The similarities between Parashat Noach's description of the world's destruction and the original creation story are in content more than language. They serve to underscore the obvious, that the deluge undid much of what the original creation had accomplished.
Separated waters re-mingle – Hashem's original separation between the waters on high and below is undone, as both the heavens and the depths release the waters of the flood.
Land re-submerges – In Parashat Bereshit, the ingathering of the waters allows for the land to emerge, while in Parashat Noach, water floods back over the dry ground.
All die – Bereshit 1 describes the creation of bird, animal, beast and human, while the Noach account tells of their deaths.
Breath of life extinguished – Whereas Bereshit 2 emphasizes Hashem's breathing life into His handiwork, Bereshit 7 highlights the extinguishing of that breath.2
The description of the re-emergence of life, in the second half of the flood narrative, similarly draws the reader back to the original creation story. Here the numerous parallels are direct and highlight how Hashem renewed the world, giving mankind a fresh start. The similarities between the two accounts include:
State of the world pre-creation – In both cases, before life is created, water filled the earth and a wind or spirit hovered or passed over it.
Dates – Chapter 8:13 records that the waters of the flood dried up on the first day of the first month, the very same day on which the world was created.
The elements and order of creation – Both stories contain explicit mention of the separation of higher and lower waters, the appearance of land and vegetation, markers of time, and the emergence of birds, animals, and man.3
Blessings – Both accounts detail Hashem's blessing of abundant procreation to both birds4 and humans and the promise that mankind will have dominion over the animals.
Command to eat – In Bereshit 1, Hashem allows man to eat from all vegetation, while in Bereshit 9, He adds that they can also eat from living creatures.5
Restrictions – Hashem bans certain foods in both stories. In Bereshit 2, the fruit of the tree of knowledge is prohibited, while in Bereshit 9, Hashem warns against eating the blood of animals.
Occupation of man – The first human is named "אָדָם" and is commanded to work the land. Noach is similarly referred to as "אִישׁ הָאֲדָמָה", and soon after the flood subsides, he plants a vineyard.
וַיִּטַּע ה' אֱלֹהִים גַּן בְּעֵדֶן... וַיְשַׁלְּחֵהוּ ה' אֱלֹהִים מִגַּן עֵדֶן לַעֲבֹד אֶת הָאֲדָמָה אֲשֶׁר לֻקַּח מִשָּׁם
וַיָּחֶל נֹחַ אִישׁ הָאֲדָמָה וַיִּטַּעכָּרֶם
Creation (Bereshit 1-2)
Creation Redux (Bereshit 8-9)
Heavens / Earth
Land / Sea
Vegetation
Luminaries / Seasons
Birds / Animals
Humans
Breath of Life
Blessing of Birds / Blessing of Man
Food
Restrictions
Working the Land
Analysis of parallels
To determine whether these parallels are intentional allusions or simply coincidental similarities one must consider the number and concentration of the parallels, the degree of their linguistic similarity, and the relative uniqueness of the shared phrases or concepts.6 In this case, there are a significant number of conceptual parallels between the two narratives, but the extent of the linguistic overlap and the rarity of the choice of terms must be examined more closely:
Wind over water – The concept of wind/spirit passing over water appears only in the stories of the Creation, the Flood, and the splitting of Yam Suf. In addition, the phrase "עַל פְּנֵי הַמָּיִם" appears, besides in these two stories,7 only in Shemot 32:20 and Kohelet 11:1.
Mingling or Separation of waters – Although there is no linguistic similarity between the descriptions of the mingling/separation between the higher and lower waters, it is only in these two stories that such a concept appears.8 The word "תְּהוֹם", though, does appear in both stories,9 accounting for three of its five appearances in Torah.10
Elements of Creation – The words used in the two accounts do not overlap significantly, and most of them are not unique to these stories.
Heavens and earth – The "יַבָּשָׁה" of Bereshit 1 is alternately referred to in Bereshit 6-9 as "אֲדָמָה" or "אָרֶץ".11 This, though, might be expected as the text states that, after its appearance, Hashem called the dry land "אֶרֶץ".12 Similarly the word "רָקִיעַ" is replaced by "שָׁמָיִם", its new name.
Vegetation – There is only an allusion to the renewed vegetation in the mention of the olive branch, with no direct connection to the plant list of Bereshit: "דֶּשֶׁא עֵשֶׂב מַזְרִיעַ זֶרַע עֵץ פְּרִי".
Animals – The combined mention of birds, animals, beasts, and swarming creatures is not unique to these stories.13
"לְמִינוֹ" / "לְמִינֵהוּ" – In contrast to the above, this term is somewhat unique, appearing only by the names of the plant and animal species created in Bereshit, the list of animals entering the ark, and the list of prohibited foods in Vayikra 11 and Devarim 14.
Blessings – The language of the two blessings is almost identical. Moreover the phrase "פְּרוּ וּרְבוּ" appears in only these two sets of chapters and in Yirmeyahu 23:3 and Yechezkel 36:11.14
"נִשְׁמַת חַיִּים" – This phrase appears only by the creation of man in Bereshit 1 and by the world's destruction in Bereshit 7.
Contrasts
In addition to the many similarities between the stories, there are several points of divergence:
Active / passive intervention – In the Creation story of Bereshit 1, Hashem plays an active role in every step of creation. Each day He speaks and commands that another aspect of the world be engendered. In the flood story, in contrast, although Hashem remembers Noach and begins the process by sending a wind over the waters, everything afterwards seems to evolve through natural processes.
Duration of creation – While Bereshit 1 gives the impression that Hashem originally made the world in a mere seven days,15 with each new life form generated instantaneously upon command, the re-creation of the world takes many months, with the waters receding gradually rather than immediately.16
Absence of fish – All of the created beings mentioned in Bereshit 1 appear in the flood narrative with the exception of fish and other water creatures. Does their absence suggest that these living beings had never been destroyed in the flood at all (and thus, there was no need of recreation)?17
Creation of man – In the original creation story, man is the pinnacle of creation, made as the grand finale. After the flood, in contrast, man emerges into the new world before the animals. Does the difference in order hint to some deterioration in the status of man, or is the change insignificant, relating, instead to practical considerations?
Food permitted – After the flood, man is allowed to eat from living creatures, while originally only vegetation had been allowed. What led to this change? For elaboration, see What was Noach Permitted to Eat.
Conclusion
On the most basic level, the many similarities between the accounts simply serve to highlight how the flood and its aftermath were both an undoing and redoing of creation. Mankind erred so grievously that there was no choice but to destroy the world. Nevertheless, Hashem did not give up on man, but rather gave the world a fresh start, creating it anew and returning it to its innocent beginnings. The new world though is not created in the same manner as the first. The miraculous nature of the original construction is replaced by a much more natural development, and Hashem is more distant.
