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The main objective of this paper is to demonstrate the uniform largedeviation principle (UDLP) for the solutions of two-dimensional stochasticNavier-Stokes equations (SNSE) in the vorticity form when perturbed by twodistinct types of noises. We first consider an infinite-dimensional additivenoise that is white in time and colored in space and then consider afinite-dimensional Wiener process with linear growth coefficient. In order toobtain the ULDP for 2D SNSE in the vorticity form, where the noise is white intime and colored in space, we utilize the existence and uniqueness result from\emph{B. Ferrario et. al., Stochastic Process. Appl., {\bf 129} (2019),1568--1604,} and the \textsl{uniform contraction principle}. For thefinite-dimensional multiplicative Wiener noise, we first prove the existence ofa unique local mild solution to the vorticity equation using a truncation andfixed point arguments. We then establish the global existence of the truncatedsystem by deriving a uniform energy estimate for the local mild solution. Byapplying stopping time arguments and a version of Skorokhod's representationtheorem, we conclude the global existence and uniqueness of a solution to ourmodel. We employ the weak convergence approach to establish the ULDP for thelaw of the solutions in two distinct topologies. We prove ULDP in the$\mathrm{C}([0,T];\mathrm{L}^p(\mathbb{T}^2))$ topology, for $p>2$, taking intoaccount the uniformity of the initial conditions contained in bounded subsetsof $\mathrm{L}^p(\mathbb{T}^2)$. Finally, in$\mathrm{C}([0,T]\times\mathbb{T}^2)$ topology, the uniformity of initialconditions lying in bounded subsets of $\mathrm{C}(\mathbb{T}^2)$ isconsidered.

Uniform large deviation principle for the solutions of two-dimensional stochastic Navier-Stokes equations in vorticity form