal waves are effectve n structure of strata of waters of south and mddle bass of Caspan Sea. 4. Effect of Internal Waves on Energy Transfer Accordng to the observatons from feld studes (drawng densty rato profle), t was found that dual dstrbuton convecton s not often created n Caspan Sea and t doesn t seems that ths convecton has a man role n stratfed structure n the Caspan Sea, but also waves have a man role n these waters. Feld studes confrm exstence of surface flows from north to south and also creaton of flow from surface water of the mddle basn and upwellng of ths flow from depth. Transfer of ths flow occurs together wth water stratfcaton and creaton of nternal waves. Also analytc studes confrm exstence of such waves and water stratfcaton and fgure 4 ndcates exstence of vertcal modes of nternal waves n Caspan Sea. Fgure 6 ndcates approprate consstency exstng between calculaton results and results obtaned from frst tour research measurements. Ths fact mples exstence of nternal waves whch cause creaton of stratfed structure. Generally, n the Caspan Sea, normal modes of nternal waves are produced wth long wavelength by entrance of rvers n an envronment wth stratfed layers, and fnally result n complete stratfcaton of Caspan Sea, so that wthn long perod of tme, the flow transfers from one stratum to another, movement of ths flow causes exctaton of the nternal waves whch propagate energy towards vertcal drecton. Internal waves, n envronments wth stable densty stratfcaton lke Caspan Sea waters, can transfer energy. Meanng that ths flow, together wth changes n velocty due to passage of varous strata of water wth dfferent denstes, reaches water surface and then the phenomenon of water rotaton on surface of the sea can be observed. Sometmes when nternal waves break, turbulence caused by ths event, creates stratfed structure [10]. The man reason of creaton of exchange flow between the two basns of the Caspan Sea s horzontal gradent of densty, that n ths phenomenon, nternal waves are created and have effect on ths exchange, and sgn of exstence of such nternal waves s stratfed structure observed. The Stratfed structure n Caspan Sea manly exsts n the part under the mxed stratum. Thckness of the strata n Caspan Sea waters s almost 10m to 0m and the number of them vares from 3 to 7. Exstence of stratfed structure also has effect on thermal dstrbuton coeffcent and cause transfer of heat n Caspan Sea waters and s also effectve n extent of exchange of waters. Also exstence of varous water strata wth dfferent denstes s effectve n propagaton of sound waves whch s consdered as mechancal waves, so that the more an stratum s denser, the more velocty of sound wave ncreases n that stratum. Hence, n varous water strata, sound wave s also dfferent and at the tme of passage of sound from one stratum to another, falure phenomenon for sound waves occurs. For convertng knematc energy of nternal waves created along vertcal drecton nsde Caspan Sea waters to the electrcal energy, buoyancy systems whch functon wth fluctuatons of nternal waves for drvng hydraulc pumps, are used. Ths system s nstalled on a buoyant rod n the sea and s fxed on a devce n bottom of the sea and a seres of buoyant devces attached to t or restraned by t fluctuate wth that wave. Ths movement strkes electrc generator and creates electrcty and electrc energy produced s transferred by electrcty cable under the sea to the coast, and for changng knematc energy of nternal waves created along vertcal drecton of Caspan Sea waters to electrc energy, some devces whch work wth water fluctuaton are used, so that by wave moton of water, and fluctuaton of water, water column s flled and empted. In ths process, water s entered the compressed column and creates energy by workng, then ths energy s taken under control and transferred to the coast by electrcty cable. 5. Concluson Consderng numercal calculatons, value of vertcal velocty related to movement of nternal waves s obtaned as 10-6 to 10-3 m/s, meanng that vertcal movements of nternal waves occurs slowly. The calculated horzontal 40

9 Modern Appled Scence Vol. 10, No. 3; 016 velocty s also obtaned as 10-3 to 10-1 m/s. Profle of vertcal and horzontal veloctes obtaned from solvng equatons and also profle of densty s drawn after pass of four dfferent tme ntegraton steps. These profles ndcate that due to passage of gravtatonal flow between the two basns, densty n varous ponts of the two basns change, and snce south and mddle basns of Caspan Sea are related to each other through a mound (Abshouran pont), n the conducted studes t s observed that flow of the mddle basn moves towards the south basn and overflows from top of the mound between the two basns, then from bottom of the mound, the flow returns towards the mddle basn. And ths fact s consstent wth measurements conducted by UNESCO (1995). Snce for creaton of dual dstrbuton convecton densty rato should be almost equal to 1, ths phenomenon does not often occur n ths sea (fgure 3), hence we cannot attrbute the observed strata to ths phenomenon. But the modal structure created from nternal waves on the mound causes creaton of shear strata observed. The created strata, n addton to dstrbutng organc substance and also oxygen exstng n Caspan Sea waters, causes energy transfer that by usng energy convertor of waves n ths place, electrc energy s produced. References Bans, W. D., & Turner, I. S. (1969). Turbulent buoyant Convecton from a source n a confned regon. J. Flud Mech., 34, Bdokht, A. A., & Grffths, R. W. (001). Internal waves as an addtonal mechansm for layerng n the outflows from sem enclosed seas.14th Australasan Flud Mechancs Conference. Bdokht, A. A., & Norooz, M. (004). A Physcal Model for the layered structure of a densty drven flow over a slope. Tenth Asan Congress of flud Mechancs, Ser Lanka. Bdokht, A. A., & Shekarbaghan, A. (011). The layered structure n exchange flows between two basns (Mddle and Southern basns of the Caspan Sea). Int. J. Mar. Sc. Eng., 1(1), 13-. Boehrer, B. (000). Modal response of a deep stratfed Lake: Western lake Constance. J. Geophys. Res., 105, Fedrov, K. N. (013). The Physcal Nature and Structure of Oceanc Fronts. Gll, A. E. (198). Atmoshperc and ocean dynamcs. Academc press N. Grffths, R. E. (008). Interleavng ntrusons produced by nternal waves: a laboratory experment. J. Flud Mech., 60, Hogg, A., Mc, C., Wnters, K. B., & Ivey, G. N. (001). Lnear nternal Waves and the control of stratfed exchange flows. J. Flud Mech., 447, Ruddck, B. R. (199). Intrusve mxng n Medterranean salt lens ntruson slopes and dynamcal mechansms. J. Phys. Oceanogr,, UNESCO, IHP-IOC-IAEA. (1995).Workshop on sea level rse and multdscplnary studes of envronmental processes n the Caspan regon 9-1 May. Pars, Farance IOC workshop, 108. Wong, B. D., Grffths, R. W., & Hughes, G. O. (001). Shear Layers drven by turbulent plumes. J. Flud Mech, 434, Appendx A 41

10 Modern Appled Scence Vol. 10, No. 3; 016 Fgure A1. Map of the Caspan Sea and the statons of measurement Fgure A. Bottom topography of the Caspan Sea s ndcated by dstance from southern shore n southern northern drecton 4

11 Modern Appled Scence Vol. 10, No. 3; 016 Fgure A3. Vertcal profle of densty raton n statons 4, 5, and 6 Fgure A4. Profles of vertcal velocty calculated by numercal method n statons 4, 5, and 6 (x dstances are from Caspan Sea south coast) Fgure A5. Profles of horzontal velocty calculated by numercal method n statons 4, 5, and6 (x dstances are from Caspan Sea south coast) 43

12 Modern Appled Scence Vol. 10, No. 3; 016 depth (m ) potental densty (kg/m*3) [1] [] depth (m ) potental densty 0 (kg/m^3) [1] [] s4 s5 depth (m ) potental densty (kg/m*3) [1] [] depth (m ) potental densty (kg/m^3) [1] [] s6 s7 Fgure A6. Comparson between the prmary potental densty profle obtaned from frst research tour measurements of UNESCO [1] and potental densty profle calculated by numercal method [] n statons 4, 5, 6, and 7 Fgure A7. Horzontal velocty made dmensonless by nternal velocty of mxng obtaned n two successve tmes created n the same stratfed structure by a plume n a closed envronment wth densty stratfcaton Copyrghts Copyrght for ths artcle s retaned by the author(s), wth frst publcaton rghts granted to the journal. Ths s an open-access artcle dstrbuted under the terms and condtons of the Creatve Commons Attrbuton lcense ( 44