Sealed and thermally insulating tank with anti-convective filler element

A sealed and thermally insulating tank for storing a fluid, wherein a tank wall comprises, successively in a thickness direction, a secondary thermal insulation barrier (1) comprising a plurality of juxtaposed secondary insulating elements (2), the secondary insulating elements (2) being retained against a support wall (3), a secondary sealing membrane (4) supported by the secondary insulating elements (2) of the secondary thermal insulation barrier (1), a primary thermal insulation barrier (5) comprising a plurality of juxtaposed primary insulating elements (6), the primary insulating elements (6) being retained against the secondary sealing membrane (4), and a primary sealing membrane (7) supported by the primary thermal insulation barrier (5) and intended to be in contact with the cryogenic fluid contained in the tank, wherein the secondary sealing membrane (4) is a corrugated metal membrane comprising a series of parallel corrugations (25, 26) forming channels and flat portions located between said corrugations (25, 26), the primary insulating elements (6) having an external face covering the flat portions of the secondary sealing membrane (4), the secondary insulating elements (2) having an internal face supporting the flat portions of the secondary sealing membrane (4), wherein anti-convection filler elements (16, 20, 22) are disposed in the corrugations (25, 26) of the secondary sealing membrane (4) to generate a head loss in said channels.