Śrīmad-Bhāgavatam 10.16.1
Blended reading (Sanskrit + English inline)
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kṛṣṇām
—
the river Yamunā
The Yamunā is called Kṛṣṇā — feminine of Kṛṣṇa, His own dark-watered consort-river. The wordplay is doctrinal: Vraja's geography is not neutral nature but the Lord's own intimate energy.
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viśuddhim
—
purification
From vi+śudh — total cleansing. Bhāgavata theology: where the demoniac contaminates, Bhagavān's līlā restores. The same word-field as bhakti's role in purifying the heart (cf. Bhakti-rasāmṛta-sindhu's anartha-nivṛtti).
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udavāsayat
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He banished him
Causative — He caused (Kāliya) to dwell elsewhere. Note the restraint: Kṛṣṇa does not kill the offender of His river but relocates him. Even the demoniac, once touched, is preserved.
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vibhuḥ
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the all-powerful Lord
Vibhu — pervading, omnipotent. Reminds the reader that the boy on the kadamba is the same all-pervading Bhagavān; the smallness of the form does not limit the greatness of the actor.
This chapter describes how Krsna brought Kaliya under control, Krsna’s pleasure with his prayers, and banishing him from the Yamuna. In this verse krsnam refers to the Yamuna river. Seeing how Kaliya was polluting the Yamuna with poison, Krsna decided to remove Kaliya from that place.
Yamunā is called kṛṣṇām here because of her dark color and because of being dear to Kṛṣṇa. Thus he had to take action when she was contaminated with poison, since she was a dear friend. The snake was black because of being full of intense poison. Kṛṣṇa did not act simply for her benefit, but for everyone’s benefit since Kṛṣṇa takes away (kṛṣ) all sorrows. The whole universe would be benefited by the rescue of such a great holy place of Vraja, since people could drink the water. Thus Kāliya would also be benefited. He is called vibhuḥ (powerful) since according to his choice as previously on some occasions, he would manifest his powers, even though he was absorbed in childhood pastimes.
Yamunā is called kṛṣṇām here because of her dark color and because of being dear to Kṛṣṇa. Thus he had to take action when she was contaminated with poison, since she was a dear friend. The snake was black because of being full of intense poison. Kṛṣṇa did not act simply for her benefit, but for everyone’s benefit since Kṛṣṇa takes away (kṛṣ) all sorrows. The whole universe would be benefited by the rescue of such a great holy place of Vraja, since people could drink the water. Thus Kāliya would also be benefited. This will be revealed later. Kṛṣṇa could perform such acts because he was able to many things by one act (vibhuḥ). Sarpa means a creature that crawls about. Kṛṣṇa prevented him from going elsewhere.
The Yamunā is the throat of Vraja — every gopa, calf and bird drinks from her. When the black serpent Kāliya poisons that throat, Kṛṣṇa does not summon a sage or a god; He Himself banishes the poison. The Lord descends not to lecture about purity but to clean His beloved's river with His own feet.
My note
Source: vedabase.io