We present the power spectrum analysis of clustering in the Durham/UKST Galaxy Redshift Survey .
The Survey covers 1450 square degrees and consists of 2501 galaxy redshifts .
The galaxies are sampled at a rate of 1 in 3 down to a magnitude limit of b _ { J } \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } } } 17 from COSMOS scanned UK-Schmidt plates .
Our measurement of the power spectrum is robust for wavenumbers in the range 0.04 h { Mpc } ^ { -1 } \leq k \leq 0.6 h { Mpc } ^ { -1 } .
The slope of the power spectrum for k > 0.1 h { Mpc } ^ { -1 } is close to k ^ { -2 } .
The fluctuations in the galaxy distribution can be expressed as the rms variance in the number of galaxies in spheres of radius 8 h ^ { -1 } { Mpc } as \sigma _ { 8 } = 1.01 \pm 0.17 .
We find remarkably good agreement between the power spectrum measured for the Durham/UKST Survey and those obtained from other optical studies on scales up to \lambda = 2 \pi / k \sim 80 h ^ { -1 } { Mpc } .
On scales larger than this we find good agreement with the power measured from the Stromlo-APM Survey ( Tadros & Efstathiou ) , but find more power than estimated from the Las Campanas Redshift Survey ( Lin et al ) .
The Durham/UKST Survey power spectrum has a higher amplitude than the power spectrum of IRAS galaxies on large scales , implying a relative bias between optically and infra-red selected samples of b _ { rel } = 1.3 .
We apply a simple model for the distortion of the pattern of clustering caused by the peculiar motions of galaxies to the APM Galaxy Survey power spectrum , which is free from such effects , and find a shape and amplitude that is in very good agreement with the power spectrum of the Durham/UKST Survey .
This implies \beta = \Omega ^ { 0.6 } / b = 0.60 \pm 0.35 , where b is the bias between fluctuations in the galaxy and mass distributions , and also suggests a one dimensional velocity dispersion of \sigma = 320 \pm 140 { kms } ^ { -1 } .
We compare the Durham/UKST power spectrum with Cold Dark Matter models of structure formation , including the effects of nonlinear growth of the density fluctuations and redshift-space distortions on the theoretical power spectra .
We find that for any choice of normalisation , the standard CDM model has a shape that can not be reconciled with the Durham/UKST Survey power spectrum , unless either unacceptably high values of the one dimensional velocity dispersion are adopted or the assumption that bias is constant is invalid on scales greater than 20 h ^ { -1 } { Mpc } .
Over the range of wavenumbers for which we have a robust measurement of the power spectrum , we find the best agreement is obtained for a critical density CDM model in which the shape of the power spectrum is modified .