taru-adjective, adverb taking the 'to' particle
tears streaming down; shedding copious tears
Literary, dramatic expression for weeping profusely. Used in classical or elevated writing; not part of everyday speech.
Upon hearing the sad news, she broke down weeping, tears streaming down her face.
号泣 is a common word for crying loudly or wailing; 落涙滂沱 is a much rarer, more literary expression focusing on the copious flow of tears.
A yojijukugo (four-character idiom) of Chinese origin. 落涙 means 'shedding tears' and 滂沱 describes heavy rain or a torrential flow, together painting a vivid image of tears streaming like a downpour.