An exhaust stack assembly includes an exhaust stack having an internal surface that defines an interior of the exhaust stack. The exhaust stack is configured to receive exhaust gas from at least one turbomachine component and exhaust the exhaust gas to atmosphere. The exhaust gas assembly further includes a plurality of attenuation assemblies disposed in the interior, each of the plurality of attenuation assemblies including a base substrate generally oriented in the direction of flow of the exhaust gas through the interior, each of the plurality of attenuation assemblies further including a plurality of attenuation modules mounted to the base substrate. Each of the plurality of attenuation modules includes a fiber mesh. The fiber mesh is exposed to the exhaust gas in the interior.