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Page 1: FGH IKJ#LNMPOQHR%J Ggershwin.ens.fr/zeitlin/pdf/1dRSW_num_1.pdf · 2003. 5. 20. · sut?v { ^ $# % ':+ - v ¶ \ % &(') *+ , '),- ./*+ ') 1 4 · ^ 4

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Page 9: FGH IKJ#LNMPOQHR%J Ggershwin.ens.fr/zeitlin/pdf/1dRSW_num_1.pdf · 2003. 5. 20. · sut?v { ^ $# % ':+ - v ¶ \ % &(') *+ , '),- ./*+ ') 1 4 · ^ 4

������������������� ����!"!#�%$'&)(��+*,��-.*,/10324$���/��65�-879���;:<��$=�=>?��*@�35BA6C<��:<��!3�+/�� 7

−20 −15 −10 −5 0 5 10 15 20

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−0.4

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0

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Check of balance at t/Tf =22 with Ro=1 and Bu=0.25

x/Rd

f*vg*hx

−20 −15 −10 −5 0 5 10 15 20

−0.6

−0.4

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0

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Check of balance at t/Tf =22.2 with Ro=1 and Bu=0.25

x/Rd

f*vg*hx

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0

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Check of balance at t/Tf =22.5 with Ro=1 and Bu=0.25

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Page 10: FGH IKJ#LNMPOQHR%J Ggershwin.ens.fr/zeitlin/pdf/1dRSW_num_1.pdf · 2003. 5. 20. · sut?v { ^ $# % ':+ - v ¶ \ % &(') *+ , '),- ./*+ ') 1 4 · ^ 4

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potential vorticity q; Ro=1 and Bu=0.25

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q

initial pvfinal pv

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Page 11: FGH IKJ#LNMPOQHR%J Ggershwin.ens.fr/zeitlin/pdf/1dRSW_num_1.pdf · 2003. 5. 20. · sut?v { ^ $# % ':+ - v ¶ \ % &(') *+ , '),- ./*+ ') 1 4 · ^ 4

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v

initial v(x,0) with α =−1

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initial v(x,0) with α =1

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initial PVfinal PV

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PV advection; α = 1

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q

initial PVfinal PV

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Page 12: FGH IKJ#LNMPOQHR%J Ggershwin.ens.fr/zeitlin/pdf/1dRSW_num_1.pdf · 2003. 5. 20. · sut?v { ^ $# % ':+ - v ¶ \ % &(') *+ , '),- ./*+ ') 1 4 · ^ 4

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Page 16: FGH IKJ#LNMPOQHR%J Ggershwin.ens.fr/zeitlin/pdf/1dRSW_num_1.pdf · 2003. 5. 20. · sut?v { ^ $# % ':+ - v ¶ \ % &(') *+ , '),- ./*+ ') 1 4 · ^ 4

������������������� ����!"!#�%$'&)(��+*,��-.*,/10324$���/��65�-879���;:<��$=�=>?��*@�35BA6C<��:<��!3�+/�� ¶

−5 −5/2 0 5/2 5

0.6

0.8

1

1.2

1.4

1.6

1.8

x/Rd

h

α = 0α = 5α = −5

II I I II

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Page 17: FGH IKJ#LNMPOQHR%J Ggershwin.ens.fr/zeitlin/pdf/1dRSW_num_1.pdf · 2003. 5. 20. · sut?v { ^ $# % ':+ - v ¶ \ % &(') *+ , '),- ./*+ ') 1 4 · ^ 4

������������������� ����!"!#�%$'&)(��+*,��-.*,/10324$���/��65�-879���;:<��$=�=>?��*@�35BA6C<��:<��!3�+/�� ·

−5 −5/2 0 5/2 5

Time evolution of the height field h

x/Rd

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° �i¥)_lZU\�e�]�s3e�f�_.�8V[fP{��#]�T?V f?_lZ=Zb_lW�^�]�_leB\¡f�r?Vm]�e#Z�T?e�c�z�Ze9° _l\1^NZb_ls3W?jkV"{�^�j`^�\8c%V[fwqpV+][|�{?Y=V[^Bz9_l\?o�_`Z�sweY�V'jk_lzBV[jk�N]�eNe�c[c%r?Yt^�]�]�T?V¡�±°B�+-k��/8*@�Z�_`f�VB�² ³ Lw?4MP½}H�Âû�G"H Å GPLµ´3MPÅ ½�RVq�R%GP»UI�H�R%Å ÄÕJ ½�O�R%Ä%Ä%Å�H�R%J GP½`A4 \?VXeBh]=T?VQs3eZb]4_ks3W�eBY�]=^B\]��9r?VdZp]=_ke\�Z4^B{8er�]}]�T?VioBV+e9Zp]=Y�eW?T?_`c�^f;qpr�Zb]�s3V+\9]�_`Z}y�T?V+]�T?V[Y

_k]t_`Z�c+eBs3W?jlV%]=VB�m��]�yU^BZtZbT�e�y�\v_k\1� ]=T�^�]m\?e�]�Y�^�W?W�V[f�s3e�f�VdZt^BY�V'W8e9Z�Z�_k{�jkV"y�_.]=T?_k\]�T�V�jke�c+^Bjk_l£+Vdf qpV+]=Z<©dhxY=eB\9]=ZU_l\¡]�T�V�swe�f�V[ji� �<|?{�r�]�]�T8^�]g�9r�^BZ�_k~�Zb]=^�]�_leB\�^BY��#Zb]=^�]=V[Z�s#^;�V%��_`Zp]ihxeBYUc%V+Y�]=^B_k\�c+eB\��8oBr?Y�^�]=_ke\�Z+��¦�e�]�T�Y�VdZbr?jk]=ZiyaV[Y�Vg{�^BZ�V[f3e\#]�T?VtZbs#^Bjkjl\?V[Z=ZQeBh}]�T?VyU^;nBV%~�W�V+Y�]�r?Y={�^�]=_ke\�Z�e�nBV[YX]�T?V�{�^�j`^�\8c%V[f�qpV+]<©dhxY=eB\9]d|9Z�e�]�T�Vg�9r?V[Zb]�_leB\#eBh�c%eBs3W?jlV%]=V+\?VdZ�Z

Page 18: FGH IKJ#LNMPOQHR%J Ggershwin.ens.fr/zeitlin/pdf/1dRSW_num_1.pdf · 2003. 5. 20. · sut?v { ^ $# % ':+ - v ¶ \ % &(') *+ , '),- ./*+ ') 1 4 · ^ 4

������������������� ����!"!#�%$'&)(��+*,��-.*,/10324$���/��65�-879���;:<��$=�=>?��*@�35BA6C<��:<��!3�+/�� 6

−5 −5/2 0 5/2 5

−0.06

−0.04

−0.02

0

0.02

u at t /Tf = 0.35

α = 0α = 5α = −5

−3 −2.5 −2 −1.5 −1

−0.06

−0.04

−0.02

0

0.02

0.04

hu at t / T

f = 0.35

x/Rd

α = 5α = 0α = −5

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Page 19: FGH IKJ#LNMPOQHR%J Ggershwin.ens.fr/zeitlin/pdf/1dRSW_num_1.pdf · 2003. 5. 20. · sut?v { ^ $# % ':+ - v ¶ \ % &(') *+ , '),- ./*+ ') 1 4 · ^ 4

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Page 20: FGH IKJ#LNMPOQHR%J Ggershwin.ens.fr/zeitlin/pdf/1dRSW_num_1.pdf · 2003. 5. 20. · sut?v { ^ $# % ':+ - v ¶ \ % &(') *+ , '),- ./*+ ') 1 4 · ^ 4

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Page 21: FGH IKJ#LNMPOQHR%J Ggershwin.ens.fr/zeitlin/pdf/1dRSW_num_1.pdf · 2003. 5. 20. · sut?v { ^ $# % ':+ - v ¶ \ % &(') *+ , '),- ./*+ ') 1 4 · ^ 4

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Page 22: FGH IKJ#LNMPOQHR%J Ggershwin.ens.fr/zeitlin/pdf/1dRSW_num_1.pdf · 2003. 5. 20. · sut?v { ^ $# % ':+ - v ¶ \ % &(') *+ , '),- ./*+ ') 1 4 · ^ 4

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Page 23: FGH IKJ#LNMPOQHR%J Ggershwin.ens.fr/zeitlin/pdf/1dRSW_num_1.pdf · 2003. 5. 20. · sut?v { ^ $# % ':+ - v ¶ \ % &(') *+ , '),- ./*+ ') 1 4 · ^ 4

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Page 26: FGH IKJ#LNMPOQHR%J Ggershwin.ens.fr/zeitlin/pdf/1dRSW_num_1.pdf · 2003. 5. 20. · sut?v { ^ $# % ':+ - v ¶ \ % &(') *+ , '),- ./*+ ') 1 4 · ^ 4

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